Add inline typing to functional (#482)

* add typing to functional

* fix minor things

* fix flake8

torchaudio/functional.py

 # -*- coding: utf-8 -*-
 
 import math
+from typing import Optional, Tuple
 
 import torch
+from torch import Tensor
 
 __all__ = [
     "istft",
@@ -37,17 +39,16 @@ __all__ = [
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
 @torch.jit.ignore
 def _stft(
-    waveform,
-    n_fft,
-    hop_length,
-    win_length,
-    window,
-    center,
-    pad_mode,
-    normalized,
-    onesided,
-):
-    # type: (Tensor, int, Optional[int], Optional[int], Optional[Tensor], bool, str, bool, bool) -> Tensor
+        waveform: Tensor,
+        n_fft: int,
+        hop_length: Optional[int],
+        win_length: Optional[int],
+        window: Optional[Tensor],
+        center: bool,
+        pad_mode: str,
+        normalized: bool,
+        onesided: bool
+) -> Tensor:
     return torch.stft(
         waveform,
         n_fft,
@@ -62,18 +63,17 @@ def _stft(
 
 
 def istft(
-    stft_matrix,  # type: Tensor
-    n_fft,  # type: int
-    hop_length=None,  # type: Optional[int]
-    win_length=None,  # type: Optional[int]
-    window=None,  # type: Optional[Tensor]
-    center=True,  # type: bool
-    pad_mode="reflect",  # type: str
-    normalized=False,  # type: bool
-    onesided=True,  # type: bool
-    length=None,  # type: Optional[int]
-):
-    # type: (...) -> Tensor
+        stft_matrix: Tensor,
+        n_fft: int,
+        hop_length: Optional[int] = None,
+        win_length: Optional[int] = None,
+        window: Optional[Tensor] = None,
+        center: bool = True,
+        pad_mode: str = "reflect",
+        normalized: bool = False,
+        onesided: bool = True,
+        length: Optional[int] = None,
+) -> Tensor:
     r"""Inverse short time Fourier Transform. This is expected to be the inverse of torch.stft.
     It has the same parameters (+ additional optional parameter of ``length``) and it should return the
     least squares estimation of the original signal. The algorithm will check using the NOLA condition (
@@ -103,26 +103,26 @@ def istft(
     IEEE Trans. ASSP, vol.32, no.2, pp.236-243, Apr. 1984.
 
     Args:
-        stft_matrix (torch.Tensor): Output of stft where each row of a channel is a frequency and each
+        stft_matrix (Tensor): Output of stft where each row of a channel is a frequency and each
             column is a window. It has a size of either (..., fft_size, n_frame, 2)
         n_fft (int): Size of Fourier transform
-        hop_length (Optional[int]): The distance between neighboring sliding window frames.
+        hop_length (int or None, optional): The distance between neighboring sliding window frames.
             (Default: ``win_length // 4``)
-        win_length (Optional[int]): The size of window frame and STFT filter. (Default: ``n_fft``)
-        window (Optional[torch.Tensor]): The optional window function.
+        win_length (int or None, optional): The size of window frame and STFT filter. (Default: ``n_fft``)
+        window (Tensor or None, optional): The optional window function.
             (Default: ``torch.ones(win_length)``)
-        center (bool): Whether ``input`` was padded on both sides so
+        center (bool, optional): Whether ``input`` was padded on both sides so
             that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`.
             (Default: ``True``)
-        pad_mode (str): Controls the padding method used when ``center`` is True. (Default:
-            ``'reflect'``)
-        normalized (bool): Whether the STFT was normalized. (Default: ``False``)
-        onesided (bool): Whether the STFT is onesided. (Default: ``True``)
-        length (Optional[int]): The amount to trim the signal by (i.e. the
+        pad_mode (str, optional): Controls the padding method used when ``center`` is True. (Default:
+            ``"reflect"``)
+        normalized (bool, optional): Whether the STFT was normalized. (Default: ``False``)
+        onesided (bool, optional): Whether the STFT is onesided. (Default: ``True``)
+        length (int or None, optional): The amount to trim the signal by (i.e. the
             original signal length). (Default: whole signal)
 
     Returns:
-        torch.Tensor: Least squares estimation of the original signal of size (..., signal_length)
+        Tensor: Least squares estimation of the original signal of size (..., signal_length)
     """
     stft_matrix_dim = stft_matrix.dim()
     assert 3 <= stft_matrix_dim, "Incorrect stft dimension: %d" % (stft_matrix_dim)
@@ -226,26 +226,32 @@ def istft(
 
 
 def spectrogram(
-    waveform, pad, window, n_fft, hop_length, win_length, power, normalized
-):
-    # type: (Tensor, int, Tensor, int, int, int, Optional[float], bool) -> Tensor
+        waveform: Tensor,
+        pad: int,
+        window: Tensor,
+        n_fft: int,
+        hop_length: int,
+        win_length: int,
+        power: Optional[float],
+        normalized: bool
+) -> Tensor:
     r"""Create a spectrogram or a batch of spectrograms from a raw audio signal.
     The spectrogram can be either magnitude-only or complex.
 
