Kaldi (#839)

* can do frames, real stft

* format

* stft complex, powspec, magspec

* add common utils

* add window process func

* using frames and matmul as stft

* read with 2d; window process

* test with dither, remove dc offset, preermphs

* add doc string

* more frontend utils

* add logspec

* fix typing

* add delpoy mergify label

deepspeech/io/dataset.py

@@ -76,19 +76,19 @@ class ManifestDataset(Dataset):
 
         Args:
             manifest_path (str): manifest josn file path
-            max_input_len ([type], optional): maximum output seq length, 
+            max_input_len ([type], optional): maximum output seq length,
                 in seconds for raw wav, in frame numbers for feature data. Defaults to float('inf').
-            min_input_len (float, optional): minimum input seq length, 
+            min_input_len (float, optional): minimum input seq length,
                 in seconds for raw wav, in frame numbers for feature data. Defaults to 0.0.
-            max_output_len (float, optional): maximum input seq length, 
+            max_output_len (float, optional): maximum input seq length,
                 in modeling units. Defaults to 500.0.
-            min_output_len (float, optional): minimum input seq length, 
+            min_output_len (float, optional): minimum input seq length,
                 in modeling units. Defaults to 0.0.
-            max_output_input_ratio (float, optional): maximum output seq length/output seq length ratio. 
+            max_output_input_ratio (float, optional): maximum output seq length/output seq length ratio.
                 Defaults to 10.0.
             min_output_input_ratio (float, optional): minimum output seq length/output seq length ratio.
                 Defaults to 0.05.
-        
+
         """
         super().__init__()
 

third_party/paddle_audio/frontend.py

-from typing import Tuple
-import numpy as np
-import paddle
-from paddle import Tensor
-from paddle import nn
-from paddle.nn import functional as F
-
-
-def frame(x: Tensor,
-          num_samples: Tensor,
-          win_length: int,
-          hop_length: int,
-          clip: bool = True) -> Tuple[Tensor, Tensor]:
-    """Extract frames from audio.
-
-    Parameters
-    ----------
-    x : Tensor
-        Shape (N, T), batched waveform.
-    num_samples : Tensor
-        Shape (N, ), number of samples of each waveform.
-    win_length : int
-        Window length.
-    hop_length : int
-        Number of samples shifted between ajancent frames.
-    clip : bool, optional
-        Whether to clip audio that does not fit into the last frame, by 
-        default True
-
-    Returns
-    -------
-    frames : Tensor
-        Shape (N, T', win_length).
-    num_frames : Tensor
-        Shape (N, ) number of valid frames
-    """
-    assert hop_length <= win_length
-    num_frames = (num_samples - win_length) // hop_length
-    padding = (0, 0)
-    if not clip:
-        num_frames += 1
-        # NOTE: pad hop_length - 1 to the right to ensure that there is at most
-        # one frame dangling to the righe edge
-        padding = (0, hop_length - 1)
-
-    weight = paddle.eye(win_length).unsqueeze(1)
-
-    frames = F.conv1d(x.unsqueeze(1),
-                      weight,
-                      padding=padding,
-                      stride=(hop_length, ))
-    return frames, num_frames
-
-
-class STFT(nn.Layer):
-    """A module for computing stft transformation in a differentiable way. 
-    
-    Parameters
-    ------------
-    n_fft : int
-        Number of samples in a frame.
-        
-    hop_length : int
-        Number of samples shifted between adjacent frames.
-        
-    win_length : int
-        Length of the window.
-
-    clip: bool
-        Whether to clip audio is necesaary.
-    """
-    def __init__(self,
-                 n_fft: int,
-                 hop_length: int,
-                 win_length: int,
-                 window_type: str = None,
-                 clip: bool = True):
-        super().__init__()
-
-        self.hop_length = hop_length
-        self.n_bin = 1 + n_fft // 2
-        self.n_fft = n_fft
-        self.clip = clip
-
-        # calculate window
-        if window_type is None:
-            window = np.ones(win_length)
-        elif window_type == "hann":
-            window = np.hanning(win_length)
-        elif window_type == "hamming":
-            window = np.hamming(win_length)
-        else:
-            raise ValueError("Not supported yet!")
-
-        if win_length < n_fft:
-            window = F.pad(window, (0, n_fft - win_length))
-        elif win_length > n_fft:
-            window = window[:n_fft]
-
-        # (n_bins, n_fft) complex
-        kernel_size = min(n_fft, win_length)
-        weight = np.fft.fft(np.eye(n_fft))[:self.n_bin, :kernel_size]
-        w_real = weight.real
-        w_imag = weight.imag
-
-        # (2 * n_bins, kernel_size)
-        w = np.concatenate([w_real, w_imag], axis=0)
-        w = w * window
-
-        # (2 * n_bins, 1, kernel_size) # (C_out, C_in, kernel_size)
-        w = np.expand_dims(w, 1)
-        weight = paddle.cast(paddle.to_tensor(w), paddle.get_default_dtype())
-        self.register_buffer("weight", weight)
-
-    def forward(self, x: Tensor, num_samples: Tensor) -> Tuple[Tensor, Tensor]:
-        """Compute the stft transform.
-        Parameters
-        ------------
-        x : Tensor [shape=(B, T)]
-            The input waveform.
-        num_samples : Tensor 
-            Number of samples of each waveform.
-        Returns
-        ------------
-        D : Tensor
-            Shape(N, T', n_bins, 2) Spectrogram.
-
-        num_frames: Tensor
-            Shape (N,) number of samples of each spectrogram
-        """
-        num_frames = (num_samples - self.win_length) // self.hop_length
-        padding = (0, 0)
-        if not self.clip:
-            num_frames += 1
-            padding = (0, self.hop_length - 1)
-
-        batch_size, _, _ = paddle.shape(x)
-        x = x.unsqueeze(-1)
-        D = F.conv1d(self.weight,
-                     x,
-                     stride=(self.hop_length, ),
-                     padding=padding,
-                     data_format="NLC")
-        D = paddle.reshape(D, [batch_size, -1, self.n_bin, 2])
-        return D, num_frames
-