     Args:
-        waveform (torch.Tensor): Tensor of audio of dimension (..., time)
+        waveform (Tensor): Tensor of audio of dimension (..., time)
         pad (int): Two sided padding of signal
-        window (torch.Tensor): Window tensor that is applied/multiplied to each frame/window
+        window (Tensor): Window tensor that is applied/multiplied to each frame/window
         n_fft (int): Size of FFT
         hop_length (int): Length of hop between STFT windows
         win_length (int): Window size
-        power (float): Exponent for the magnitude spectrogram,
+        power (float or None): Exponent for the magnitude spectrogram,
             (must be > 0) e.g., 1 for energy, 2 for power, etc.
             If None, then the complex spectrum is returned instead.
         normalized (bool): Whether to normalize by magnitude after stft
 
     Returns:
-        torch.Tensor: Dimension (..., freq, time), freq is
+        Tensor: Dimension (..., freq, time), freq is
         ``n_fft // 2 + 1`` and ``n_fft`` is the number of
         Fourier bins, and time is the number of window hops (n_frame).
     """
@@ -275,9 +281,18 @@ def spectrogram(
 
 
 def griffinlim(
-    specgram, window, n_fft, hop_length, win_length, power, normalized, n_iter, momentum, length, rand_init
-):
-    # type: (Tensor, Tensor, int, int, int, float, bool, int, float, Optional[int], bool) -> Tensor
+        specgram: Tensor,
+        window: Tensor,
+        n_fft: int,
+        hop_length: int,
+        win_length: int,
+        power: float,
+        normalized: bool,
+        n_iter: int,
+        momentum: float,
+        length: Optional[int],
+        rand_init: bool
+) -> Tensor:
     r"""Compute waveform from a linear scale magnitude spectrogram using the Griffin-Lim transformation.
         Implementation ported from `librosa`.
 
@@ -295,22 +310,22 @@ def griffinlim(
         IEEE Trans. ASSP, vol.32, no.2, pp.236–243, Apr. 1984.
 
     Args:
-        specgram (torch.Tensor): A magnitude-only STFT spectrogram of dimension (..., freq, frames)
+        specgram (Tensor): A magnitude-only STFT spectrogram of dimension (..., freq, frames)
             where freq is ``n_fft // 2 + 1``.
-        window (torch.Tensor): Window tensor that is applied/multiplied to each frame/window
+        window (Tensor): Window tensor that is applied/multiplied to each frame/window
         n_fft (int): Size of FFT, creates ``n_fft // 2 + 1`` bins
         hop_length (int): Length of hop between STFT windows. (
             Default: ``win_length // 2``)
         win_length (int): Window size. (Default: ``n_fft``)
         power (float): Exponent for the magnitude spectrogram,
-            (must be > 0) e.g., 1 for energy, 2 for power, etc. (Default: ``2``)
-        normalized (bool): Whether to normalize by magnitude after stft. (Default: ``False``)
+            (must be > 0) e.g., 1 for energy, 2 for power, etc.
+        normalized (bool): Whether to normalize by magnitude after stft.
         n_iter (int): Number of iteration for phase recovery process.
         momentum (float): The momentum parameter for fast Griffin-Lim.
             Setting this to 0 recovers the original Griffin-Lim method.
-            Values near 1 can lead to faster convergence, but above 1 may not converge. (Default: 0.99)
-        length (Optional[int]): Array length of the expected output. (Default: ``None``)
-        rand_init (bool): Initializes phase randomly if True, to zero otherwise. (Default: ``True``)
+            Values near 1 can lead to faster convergence, but above 1 may not converge.
+        length (int or None): Array length of the expected output.
+        rand_init (bool): Initializes phase randomly if True, to zero otherwise.
 
     Returns:
         torch.Tensor: waveform of (..., time), where time equals the ``length`` parameter if given.
@@ -331,7 +346,7 @@ def griffinlim(
     else:
         angles = torch.zeros(batch, freq, frames)
     angles = torch.stack([angles.cos(), angles.sin()], dim=-1) \
-                  .to(dtype=specgram.dtype, device=specgram.device)
+        .to(dtype=specgram.dtype, device=specgram.device)
     specgram = specgram.unsqueeze(-1).expand_as(angles)
 
     # And initialize the previous iterate to 0
@@ -371,8 +386,13 @@ def griffinlim(
     return waveform
 
 
-def amplitude_to_DB(x, multiplier, amin, db_multiplier, top_db=None):
-    # type: (Tensor, float, float, float, Optional[float]) -> Tensor
+def amplitude_to_DB(
+        x: Tensor,
+        multiplier: float,
+        amin: float,
+        db_multiplier: float,
+        top_db: Optional[float] = None
+) -> Tensor:
     r"""Turn a tensor from the power/amplitude scale to the decibel scale.
 
     This output depends on the maximum value in the input tensor, and so
@@ -380,15 +400,15 @@ def amplitude_to_DB(x, multiplier, amin, db_multiplier, top_db=None):
     a full clip.
 
     Args:
-        x (torch.Tensor): Input tensor before being converted to decibel scale
+        x (Tensor): Input tensor before being converted to decibel scale
         multiplier (float): Use 10. for power and 20. for amplitude
         amin (float): Number to clamp ``x``
         db_multiplier (float): Log10(max(reference value and amin))
-        top_db (Optional[float]): Minimum negative cut-off in decibels. A reasonable number
+        top_db (float or None, optional): Minimum negative cut-off in decibels. A reasonable number
             is 80. (Default: ``None``)
 
     Returns:
-        torch.Tensor: Output tensor in decibel scale
+        Tensor: Output tensor in decibel scale
     """
     x_db = multiplier * torch.log10(torch.clamp(x, min=amin))
     x_db -= multiplier * db_multiplier
@@ -399,23 +419,31 @@ def amplitude_to_DB(x, multiplier, amin, db_multiplier, top_db=None):
     return x_db
 
 
-def DB_to_amplitude(x, ref, power):
-    # type: (Tensor, float, float) -> Tensor
+def DB_to_amplitude(
+        x: Tensor,
+        ref: float,
+        power: float
+) -> Tensor:
     r"""Turn a tensor from the decibel scale to the power/amplitude scale.
 