third_party/paddle_audio/frontend/common.py

+import paddle
+import numpy as np
+from typing import Tuple, Optional, Union
+
+
+# https://github.com/kaldi-asr/kaldi/blob/cbed4ff688/src/feat/feature-window.cc#L109
+def povey_window(frame_len:int) -> np.ndarray:
+    win = np.empty(frame_len)
+    a = 2 * np.pi / (frame_len -1)
+    for i in range(frame_len):
+        win[i] = (0.5 - 0.5 * np.cos(a * i) )**0.85 
+    return win
+
+def hann_window(frame_len:int) -> np.ndarray:
+    win = np.empty(frame_len)
+    a = 2 * np.pi / (frame_len -1)
+    for i in range(frame_len):
+        win[i] = 0.5 - 0.5 * np.cos(a * i)
+    return win
+
+def sine_window(frame_len:int) -> np.ndarray:
+    win = np.empty(frame_len)
+    a = 2 * np.pi / (frame_len -1)
+    for i in range(frame_len):
+        win[i] = np.sin(0.5 * a * i)
+    return win
+
+def hamm_window(frame_len:int) -> np.ndarray:
+    win = np.empty(frame_len)
+    a = 2 * np.pi / (frame_len -1)
+    for i in range(frame_len):
+        win[i] = 0.54 - 0.46 * np.cos(a * i)
+    return win
+
+def get_window(wintype:Optional[str], winlen:int) -> np.ndarray:
+    """get window function
+
+    Args:
+        wintype (Optional[str]): window type.
+        winlen (int): window length in samples.
+
+    Raises:
+        ValueError: not support window.
+
+    Returns:
+        np.ndarray: window coeffs.
+    """
+    # calculate window
+    if not wintype or wintype == 'rectangular':
+        window = np.ones(winlen)
+    elif wintype == "hann":
+        window = hann_window(winlen)
+    elif wintype == "hamm":
+        window = hamm_window(winlen)
+    elif wintype == "povey":
+        window = povey_window(winlen)
+    else:
+        msg = f"{wintype} Not supported yet!"
+        raise ValueError(msg)
+    return window
+    
+   
+def dft_matrix(n_fft:int, winlen:int=None, n_bin:int=None) -> Tuple[np.ndarray, np.ndarray, int]:
+    # https://en.wikipedia.org/wiki/Discrete_Fourier_transform
+    # (n_bins, n_fft) complex
+    if n_bin is None:
+        n_bin = 1 + n_fft // 2
+    if winlen is None:
+        winlen = n_bin
+    # https://github.com/numpy/numpy/blob/v1.20.0/numpy/fft/_pocketfft.py#L49
+    kernel_size = min(n_fft, winlen)
+        
+    n = np.arange(0, n_fft, 1.)
+    wsin = np.empty((n_bin, kernel_size)) #[Cout, kernel_size]
+    wcos = np.empty((n_bin, kernel_size)) #[Cout, kernel_size]
+    for k in range(n_bin): # Only half of the bins contain useful info
+        wsin[k,:] = -np.sin(2*np.pi*k*n/n_fft)[:kernel_size]
+        wcos[k,:] = np.cos(2*np.pi*k*n/n_fft)[:kernel_size]
+    w_real = wcos
+    w_imag = wsin
+    return w_real, w_imag, kernel_size
+    
+
+def dft_matrix_fast(n_fft:int, winlen:int=None, n_bin:int=None) -> Tuple[np.ndarray, np.ndarray, int]:
+    # (n_bins, n_fft) complex
+    if n_bin is None:
+        n_bin = 1 + n_fft // 2
+    if winlen is None:
+        winlen = n_bin
+    # https://github.com/numpy/numpy/blob/v1.20.0/numpy/fft/_pocketfft.py#L49
+    kernel_size = min(n_fft, winlen)
+    
+    # https://en.wikipedia.org/wiki/DFT_matrix
+    # https://ccrma.stanford.edu/~jos/st/Matrix_Formulation_DFT.html
+    weight = np.fft.fft(np.eye(n_fft))[:self.n_bin, :kernel_size]
+    w_real = weight.real
+    w_imag = weight.imag
+    return w_real, w_imag, kernel_size
+    
+
+def bin2hz(bin:Union[List[int], np.ndarray], N:int, sr:int)->List[float]:
+    """FFT bins to Hz.
+    
+    http://practicalcryptography.com/miscellaneous/machine-learning/intuitive-guide-discrete-fourier-transform/
+
+    Args:
+        bins (List[int] or np.ndarray): bin index.
+        N (int): the number of samples, or FFT points.
+        sr (int): sampling rate.
+
+    Returns:
+        List[float]: Hz's.
+    """
+    hz = bin * float(sr) / N
+        
+        
+def hz2mel(hz):
+    """Convert a value in Hertz to Mels
+
+    :param hz: a value in Hz. This can also be a numpy array, conversion proceeds element-wise.
+    :returns: a value in Mels. If an array was passed in, an identical sized array is returned.
+    """
+    return 1127 * np.log(1+hz/700.0)
+
+
+def mel2hz(mel):
+    """Convert a value in Mels to Hertz
+
+    :param mel: a value in Mels. This can also be a numpy array, conversion proceeds element-wise.
+    :returns: a value in Hertz. If an array was passed in, an identical sized array is returned.
+    """
+    return 700 * (np.exp(mel/1127.0)-1)
+
+
+
+def rms_to_db(rms: float):
+    """Root Mean Square to dB.
+
+    Args:
+        rms ([float]): root mean square
+
+    Returns:
+        float: dB
+    """
+    return 20.0 * math.log10(max(1e-16, rms))
+
+
+def rms_to_dbfs(rms: float):
+    """Root Mean Square to dBFS.
+    https://fireattack.wordpress.com/2017/02/06/replaygain-loudness-normalization-and-applications/
+    Audio is mix of sine wave, so 1 amp sine wave's Full scale is 0.7071, equal to -3.0103dB.
+   
+    dB = dBFS + 3.0103
+    dBFS = db - 3.0103
+    e.g. 0 dB = -3.0103 dBFS
+
+    Args:
+        rms ([float]): root mean square
+
+    Returns:
+        float: dBFS
+    """
+    return rms_to_db(rms) - 3.0103
+
+
+def max_dbfs(sample_data: np.ndarray):
+    """Peak dBFS based on the maximum energy sample. 
+
+    Args:
+        sample_data ([np.ndarray]): float array, [-1, 1].
+
+    Returns:
+        float: dBFS 
+    """
+    # Peak dBFS based on the maximum energy sample. Will prevent overdrive if used for normalization.
+    return rms_to_dbfs(max(abs(np.min(sample_data)), abs(np.max(sample_data))))
+
+
+def mean_dbfs(sample_data):
+    """Peak dBFS based on the RMS energy. 
+
+    Args:
+        sample_data ([np.ndarray]): float array, [-1, 1].
+
+    Returns:
+        float: dBFS 
+    """
+    return rms_to_dbfs(
+        math.sqrt(np.mean(np.square(sample_data, dtype=np.float64))))
+
+
+def gain_db_to_ratio(gain_db: float):
+    """dB to ratio
+
+    Args:
+        gain_db (float): gain in dB
+
+    Returns:
+        float: scale in amp
+    """
+    return math.pow(10.0, gain_db / 20.0)
\ No newline at end of file

third_party/paddle_audio/frontend/kaldi.py

+from typing import Tuple
+import numpy as np
+import paddle
+from paddle import Tensor
+from paddle import nn
+from paddle.nn import functional as F
+import soundfile as sf
+
+from .common import get_window
+from .common import dft_matrix
+
+
+def read(wavpath:str, sr:int = None, start=0, stop=None, dtype='int16', always_2d=True)->Tuple[int, np.ndarray]:
+    """load wav file.
+
+    Args:
+        wavpath (str): wav path.
+        sr (int, optional): expect sample rate. Defaults to None.
+        dtype (str, optional): wav data bits. Defaults to 'int16'.
+
+    Returns:
+        Tuple[int, np.ndarray]: sr (int), wav (int16) [T, C].
+    """
+    wav, r_sr = sf.read(wavpath, start=start, stop=stop, dtype=dtype, always_2d=always_2d)
+    if sr:
+        assert sr == r_sr
+    return r_sr, wav
+
+
+def write(wavpath:str, wav:np.ndarray, sr:int, dtype='PCM_16'):
+    """write wav file.
+
+    Args:
+        wavpath (str): file path to save.
+        wav (np.ndarray): wav data.
+        sr (int): data samplerate.
+        dtype (str, optional): wav bit format. Defaults to 'PCM_16'.
+    """
+    sf.write(wavpath, wav, sr, subtype=dtype)
+
+
+def frames(x: Tensor,
+          num_samples: Tensor,
+          sr: int,
+          win_length: float,
+          stride_length: float,
+          clip: bool = False) -> Tuple[Tensor, Tensor]:
+    """Extract frames from audio.
+
+    Parameters
+    ----------
+    x : Tensor
+        Shape (B, T), batched waveform.
+    num_samples : Tensor
+        Shape (B, ), number of samples of each waveform.
+    sr: int
+        Sampling Rate.
+    win_length : float
+        Window length in ms.
+    stride_length : float
+        Stride length in ms.
+    clip : bool, optional
+        Whether to clip audio that does not fit into the last frame, by
+        default True
+
+    Returns
+    -------
+    frames : Tensor
+        Shape (B, T', win_length).
+    num_frames : Tensor
+        Shape (B, ) number of valid frames
+    """
+    assert stride_length <= win_length
+    stride_length = int(stride_length * sr)
+    win_length = int(win_length * sr)
+
+    num_frames = (num_samples - win_length) // stride_length
+    padding = (0, 0)
+    if not clip:
+        num_frames += 1
+        need_samples = num_frames * stride_length + win_length
+        padding = (0, need_samples - num_samples - 1)
+
+    weight = paddle.eye(win_length).unsqueeze(1) #[win_length, 1, win_length]
+
+    frames = F.conv1d(x.unsqueeze(-1),
+                      weight,
+                      padding=padding,
+                      stride=(stride_length, ),
+                      data_format='NLC')
+    return frames, num_frames
+
+
+def dither(signal:Tensor, dither_value=1.0)->Tensor:
+    """dither frames for log compute.
+
+    Args:
+        signal (Tensor): [B, T, D]
+        dither_value (float, optional): [scalar]. Defaults to 1.0.
+
+    Returns:
+        Tensor: [B, T, D]
+    """
+    D = paddle.shape(signal)[-1]
+    signal += paddle.normal(shape=[1, 1, D]) * dither_value
+    return signal
+
+
+def remove_dc_offset(signal:Tensor)->Tensor:
+    """remove dc.
+
+    Args:
+        signal (Tensor): [B, T, D]
+
+    Returns:
+        Tensor: [B, T, D]
+    """
+    signal -= paddle.mean(signal, axis=-1, keepdim=True)
+    return signal
+
+def preemphasis(signal:Tensor, coeff=0.97)->Tensor:
+    """perform preemphasis on the input signal.
+
+    Args:
+        signal (Tensor): [B, T, D], The signal to filter.
+        coeff (float, optional): [scalar].The preemphasis coefficient. 0 is no filter, Defaults to 0.97.
+
+    Returns:
+        Tensor: [B, T, D]
+    """
+    return paddle.concat([
+        (1-coeff)*signal[:, :, 0:1],
+        signal[:, :, 1:] - coeff * signal[:, :, :-1]
+    ], axis=-1)
+
+
+class STFT(nn.Layer):