     Args:
-        x (torch.Tensor): Input tensor before being converted to power/amplitude scale.
+        x (Tensor): Input tensor before being converted to power/amplitude scale.
         ref (float): Reference which the output will be scaled by.
         power (float): If power equals 1, will compute DB to power. If 0.5, will compute DB to amplitude.
 
     Returns:
-        torch.Tensor: Output tensor in power/amplitude scale.
+        Tensor: Output tensor in power/amplitude scale.
     """
     return ref * torch.pow(torch.pow(10.0, 0.1 * x), power)
 
 
-def create_fb_matrix(n_freqs, f_min, f_max, n_mels, sample_rate):
-    # type: (int, float, float, int, int) -> Tensor
+def create_fb_matrix(
+        n_freqs: int,
+        f_min: float,
+        f_max: float,
+        n_mels: int,
+        sample_rate: int
+) -> Tensor:
     r"""Create a frequency bin conversion matrix.
 
     Args:
@@ -426,7 +454,7 @@ def create_fb_matrix(n_freqs, f_min, f_max, n_mels, sample_rate):
         sample_rate (int): Sample rate of the audio waveform
 
     Returns:
-        torch.Tensor: Triangular filter banks (fb matrix) of size (``n_freqs``, ``n_mels``)
+        Tensor: Triangular filter banks (fb matrix) of size (``n_freqs``, ``n_mels``)
         meaning number of frequencies to highlight/apply to x the number of filterbanks.
         Each column is a filterbank so that assuming there is a matrix A of
         size (..., ``n_freqs``), the applied result would be
@@ -456,18 +484,21 @@ def create_fb_matrix(n_freqs, f_min, f_max, n_mels, sample_rate):
     return fb
 
 
-def create_dct(n_mfcc, n_mels, norm):
-    # type: (int, int, Optional[str]) -> Tensor
+def create_dct(
+        n_mfcc: int,
+        n_mels: int,
+        norm: Optional[str]
+) -> Tensor:
     r"""Create a DCT transformation matrix with shape (``n_mels``, ``n_mfcc``),
     normalized depending on norm.
 
     Args:
         n_mfcc (int): Number of mfc coefficients to retain
         n_mels (int): Number of mel filterbanks
-        norm (Optional[str]): Norm to use (either 'ortho' or None)
+        norm (str or None): Norm to use (either 'ortho' or None)
 
     Returns:
-        torch.Tensor: The transformation matrix, to be right-multiplied to
+        Tensor: The transformation matrix, to be right-multiplied to
         row-wise data of size (``n_mels``, ``n_mfcc``).
     """
     # http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II
@@ -483,8 +514,10 @@ def create_dct(n_mfcc, n_mels, norm):
     return dct.t()
 
 
-def mu_law_encoding(x, quantization_channels):
-    # type: (Tensor, int) -> Tensor
+def mu_law_encoding(
+        x: Tensor,
+        quantization_channels: int
+) -> Tensor:
     r"""Encode signal based on mu-law companding.  For more info see the
     `Wikipedia Entry <https://en.wikipedia.org/wiki/%CE%9C-law_algorithm>`_
 
@@ -492,11 +525,11 @@ def mu_law_encoding(x, quantization_channels):
     returns a signal encoded with values from 0 to quantization_channels - 1.
 
     Args:
-        x (torch.Tensor): Input tensor
+        x (Tensor): Input tensor
         quantization_channels (int): Number of channels
 
     Returns:
-        torch.Tensor: Input after mu-law encoding
+        Tensor: Input after mu-law encoding
     """
     mu = quantization_channels - 1.0
     if not x.is_floating_point():
@@ -507,8 +540,10 @@ def mu_law_encoding(x, quantization_channels):
     return x_mu
 
 
-def mu_law_decoding(x_mu, quantization_channels):
-    # type: (Tensor, int) -> Tensor
+def mu_law_decoding(
+        x_mu: Tensor,
+        quantization_channels: int
+) -> Tensor:
     r"""Decode mu-law encoded signal.  For more info see the
     `Wikipedia Entry <https://en.wikipedia.org/wiki/%CE%9C-law_algorithm>`_
 
@@ -516,11 +551,11 @@ def mu_law_decoding(x_mu, quantization_channels):
     and returns a signal scaled between -1 and 1.
 
     Args:
-        x_mu (torch.Tensor): Input tensor
+        x_mu (Tensor): Input tensor
         quantization_channels (int): Number of channels
 
     Returns:
-        torch.Tensor: Input after mu-law decoding
+        Tensor: Input after mu-law decoding
     """
     mu = quantization_channels - 1.0
     if not x_mu.is_floating_point():
@@ -531,65 +566,71 @@ def mu_law_decoding(x_mu, quantization_channels):
     return x
 
 
-def complex_norm(complex_tensor, power=1.0):
-    # type: (Tensor, float) -> Tensor
+def complex_norm(
+        complex_tensor: Tensor,
+        power: float = 1.0
+) -> Tensor:
     r"""Compute the norm of complex tensor input.
 