+    """A module for computing stft transformation in a differentiable way.
+
+    http://practicalcryptography.com/miscellaneous/machine-learning/intuitive-guide-discrete-fourier-transform/
+
+    Parameters
+    ------------
+    n_fft : int
+        Number of samples in a frame.
+
+    sr: int
+        Number of Samplilng rate.
+
+    stride_length : float
+        Number of samples shifted between adjacent frames.
+
+    win_length : float
+        Length of the window.
+
+    clip: bool
+        Whether to clip audio is necesaary.
+    """
+    def __init__(self,
+                 n_fft: int,
+                 sr: int,
+                 win_length: float,
+                 stride_length: float,
+                 dither:float=0.0,
+                 preemph_coeff:float=0.97,
+                 remove_dc_offset:bool=True,
+                 window_type: str = 'povey',
+                 clip: bool = False):
+        super().__init__()
+        self.sr = sr
+        self.win_length = win_length
+        self.stride_length = stride_length
+        self.dither = dither
+        self.preemph_coeff = preemph_coeff
+        self.remove_dc_offset = remove_dc_offset
+        self.window_type = window_type
+        self.clip = clip
+
+        self.n_fft = n_fft
+        self.n_bin = 1 + n_fft // 2
+
+        w_real, w_imag, kernel_size = dft_matrix(
+            self.n_fft, int(self.win_length * self.sr), self.n_bin
+        )
+
+        # calculate window
+        window = get_window(window_type, kernel_size)
+
+        # (2 * n_bins, kernel_size)
+        w = np.concatenate([w_real, w_imag], axis=0)
+        w = w * window
+        # (kernel_size, 2 * n_bins)
+        w = np.transpose(w)
+        weight = paddle.cast(paddle.to_tensor(w), paddle.get_default_dtype())
+        self.register_buffer("weight", weight)
+
+    def forward(self, x: Tensor, num_samples: Tensor) -> Tuple[Tensor, Tensor]:
+        """Compute the stft transform.
+        Parameters
+        ------------
+        x : Tensor [shape=(B, T)]
+            The input waveform.
+        num_samples : Tensor [shape=(B,)]
+            Number of samples of each waveform.
+        Returns
+        ------------
+        C : Tensor
+            Shape(B, T', n_bins, 2) Spectrogram.
+
+        num_frames: Tensor
+            Shape (B,) number of samples of each spectrogram
+        """
+        batch_size = paddle.shape(num_samples)
+        F, nframe = frames(x, num_samples, self.sr, self.win_length, self.stride_length, clip=self.clip)
+        if self.dither:
+            F = dither(F, self.dither)
+        if self.remove_dc_offset:
+            F = remove_dc_offset(F)
+        if self.preemph_coeff:
+            F = preemphasis(F)
+        C = paddle.matmul(F, self.weight) # [B, T, K] [K, 2 * n_bins]
+        C = paddle.reshape(C, [batch_size, -1, 2, self.n_bin])
+        C = C.transpose([0, 1, 3, 2])
+        return C, nframe
+
+
+def powspec(C:Tensor) -> Tensor:
+    """Compute the power spectrum |X_k|^2.
+
+    Args:
+        C (Tensor): [B, T, C, 2]
+
+    Returns:
+        Tensor: [B, T, C]
+    """
+    real, imag = paddle.chunk(C, 2, axis=-1)
+    return paddle.square(real.squeeze(-1)) + paddle.square(imag.squeeze(-1))
+
+
+def magspec(C: Tensor, eps=1e-10) -> Tensor:
+    """Compute the magnitude spectrum |X_k|.
+
+    Args:
+        C (Tensor): [B, T, C, 2]
+        eps (float): epsilon.
+
+    Returns:
+        Tensor: [B, T, C]
+    """
+    pspec = powspec(C)
+    return paddle.sqrt(pspec + eps)
+
+
+def logspec(C: Tensor, eps=1e-10) -> Tensor:
+    """Compute log-spectrum  20log10∣X_k∣.
+
+    Args:
+        C (Tensor): [description]
+        eps ([type], optional): [description]. Defaults to 1e-10.
+
+    Returns:
+        Tensor: [description]
+    """
+    spec = magspec(C)
+    return 20 * paddle.log10(spec + eps)
+