     Args:
-        complex_tensor (torch.Tensor): Tensor shape of `(..., complex=2)`
+        complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
         power (float): Power of the norm. (Default: `1.0`).
 
     Returns:
-        torch.Tensor: Power of the normed input tensor. Shape of `(..., )`
+        Tensor: Power of the normed input tensor. Shape of `(..., )`
     """
     if power == 1.0:
         return torch.norm(complex_tensor, 2, -1)
     return torch.norm(complex_tensor, 2, -1).pow(power)
 
 
-def angle(complex_tensor):
-    # type: (Tensor) -> Tensor
+def angle(
+        complex_tensor: Tensor
+) -> Tensor:
     r"""Compute the angle of complex tensor input.
 
     Args:
-        complex_tensor (torch.Tensor): Tensor shape of `(..., complex=2)`
+        complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
 
     Return:
-        torch.Tensor: Angle of a complex tensor. Shape of `(..., )`
+        Tensor: Angle of a complex tensor. Shape of `(..., )`
     """
     return torch.atan2(complex_tensor[..., 1], complex_tensor[..., 0])
 
 
-def magphase(complex_tensor, power=1.0):
-    # type: (Tensor, float) -> Tuple[Tensor, Tensor]
+def magphase(
+        complex_tensor: Tensor,
+        power: float = 1.0
+) -> Tuple[Tensor, Tensor]:
     r"""Separate a complex-valued spectrogram with shape `(..., 2)` into its magnitude and phase.
 
     Args:
-        complex_tensor (torch.Tensor): Tensor shape of `(..., complex=2)`
+        complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
         power (float): Power of the norm. (Default: `1.0`)
 
     Returns:
-        Tuple[torch.Tensor, torch.Tensor]: The magnitude and phase of the complex tensor
+        (Tensor, Tensor): The magnitude and phase of the complex tensor
     """
     mag = complex_norm(complex_tensor, power)
     phase = angle(complex_tensor)
     return mag, phase
 
 
-def phase_vocoder(complex_specgrams, rate, phase_advance):
-    # type: (Tensor, float, Tensor) -> Tensor
+def phase_vocoder(
+        complex_specgrams: Tensor,
+        rate: float,
+        phase_advance: Tensor
+) -> Tensor:
     r"""Given a STFT tensor, speed up in time without modifying pitch by a
     factor of ``rate``.
 
     Args:
-        complex_specgrams (torch.Tensor): Dimension of `(..., freq, time, complex=2)`
+        complex_specgrams (Tensor): Dimension of `(..., freq, time, complex=2)`
         rate (float): Speed-up factor
-        phase_advance (torch.Tensor): Expected phase advance in each bin. Dimension
-            of (freq, 1)
+        phase_advance (Tensor): Expected phase advance in each bin. Dimension of (freq, 1)
 
     Returns:
-        complex_specgrams_stretch (torch.Tensor): Dimension of `(...,
-        freq, ceil(time/rate), complex=2)`
+        Tensor: Complex Specgrams Stretch with dimension of `(..., freq, ceil(time/rate), complex=2)`
 
     Example
         >>> freq, hop_length = 1025, 512
@@ -650,22 +691,24 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-def lfilter(waveform, a_coeffs, b_coeffs):
-    # type: (Tensor, Tensor, Tensor) -> Tensor
+def lfilter(
+        waveform: Tensor,
+        a_coeffs: Tensor,
+        b_coeffs: Tensor
+) -> Tensor:
     r"""Perform an IIR filter by evaluating difference equation.
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(..., time)`.  Must be normalized to -1 to 1.
-        a_coeffs (torch.Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.
+        waveform (Tensor): audio waveform of dimension of `(..., time)`.  Must be normalized to -1 to 1.
+        a_coeffs (Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.
                                 Lower delays coefficients are first, e.g. `[a0, a1, a2, ...]`.
                                 Must be same size as b_coeffs (pad with 0's as necessary).
-        b_coeffs (torch.Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.
+        b_coeffs (Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.
                                  Lower delays coefficients are first, e.g. `[b0, b1, b2, ...]`.
                                  Must be same size as a_coeffs (pad with 0's as necessary).
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`.  Output will be clipped to -1 to 1.
-
+        Tensor: Waveform with dimension of `(..., time)`.  Output will be clipped to -1 to 1.
     """
 
     dim = waveform.dim()
@@ -674,17 +717,17 @@ def lfilter(waveform, a_coeffs, b_coeffs):
     shape = waveform.size()
     waveform = waveform.view(-1, shape[-1])
 
-    assert(a_coeffs.size(0) == b_coeffs.size(0))
-    assert(len(waveform.size()) == 2)
-    assert(waveform.device == a_coeffs.device)
-    assert(b_coeffs.device == a_coeffs.device)
+    assert (a_coeffs.size(0) == b_coeffs.size(0))
+    assert (len(waveform.size()) == 2)
+    assert (waveform.device == a_coeffs.device)
+    assert (b_coeffs.device == a_coeffs.device)
 
     device = waveform.device
     dtype = waveform.dtype
     n_channel, n_sample = waveform.size()
     n_order = a_coeffs.size(0)
     n_sample_padded = n_sample + n_order - 1
-    assert(n_order > 0)
+    assert (n_order > 0)
 