third_party/paddle_audio/frontend/kaldi_test.py

+from typing import Tuple
+import numpy as np
+import paddle
+import unittest
+
+import decimal
+import numpy
+import math
+import logging
+from pathlib import Path
+
+from scipy.fftpack import dct
+
+from third_party.paddle_audio.frontend import kaldi
+
+def round_half_up(number):
+    return int(decimal.Decimal(number).quantize(decimal.Decimal('1'), rounding=decimal.ROUND_HALF_UP))
+
+def rolling_window(a, window, step=1):
+    # http://ellisvalentiner.com/post/2017-03-21-np-strides-trick
+    shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
+    strides = a.strides + (a.strides[-1],)
+    return numpy.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)[::step]
+
+
+def do_dither(signal, dither_value=1.0):
+    signal += numpy.random.normal(size=signal.shape) * dither_value
+    return signal
+    
+def do_remove_dc_offset(signal):
+    signal -= numpy.mean(signal)
+    return signal
+
+def do_preemphasis(signal, coeff=0.97):
+    """perform preemphasis on the input signal.
+
+    :param signal: The signal to filter.
+    :param coeff: The preemphasis coefficient. 0 is no filter, default is 0.95.
+    :returns: the filtered signal.
+    """
+    return numpy.append((1-coeff)*signal[0], signal[1:] - coeff * signal[:-1])
+
+
+def framesig(sig, frame_len, frame_step, dither=1.0, preemph=0.97, remove_dc_offset=True, wintype='hamming', stride_trick=True):
+    """Frame a signal into overlapping frames.
+
+    :param sig: the audio signal to frame.
+    :param frame_len: length of each frame measured in samples.
+    :param frame_step: number of samples after the start of the previous frame that the next frame should begin.
+    :param winfunc: the analysis window to apply to each frame. By default no window is applied.
+    :param stride_trick: use stride trick to compute the rolling window and window multiplication faster
+    :returns: an array of frames. Size is NUMFRAMES by frame_len.
+    """
+    slen = len(sig)
+    frame_len = int(round_half_up(frame_len))
+    frame_step = int(round_half_up(frame_step))
+    if slen <= frame_len:
+        numframes = 1
+    else:
+        numframes = 1 + (( slen - frame_len) // frame_step)
+
+    # check kaldi/src/feat/feature-window.h
+    padsignal = sig[:(numframes-1)*frame_step+frame_len]
+    if wintype is 'povey':
+        win = numpy.empty(frame_len)
+        for i in range(frame_len):
+            win[i] = (0.5-0.5*numpy.cos(2*numpy.pi/(frame_len-1)*i))**0.85     
+    else: # the hamming window
+        win = numpy.hamming(frame_len)
+        
+    if stride_trick:
+        frames = rolling_window(padsignal, window=frame_len, step=frame_step)
+    else:
+        indices = numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(
+            numpy.arange(0, numframes * frame_step, frame_step), (frame_len, 1)).T
+        indices = numpy.array(indices, dtype=numpy.int32)
+        frames = padsignal[indices]
+        win = numpy.tile(win, (numframes, 1))
+        
+    frames = frames.astype(numpy.float32)
+    raw_frames = numpy.zeros(frames.shape)
+    for frm in range(frames.shape[0]):
+        frames[frm,:] = do_dither(frames[frm,:], dither)        # dither
+        frames[frm,:] = do_remove_dc_offset(frames[frm,:])      # remove dc offset
+        raw_frames[frm,:] = frames[frm,:]
+        frames[frm,:] = do_preemphasis(frames[frm,:], preemph)    # preemphasize
+
+    return frames * win, raw_frames
+
+
+def magspec(frames, NFFT):
+    """Compute the magnitude spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
+
+    :param frames: the array of frames. Each row is a frame.
+    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
+    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the magnitude spectrum of the corresponding frame.
+    """
+    if numpy.shape(frames)[1] > NFFT:
+        logging.warn(
+            'frame length (%d) is greater than FFT size (%d), frame will be truncated. Increase NFFT to avoid.',
+            numpy.shape(frames)[1], NFFT)
+    complex_spec = numpy.fft.rfft(frames, NFFT)
+    return numpy.absolute(complex_spec)
+
+
+def powspec(frames, NFFT):
+    """Compute the power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
+
+    :param frames: the array of frames. Each row is a frame.
+    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
+    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the power spectrum of the corresponding frame.
+    """
+    return numpy.square(magspec(frames, NFFT))
+
+
+
+def mfcc(signal,samplerate=16000,winlen=0.025,winstep=0.01,numcep=13,
+         nfilt=23,nfft=512,lowfreq=20,highfreq=None,dither=1.0,remove_dc_offset=True,preemph=0.97,
+         ceplifter=22,useEnergy=True,wintype='povey'):
+    """Compute MFCC features from an audio signal.
+
+    :param signal: the audio signal from which to compute features. Should be an N*1 array
+    :param samplerate: the samplerate of the signal we are working with.
+    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
+    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
+    :param numcep: the number of cepstrum to return, default 13
+    :param nfilt: the number of filters in the filterbank, default 26.
+    :param nfft: the FFT size. Default is 512.
+    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
+    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
+    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
+    :param ceplifter: apply a lifter to final cepstral coefficients. 0 is no lifter. Default is 22.
+    :param appendEnergy: if this is true, the zeroth cepstral coefficient is replaced with the log of the total frame energy.
+    :param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
+    :returns: A numpy array of size (NUMFRAMES by numcep) containing features. Each row holds 1 feature vector.
+    """
+    feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,dither,remove_dc_offset,preemph,wintype)
+    feat = numpy.log(feat)
+    feat = dct(feat, type=2, axis=1, norm='ortho')[:,:numcep]
+    feat = lifter(feat,ceplifter)
+    if useEnergy: feat[:,0] = numpy.log(energy) # replace first cepstral coefficient with log of frame energy
+    return feat
+
+def fbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
+          nfilt=40,nfft=512,lowfreq=0,highfreq=None,dither=1.0,remove_dc_offset=True, preemph=0.97, 
+          wintype='hamming'):
+    """Compute Mel-filterbank energy features from an audio signal.
+
+    :param signal: the audio signal from which to compute features. Should be an N*1 array
+    :param samplerate: the samplerate of the signal we are working with.
+    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
+    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
+    :param nfilt: the number of filters in the filterbank, default 26.
+    :param nfft: the FFT size. Default is 512.
+    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
+    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
+    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
+    :param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
+     winfunc=lambda x:numpy.ones((x,))   
+    :returns: 2 values. The first is a numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector. The
+        second return value is the energy in each frame (total energy, unwindowed)
+    """
+    highfreq= highfreq or samplerate/2
+    frames,raw_frames = sigproc.framesig(signal, winlen*samplerate, winstep*samplerate, dither, preemph, remove_dc_offset, wintype)
+    pspec = sigproc.powspec(frames,nfft) # nearly the same until this part
+    energy = numpy.sum(raw_frames**2,1) # this stores the raw energy in each frame
+    energy = numpy.where(energy == 0,numpy.finfo(float).eps,energy) # if energy is zero, we get problems with log
+
+    fb = get_filterbanks(nfilt,nfft,samplerate,lowfreq,highfreq)
+    feat = numpy.dot(pspec,fb.T) # compute the filterbank energies
+    feat = numpy.where(feat == 0,numpy.finfo(float).eps,feat) # if feat is zero, we get problems with log
+
+    return feat,energy
+
+def logfbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
+          nfilt=40,nfft=512,lowfreq=64,highfreq=None,dither=1.0,remove_dc_offset=True,preemph=0.97,wintype='hamming'):
+    """Compute log Mel-filterbank energy features from an audio signal.
+
+    :param signal: the audio signal from which to compute features. Should be an N*1 array
+    :param samplerate: the samplerate of the signal we are working with.
+    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
+    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
+    :param nfilt: the number of filters in the filterbank, default 26.
+    :param nfft: the FFT size. Default is 512.
+    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
+    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
+    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
+    :returns: A numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector.
+    """
+    feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,dither, remove_dc_offset,preemph,wintype)
+    return numpy.log(feat)
+
+def hz2mel(hz):
+    """Convert a value in Hertz to Mels
+
+    :param hz: a value in Hz. This can also be a numpy array, conversion proceeds element-wise.
+    :returns: a value in Mels. If an array was passed in, an identical sized array is returned.
+    """
+    return 1127 * numpy.log(1+hz/700.0)
+
+def mel2hz(mel):
+    """Convert a value in Mels to Hertz
+
+    :param mel: a value in Mels. This can also be a numpy array, conversion proceeds element-wise.
+    :returns: a value in Hertz. If an array was passed in, an identical sized array is returned.
+    """
+    return 700 * (numpy.exp(mel/1127.0)-1)
+
+def get_filterbanks(nfilt=26,nfft=512,samplerate=16000,lowfreq=0,highfreq=None):
+    """Compute a Mel-filterbank. The filters are stored in the rows, the columns correspond
+    to fft bins. The filters are returned as an array of size nfilt * (nfft/2 + 1)
+
+    :param nfilt: the number of filters in the filterbank, default 20.
+    :param nfft: the FFT size. Default is 512.
+    :param samplerate: the samplerate of the signal we are working with. Affects mel spacing.
+    :param lowfreq: lowest band edge of mel filters, default 0 Hz
+    :param highfreq: highest band edge of mel filters, default samplerate/2
+    :returns: A numpy array of size nfilt * (nfft/2 + 1) containing filterbank. Each row holds 1 filter.
+    """
+    highfreq= highfreq or samplerate/2
+    assert highfreq <= samplerate/2, "highfreq is greater than samplerate/2"
+
+    # compute points evenly spaced in mels
+    lowmel = hz2mel(lowfreq)
+    highmel = hz2mel(highfreq)
+
+    # check kaldi/src/feat/Mel-computations.h    
+    fbank = numpy.zeros([nfilt,nfft//2+1])
+    mel_freq_delta = (highmel-lowmel)/(nfilt+1)
+    for j in range(0,nfilt):
+        leftmel = lowmel+j*mel_freq_delta
+        centermel = lowmel+(j+1)*mel_freq_delta
+        rightmel = lowmel+(j+2)*mel_freq_delta
+        for i in range(0,nfft//2):
+            mel=hz2mel(i*samplerate/nfft)
+            if mel>leftmel and mel<rightmel:
+                if mel<centermel:
+                    fbank[j,i]=(mel-leftmel)/(centermel-leftmel)
+                else:
+                    fbank[j,i]=(rightmel-mel)/(rightmel-centermel)