     # Pad the input and create output
     padded_waveform = torch.zeros(n_channel, n_sample_padded, dtype=dtype, device=device)
@@ -720,13 +763,20 @@ def lfilter(waveform, a_coeffs, b_coeffs):
     return output
 
 
-def biquad(waveform, b0, b1, b2, a0, a1, a2):
-    # type: (Tensor, float, float, float, float, float, float) -> Tensor
+def biquad(
+        waveform: Tensor,
+        b0: float,
+        b1: float,
+        b2: float,
+        a0: float,
+        a1: float,
+        a2: float
+) -> Tensor:
     r"""Perform a biquad filter of input tensor.  Initial conditions set to 0.
     https://en.wikipedia.org/wiki/Digital_biquad_filter
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         b0 (float): numerator coefficient of current input, x[n]
         b1 (float): numerator coefficient of input one time step ago x[n-1]
         b2 (float): numerator coefficient of input two time steps ago x[n-2]
@@ -735,7 +785,7 @@ def biquad(waveform, b0, b1, b2, a0, a1, a2):
         a2 (float): denominator coefficient of current output y[n-2]
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform with dimension of `(..., time)`
     """
 
     device = waveform.device
@@ -749,23 +799,26 @@ def biquad(waveform, b0, b1, b2, a0, a1, a2):
     return output_waveform
 
 
-def _dB2Linear(x):
-    # type: (float) -> float
+def _dB2Linear(x: float) -> float:
     return math.exp(x * math.log(10) / 20.0)
 
 
-def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, float) -> Tensor
+def highpass_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        cutoff_freq: float,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design biquad highpass filter and perform filtering.  Similar to SoX implementation.
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform dimension of `(..., time)`
     """
 
     GAIN = 1.
@@ -783,18 +836,22 @@ def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, float) -> Tensor
+def lowpass_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        cutoff_freq: float,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design biquad lowpass filter and perform filtering.  Similar to SoX implementation.
 
     Args:
         waveform (torch.Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
     """
 
     GAIN = 1.
@@ -812,18 +869,22 @@ def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def allpass_biquad(waveform, sample_rate, central_freq, Q=0.707):
-    # type: (Tensor, int, float, float) -> Tensor
+def allpass_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        central_freq: float,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design two-pole all-pass filter.  Similar to SoX implementation.
 
     Args:
         waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         central_freq (float): central frequency (in Hz)
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -841,20 +902,25 @@ def allpass_biquad(waveform, sample_rate, central_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def bandpass_biquad(waveform, sample_rate, central_freq, Q=0.707, const_skirt_gain=False):
-    # type: (Tensor, int, float, float, bool) -> Tensor
+def bandpass_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        central_freq: float,
+        Q: float = 0.707,
+        const_skirt_gain: bool = False
+) -> Tensor:
     r"""Design two-pole band-pass filter.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         central_freq (float): central frequency (in Hz)
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
-        const_skirt_gain (bool) : If ``True``, uses a constant skirt gain (peak gain = Q).
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
+        const_skirt_gain (bool, optional) : If ``True``, uses a constant skirt gain (peak gain = Q).
             If ``False``, uses a constant 0dB peak gain. (Default: ``False``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -873,18 +939,22 @@ def bandpass_biquad(waveform, sample_rate, central_freq, Q=0.707, const_skirt_ga
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def bandreject_biquad(waveform, sample_rate, central_freq, Q=0.707):
-    # type: (Tensor, int, float, float) -> Tensor
+def bandreject_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        central_freq: float,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design two-pole band-reject filter.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         central_freq (float): central frequency (in Hz)
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -902,19 +972,24 @@ def bandreject_biquad(waveform, sample_rate, central_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def equalizer_biquad(waveform, sample_rate, center_freq, gain, Q=0.707):
-    # type: (Tensor, int, float, float, float) -> Tensor
+def equalizer_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        center_freq: float,
+        gain: float,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design biquad peaking equalizer filter and perform filtering.  Similar to SoX implementation.
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         center_freq (float): filter's central frequency
         gain (float): desired gain at the boost (or attenuation) in dB
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``)
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
     """
     w0 = 2 * math.pi * center_freq / sample_rate
     A = math.exp(gain / 40.0 * math.log(10))
@@ -929,21 +1004,26 @@ def equalizer_biquad(waveform, sample_rate, center_freq, gain, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def band_biquad(waveform, sample_rate, central_freq, Q=0.707, noise=False):
-    # type: (Tensor, int, float, float, bool) -> Tensor
+def band_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        central_freq: float,
+        Q: float = 0.707,
+        noise: bool = False
+) -> Tensor:
     r"""Design two-pole band filter.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         central_freq (float): central frequency (in Hz)
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
-        noise (bool) : If ``True``, uses the alternate mode for un-pitched audio (e.g. percussion).
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``).
+        noise (bool, optional) : If ``True``, uses the alternate mode for un-pitched audio (e.g. percussion).
             If ``False``, uses mode oriented to pitched audio, i.e. voice, singing,
-            or instrumental music. (Default: ``False``)
+            or instrumental music (Default: ``False``).
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -969,19 +1049,24 @@ def band_biquad(waveform, sample_rate, central_freq, Q=0.707, noise=False):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def treble_biquad(waveform, sample_rate, gain, central_freq=3000, Q=0.707):
-    # type: (Tensor, int, float, float, float) -> Tensor
+def treble_biquad(
+        waveform: Tensor,
+        sample_rate: int,
+        gain: float,
+        central_freq: float = 3000,
+        Q: float = 0.707
+) -> Tensor:
     r"""Design a treble tone-control effect.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
         gain (float): desired gain at the boost (or attenuation) in dB.
-        central_freq (float): central frequency (in Hz). (Default: ``3000``)
-        q_factor (float): https://en.wikipedia.org/wiki/Q_factor
+        central_freq (float, optional): central frequency (in Hz). (Default: ``3000``)
+        Q (float, optional): https://en.wikipedia.org/wiki/Q_factor (Default: ``0.707``).
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -1005,16 +1090,18 @@ def treble_biquad(waveform, sample_rate, gain, central_freq=3000, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def deemph_biquad(waveform, sample_rate):
-    # type: (Tensor, int) -> Tensor
+def deemph_biquad(
+        waveform: Tensor,
+        sample_rate: int
+) -> Tensor:
     r"""Apply ISO 908 CD de-emphasis (shelving) IIR filter.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, Allowed sample rate ``44100`` or ``48000``
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -1050,17 +1137,19 @@ def deemph_biquad(waveform, sample_rate):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def riaa_biquad(waveform, sample_rate):
-    # type: (Tensor, int) -> Tensor
+def riaa_biquad(
+        waveform: Tensor,
+        sample_rate: int
+) -> Tensor:
     r"""Apply RIAA vinyl playback equalisation.  Similar to SoX implementation.
 