+    return fbank
+
+def lifter(cepstra, L=22):
+    """Apply a cepstral lifter the the matrix of cepstra. This has the effect of increasing the
+    magnitude of the high frequency DCT coeffs.
+
+    :param cepstra: the matrix of mel-cepstra, will be numframes * numcep in size.
+    :param L: the liftering coefficient to use. Default is 22. L <= 0 disables lifter.
+    """
+    if L > 0:
+        nframes,ncoeff = numpy.shape(cepstra)
+        n = numpy.arange(ncoeff)
+        lift = 1 + (L/2.)*numpy.sin(numpy.pi*n/L)
+        return lift*cepstra
+    else:
+        # values of L <= 0, do nothing
+        return cepstra
+
+def delta(feat, N):
+    """Compute delta features from a feature vector sequence.
+
+    :param feat: A numpy array of size (NUMFRAMES by number of features) containing features. Each row holds 1 feature vector.
+    :param N: For each frame, calculate delta features based on preceding and following N frames
+    :returns: A numpy array of size (NUMFRAMES by number of features) containing delta features. Each row holds 1 delta feature vector.
+    """
+    if N < 1:
+        raise ValueError('N must be an integer >= 1')
+    NUMFRAMES = len(feat)
+    denominator = 2 * sum([i**2 for i in range(1, N+1)])
+    delta_feat = numpy.empty_like(feat)
+    padded = numpy.pad(feat, ((N, N), (0, 0)), mode='edge')   # padded version of feat
+    for t in range(NUMFRAMES):
+        delta_feat[t] = numpy.dot(numpy.arange(-N, N+1), padded[t : t+2*N+1]) / denominator   # [t : t+2*N+1] == [(N+t)-N : (N+t)+N+1]
+    return delta_feat
+
+##### modify for test ######
+
+def framesig_without_dither_dc_preemphasize(sig, frame_len, frame_step, wintype='hamming', stride_trick=True):
+    """Frame a signal into overlapping frames.
+
+    :param sig: the audio signal to frame.
+    :param frame_len: length of each frame measured in samples.
+    :param frame_step: number of samples after the start of the previous frame that the next frame should begin.
+    :param winfunc: the analysis window to apply to each frame. By default no window is applied.
+    :param stride_trick: use stride trick to compute the rolling window and window multiplication faster
+    :returns: an array of frames. Size is NUMFRAMES by frame_len.
+    """
+    slen = len(sig)
+    frame_len = int(round_half_up(frame_len))
+    frame_step = int(round_half_up(frame_step))
+    if slen <= frame_len:
+        numframes = 1
+    else:
+        numframes = 1 + (( slen - frame_len) // frame_step)
+
+    # check kaldi/src/feat/feature-window.h
+    padsignal = sig[:(numframes-1)*frame_step+frame_len]
+    
+    if wintype is 'povey':
+        win = numpy.empty(frame_len)
+        for i in range(frame_len):
+            win[i] = (0.5-0.5*numpy.cos(2*numpy.pi/(frame_len-1)*i))**0.85 
+    elif wintype == '':
+        win = numpy.ones(frame_len)
+    elif wintype == 'hann':
+        win = numpy.hanning(frame_len)
+    else: # the hamming window
+        win = numpy.hamming(frame_len)
+        
+    if stride_trick:
+        frames = rolling_window(padsignal, window=frame_len, step=frame_step)
+    else:
+        indices = numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(
+            numpy.arange(0, numframes * frame_step, frame_step), (frame_len, 1)).T
+        indices = numpy.array(indices, dtype=numpy.int32)
+        frames = padsignal[indices]
+        win = numpy.tile(win, (numframes, 1))
+        
+    frames = frames.astype(numpy.float32)
+    raw_frames = frames
+    return frames * win, raw_frames
+
+
+def frames(signal,samplerate=16000,winlen=0.025,winstep=0.01,
+          nfilt=40,nfft=512,lowfreq=0,highfreq=None, wintype='hamming'):
+    frames_with_win, raw_frames = framesig_without_dither_dc_preemphasize(signal, winlen*samplerate, winstep*samplerate, wintype)
+    return frames_with_win, raw_frames
+
+
+def complexspec(frames, NFFT):
+    """Compute the magnitude spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
+
+    :param frames: the array of frames. Each row is a frame.
+    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
+    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the magnitude spectrum of the corresponding frame.
+    """
+    if numpy.shape(frames)[1] > NFFT:
+        logging.warn(
+            'frame length (%d) is greater than FFT size (%d), frame will be truncated. Increase NFFT to avoid.',
+            numpy.shape(frames)[1], NFFT)
+    complex_spec = numpy.fft.rfft(frames, NFFT)
+    return complex_spec
+
+
+def stft_with_window(signal,samplerate=16000,winlen=0.025,winstep=0.01,
+          nfilt=40,nfft=512,lowfreq=0,highfreq=None,dither=1.0,remove_dc_offset=True, preemph=0.97, 
+          wintype='hamming'):
+    frames_with_win, raw_frames = framesig_without_dither_dc_preemphasize(signal, winlen*samplerate, winstep*samplerate, wintype)
+    
+    spec = magspec(frames_with_win, nfft) # nearly the same until this part
+    scomplex = complexspec(frames_with_win, nfft)
+    
+    rspec = magspec(raw_frames, nfft)
+    rcomplex = complexspec(raw_frames, nfft)
+    return spec, scomplex, rspec, rcomplex
+
+
+class TestKaldiFE(unittest.TestCase):
+    def setUp(self):
+        self. this_dir = Path(__file__).parent
+        
+        self.wavpath = str(self.this_dir / 'english.wav')
+        self.winlen=0.025 # ms
+        self.winstep=0.01 # ms
+        self.nfft=512
+        self.lowfreq = 0
+        self.highfreq = None
+        self.wintype='hamm'
+        self.nfilt=40
+        
+        paddle.set_device('cpu')
+        
+        
+    def test_read(self):
+        import scipy.io.wavfile as wav
+        rate, sig = wav.read(self.wavpath)