     Args:
-        waveform(torch.Tensor): audio waveform of dimension of `(..., time)`
+        waveform (Tensor): audio waveform of dimension of `(..., time)`
         sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz).
             Allowed sample rates in Hz : ``44100``,``48000``,``88200``,``96000``
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(..., time)`
+        Tensor: Waveform of dimension of `(..., time)`
 
     References:
         http://sox.sourceforge.net/sox.html
@@ -1102,7 +1191,7 @@ def riaa_biquad(waveform, sample_rate):
     a_re = a0 + a1 * math.cos(-y) + a2 * math.cos(-2 * y)
     b_im = b1 * math.sin(-y) + b2 * math.sin(-2 * y)
     a_im = a1 * math.sin(-y) + a2 * math.sin(-2 * y)
-    g = 1 / math.sqrt((b_re**2 + b_im**2) / (a_re**2 + a_im**2))
+    g = 1 / math.sqrt((b_re ** 2 + b_im ** 2) / (a_re ** 2 + a_im ** 2))
 
     b0 *= g
     b1 *= g
@@ -1111,8 +1200,12 @@ def riaa_biquad(waveform, sample_rate):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def mask_along_axis_iid(specgrams, mask_param, mask_value, axis):
-    # type: (Tensor, int, float, int) -> Tensor
+def mask_along_axis_iid(
+        specgrams: Tensor,
+        mask_param: int,
+        mask_value: float,
+        axis: int
+) -> Tensor:
     r"""
     Apply a mask along ``axis``. Mask will be applied from indices ``[v_0, v_0 + v)``, where
     ``v`` is sampled from ``uniform(0, mask_param)``, and ``v_0`` from ``uniform(0, max_v - v)``.
@@ -1125,7 +1218,7 @@ def mask_along_axis_iid(specgrams, mask_param, mask_value, axis):
         axis (int): Axis to apply masking on (2 -> frequency, 3 -> time)
 
     Returns:
-        torch.Tensor: Masked spectrograms of dimensions (batch, channel, freq, time)
+        Tensor: Masked spectrograms of dimensions (batch, channel, freq, time)
     """
 
     if axis != 2 and axis != 3:
@@ -1147,8 +1240,12 @@ def mask_along_axis_iid(specgrams, mask_param, mask_value, axis):
     return specgrams
 
 
-def mask_along_axis(specgram, mask_param, mask_value, axis):
-    # type: (Tensor, int, float, int) -> Tensor
+def mask_along_axis(
+        specgram: Tensor,
+        mask_param: int,
+        mask_value: float,
+        axis: int
+) -> Tensor:
     r"""
     Apply a mask along ``axis``. Mask will be applied from indices ``[v_0, v_0 + v)``, where
     ``v`` is sampled from ``uniform(0, mask_param)``, and ``v_0`` from ``uniform(0, max_v - v)``.
@@ -1161,7 +1258,7 @@ def mask_along_axis(specgram, mask_param, mask_value, axis):
         axis (int): Axis to apply masking on (1 -> frequency, 2 -> time)
 
     Returns:
-        torch.Tensor: Masked spectrogram of dimensions (channel, freq, time)
+        Tensor: Masked spectrogram of dimensions (channel, freq, time)
     """
 
     # pack batch
@@ -1188,8 +1285,11 @@ def mask_along_axis(specgram, mask_param, mask_value, axis):
     return specgram
 
 
-def compute_deltas(specgram, win_length=5, mode="replicate"):
-    # type: (Tensor, int, str) -> Tensor
+def compute_deltas(
+        specgram: Tensor,
+        win_length: int = 5,
+        mode: str = "replicate"
+) -> Tensor:
     r"""Compute delta coefficients of a tensor, usually a spectrogram:
 
     .. math::
@@ -1200,12 +1300,12 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
     :math:`N` is (`win_length`-1)//2.
 
     Args:
-        specgram (torch.Tensor): Tensor of audio of dimension (..., freq, time)
-        win_length (int): The window length used for computing delta
-        mode (str): Mode parameter passed to padding
+        specgram (Tensor): Tensor of audio of dimension (..., freq, time)
+        win_length (int, optional): The window length used for computing delta (Default: ``5``)
+        mode (str, optional): Mode parameter passed to padding (Default: ``"replicate"``)
 
     Returns:
-        deltas (torch.Tensor): Tensor of audio of dimension (..., freq, time)
+        Tensor: Tensor of deltas of dimension (..., freq, time)
 
     Example
         >>> specgram = torch.randn(1, 40, 1000)
@@ -1226,11 +1326,7 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
 
     specgram = torch.nn.functional.pad(specgram, (n, n), mode=mode)
 
-    kernel = (
-        torch
-        .arange(-n, n + 1, 1, device=specgram.device, dtype=specgram.dtype)
-        .repeat(specgram.shape[1], 1, 1)
-    )
+    kernel = (torch.arange(-n, n + 1, 1, device=specgram.device, dtype=specgram.dtype).repeat(specgram.shape[1], 1, 1))
 
     output = torch.nn.functional.conv1d(specgram, kernel, groups=specgram.shape[1]) / denom
 
@@ -1240,16 +1336,18 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
     return output
 
 
-def gain(waveform, gain_db=1.0):
-    # type: (Tensor, float) -> Tensor
+def gain(
+        waveform: Tensor,
+        gain_db: float = 1.0
+) -> Tensor:
     r"""Apply amplification or attenuation to the whole waveform.
 
     Args:
-       waveform (torch.Tensor): Tensor of audio of dimension (..., time).
-       gain_db (float) Gain adjustment in decibels (dB) (Default: `1.0`).
+       waveform (Tensor): Tensor of audio of dimension (..., time).
+       gain_db (float, optional) Gain adjustment in decibels (dB) (Default: ``1.0``).
 
     Returns:
-       torch.Tensor: the whole waveform amplified by gain_db.
+       Tensor: the whole waveform amplified by gain_db.
     """
     if (gain_db == 0):
         return waveform
@@ -1259,7 +1357,10 @@ def gain(waveform, gain_db=1.0):
     return waveform * ratio
 
 
-def _add_noise_shaping(dithered_waveform, waveform):
+def _add_noise_shaping(
+        dithered_waveform: Tensor,
+        waveform: Tensor
+) -> Tensor:
     r"""Noise shaping is calculated by error:
     error[n] = dithered[n] - original[n]
     noise_shaped_waveform[n] = dithered[n] + error[n-1]
@@ -1281,8 +1382,10 @@ def _add_noise_shaping(dithered_waveform, waveform):
     return noise_shaped.view(dithered_shape[:-1] + noise_shaped.shape[-1:])
 
 
-def _apply_probability_distribution(waveform, density_function="TPDF"):
-    # type: (Tensor, str) -> Tensor
+def _apply_probability_distribution(
+        waveform: Tensor,
+        density_function: str = "TPDF"
+) -> Tensor:
     r"""Apply a probability distribution function on a waveform.
 
     Triangular probability density function (TPDF) dither noise has a
@@ -1297,14 +1400,14 @@ def _apply_probability_distribution(waveform, density_function="TPDF"):
     The relationship of probabilities of results follows a bell-shaped,
     or Gaussian curve, typical of dither generated by analog sources.
     Args:
-        waveform (torch.Tensor): Tensor of audio of dimension (..., time)
-        probability_density_function (string): The density function of a
-           continuous random variable (Default: `TPDF`)
+        waveform (Tensor): Tensor of audio of dimension (..., time)
+        probability_density_function (str, optional): The density function of a
+           continuous random variable (Default: ``"TPDF"``)
            Options: Triangular Probability Density Function - `TPDF`
                     Rectangular Probability Density Function - `RPDF`
                     Gaussian Probability Density Function - `GPDF`
     Returns:
-        torch.Tensor: waveform dithered with TPDF
+        Tensor: waveform dithered with TPDF
     """
 
     # pack batch
@@ -1353,23 +1456,25 @@ def _apply_probability_distribution(waveform, density_function="TPDF"):
     return quantised_signal.view(shape[:-1] + quantised_signal.shape[-1:])
 
 
-def dither(waveform, density_function="TPDF", noise_shaping=False):
-    # type: (Tensor, str, bool) -> Tensor
+def dither(
+        waveform: Tensor,
+        density_function: str = "TPDF",
+        noise_shaping: bool = False
+) -> Tensor:
     r"""Dither increases the perceived dynamic range of audio stored at a
     particular bit-depth by eliminating nonlinear truncation distortion
     (i.e. adding minimally perceived noise to mask distortion caused by quantization).
     Args:
-       waveform (torch.Tensor): Tensor of audio of dimension (..., time)
-       density_function (string): The density function of a
-           continuous random variable (Default: `TPDF`)
+       waveform (Tensor): Tensor of audio of dimension (..., time)
+       density_function (str, optional): The density function of a continuous random variable (Default: ``"TPDF"``)
            Options: Triangular Probability Density Function - `TPDF`
                     Rectangular Probability Density Function - `RPDF`
                     Gaussian Probability Density Function - `GPDF`
-       noise_shaping (boolean): a filtering process that shapes the spectral
-           energy of quantisation error (Default: `False`)
+       noise_shaping (bool, optional): a filtering process that shapes the spectral
+           energy of quantisation error (Default: ``False``)
 
     Returns:
-       torch.Tensor: waveform dithered
+       Tensor: waveform dithered
     """
     dithered = _apply_probability_distribution(waveform, density_function=density_function)
 
@@ -1379,8 +1484,12 @@ def dither(waveform, density_function="TPDF", noise_shaping=False):
         return dithered
 
 
-def _compute_nccf(waveform, sample_rate, frame_time, freq_low):
-    # type: (Tensor, int, float, int) -> Tensor
+def _compute_nccf(
+        waveform: Tensor,
+        sample_rate: int,
+        frame_time: float,
+        freq_low: int
+) -> Tensor:
     r"""
     Compute Normalized Cross-Correlation Function (NCCF).
 
@@ -1390,7 +1499,7 @@ def _compute_nccf(waveform, sample_rate, frame_time, freq_low):
     where
     :math:`\phi_i(m)` is the NCCF at frame :math:`i` with lag :math:`m`,
     :math:`w` is the waveform,
-    :math:`N` is the lenght of a frame,
+    :math:`N` is the length of a frame,
     :math:`b_i` is the beginning of frame :math:`i`,
     :math:`E(j)` is the energy :math:`\sum_{n=j}^{j+N-1} w^2(n)`.
     """
@@ -1411,12 +1520,8 @@ def _compute_nccf(waveform, sample_rate, frame_time, freq_low):
     # Compute lags
     output_lag = []
     for lag in range(1, lags + 1):
-        s1 = waveform[..., :-lag].unfold(-1, frame_size, frame_size)[
-            ..., :num_of_frames, :
-        ]
-        s2 = waveform[..., lag:].unfold(-1, frame_size, frame_size)[
-            ..., :num_of_frames, :
-        ]
+        s1 = waveform[..., :-lag].unfold(-1, frame_size, frame_size)[..., :num_of_frames, :]
+        s2 = waveform[..., lag:].unfold(-1, frame_size, frame_size)[..., :num_of_frames, :]
 
         output_frames = (
             (s1 * s2).sum(-1)
@@ -1431,8 +1536,11 @@ def _compute_nccf(waveform, sample_rate, frame_time, freq_low):
     return nccf
 
 
-def _combine_max(a, b, thresh=0.99):
-    # type: (Tuple[Tensor, Tensor], Tuple[Tensor, Tensor], float) -> Tuple[Tensor, Tensor]
+def _combine_max(
+        a: Tuple[Tensor, Tensor],
+        b: Tuple[Tensor, Tensor],
+        thresh: float = 0.99
+) -> Tuple[Tensor, Tensor]:
     """
     Take value from first if bigger than a multiplicative factor of the second, elementwise.
     """
@@ -1442,8 +1550,11 @@ def _combine_max(a, b, thresh=0.99):
     return values, indices
 
 
-def _find_max_per_frame(nccf, sample_rate, freq_high):
-    # type: (Tensor, int, int) -> Tensor
+def _find_max_per_frame(
+        nccf: Tensor,
+        sample_rate: int,
+        freq_high: int
+) -> Tensor:
     r"""
     For each frame, take the highest value of NCCF,
     apply centered median smoothing, and convert to frequency.
@@ -1472,8 +1583,10 @@ def _find_max_per_frame(nccf, sample_rate, freq_high):
     return indices
 
 
-def _median_smoothing(indices, win_length):
-    # type: (Tensor, int) -> Tensor
+def _median_smoothing(
+        indices: Tensor,
+        win_length: int
+) -> Tensor:
     r"""
     Apply median smoothing to the 1D tensor over the given window.
     """
@@ -1494,31 +1607,28 @@ def _median_smoothing(indices, win_length):
 
 
 def detect_pitch_frequency(
-    waveform,
-    sample_rate,
-    frame_time=10 ** (-2),
-    win_length=30,
-    freq_low=85,
-    freq_high=3400,
-):
-    # type: (Tensor, int, float, int, int, int) -> Tensor
+        waveform: Tensor,
+        sample_rate: int,
+        frame_time: float = 10 ** (-2),
+        win_length: int = 30,
+        freq_low: int = 85,
+        freq_high: int = 3400,
+) -> Tensor:
     r"""Detect pitch frequency.
 
     It is implemented using normalized cross-correlation function and median smoothing.
 
     Args:
-        waveform (torch.Tensor): Tensor of audio of dimension (..., freq, time)
+        waveform (Tensor): Tensor of audio of dimension (..., freq, time)
         sample_rate (int): The sample rate of the waveform (Hz)
-        win_length (int): The window length for median smoothing (in number of frames)
-        freq_low (int): Lowest frequency that can be detected (Hz)
-        freq_high (int): Highest frequency that can be detected (Hz)
+        frame_time (float, optional): Duration of a frame (Default: ``10 ** (-2)``).
+        win_length (int, optional): The window length for median smoothing (in number of frames) (Default: ``30``).
+        freq_low (int, optional): Lowest frequency that can be detected (Hz) (Default: ``85``).
+        freq_high (int, optional): Highest frequency that can be detected (Hz) (Default: ``3400``).
 
     Returns:
-        freq (torch.Tensor): Tensor of audio of dimension (..., frame)
+        Tensor: Tensor of freq of dimension (..., frame)
     """
-
-    dim = waveform.dim()
-
     # pack batch
     shape = list(waveform.size())
     waveform = waveform.view([-1] + shape[-1:])