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        self.assertTrue(np.all(sig == wav))
+        self.assertEqual(rate, sr)
+        
+    def test_frames(self):
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        _, fs = frames(wav, samplerate=sr, 
+                            winlen=self.winlen, winstep=self.winstep, 
+                            nfilt=self.nfilt, nfft=self.nfft, 
+                            lowfreq=self.lowfreq, highfreq=self.highfreq, 
+                            wintype=self.wintype)
+        
+        t_wav = paddle.to_tensor([wav], dtype='float32')
+        t_wavlen = paddle.to_tensor([len(wav)])
+        t_fs, t_nframe = kaldi.frames(t_wav, t_wavlen, sr, self.winlen, self.winstep, clip=False)
+        t_fs = t_fs.astype(fs.dtype)[0]
+        
+        self.assertEqual(t_nframe.item(), fs.shape[0])
+        self.assertTrue(np.allclose(t_fs.numpy(), fs))
+        
+         
+    def test_stft(self):
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        
+        for wintype in ['', 'hamm', 'hann', 'povey']:
+            self.wintype=wintype
+            _, stft_c_win, _, _ = stft_with_window(wav, samplerate=sr, 
+                                winlen=self.winlen, winstep=self.winstep, 
+                                nfilt=self.nfilt, nfft=self.nfft, 
+                                lowfreq=self.lowfreq, highfreq=self.highfreq, 
+                                wintype=self.wintype)
+            
+            t_wav = paddle.to_tensor([wav], dtype='float32')
+            t_wavlen = paddle.to_tensor([len(wav)])
+            
+            stft_class = kaldi.STFT(self.nfft, sr, self.winlen, self.winstep, window_type=self.wintype, dither=0.0, preemph_coeff=0.0, remove_dc_offset=False, clip=False)
+            t_stft, t_nframe = stft_class(t_wav, t_wavlen)
+            t_stft = t_stft.astype(stft_c_win.real.dtype)[0]
+            t_real = t_stft[:, :, 0]
+            t_imag = t_stft[:, :, 1]
+            
+            self.assertEqual(t_nframe.item(), stft_c_win.real.shape[0])
+
+            self.assertLess(np.sum(t_real.numpy()) - np.sum(stft_c_win.real), 1)
+            self.assertTrue(np.allclose(t_real.numpy(), stft_c_win.real, atol=1e-1))
+            
+            self.assertLess(np.sum(t_imag.numpy()) - np.sum(stft_c_win.imag), 1)
+            self.assertTrue(np.allclose(t_imag.numpy(), stft_c_win.imag, atol=1e-1))
+        
+        
+    def test_magspec(self):
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        for wintype in ['', 'hamm', 'hann', 'povey']:
+            self.wintype=wintype
+            stft_win, _, _, _ = stft_with_window(wav, samplerate=sr, 
+                                winlen=self.winlen, winstep=self.winstep, 
+                                nfilt=self.nfilt, nfft=self.nfft, 
+                                lowfreq=self.lowfreq, highfreq=self.highfreq, 
+                                wintype=self.wintype)
+
+            t_wav = paddle.to_tensor([wav], dtype='float32')
+            t_wavlen = paddle.to_tensor([len(wav)])
+            
+            stft_class = kaldi.STFT(self.nfft, sr, self.winlen, self.winstep, window_type=self.wintype, dither=0.0, preemph_coeff=0.0, remove_dc_offset=False, clip=False)
+            t_stft, t_nframe = stft_class(t_wav, t_wavlen)
+            t_stft = t_stft.astype(stft_win.dtype)
+            t_spec = kaldi.magspec(t_stft)[0]
+
+            self.assertEqual(t_nframe.item(), stft_win.shape[0])
+            
+            self.assertLess(np.sum(t_spec.numpy()) - np.sum(stft_win), 1)
+            self.assertTrue(np.allclose(t_spec.numpy(), stft_win, atol=1e-1))
+           
+            
+     def test_magsepc_winprocess(self):
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        fs, _= framesig(wav, self.winlen*sr, self.winstep*sr, 
+                        dither=0.0, preemph=0.97, remove_dc_offset=True, wintype='povey', stride_trick=True)
+        spec = magspec(fs, self.nfft) # nearly the same until this part
+        
+        t_wav = paddle.to_tensor([wav], dtype='float32')
+        t_wavlen = paddle.to_tensor([len(wav)])
+        stft_class = kaldi.STFT(
+            self.nfft, sr, self.winlen, self.winstep,
+            window_type='povey', dither=0.0, preemph_coeff=0.97, remove_dc_offset=True, clip=False)
+        t_stft, t_nframe = stft_class(t_wav, t_wavlen)
+        t_stft = t_stft.astype(spec.dtype)
+        t_spec = kaldi.magspec(t_stft)[0]
+        
+        self.assertEqual(t_nframe.item(), fs.shape[0])
+        
+        self.assertLess(np.sum(t_spec.numpy()) - np.sum(spec), 1)
+        self.assertTrue(np.allclose(t_spec.numpy(), spec, atol=1e-1))
+        
+        
+    def test_powspec(self):
+        sr, wav = kaldi.read(self.wavpath)
+        wav = wav[:, 0]
+        for wintype in ['', 'hamm', 'hann', 'povey']:
+            self.wintype=wintype
+            stft_win, _, _, _ = stft_with_window(wav, samplerate=sr, 
+                                winlen=self.winlen, winstep=self.winstep, 
+                                nfilt=self.nfilt, nfft=self.nfft, 
+                                lowfreq=self.lowfreq, highfreq=self.highfreq, 
+                                wintype=self.wintype)
+            stft_win = np.square(stft_win)
+
+            t_wav = paddle.to_tensor([wav], dtype='float32')
+            t_wavlen = paddle.to_tensor([len(wav)])
+            
+            stft_class = kaldi.STFT(self.nfft, sr, self.winlen, self.winstep, window_type=self.wintype, dither=0.0, preemph_coeff=0.0, remove_dc_offset=False, clip=False)
+            t_stft, t_nframe = stft_class(t_wav, t_wavlen)
+            t_stft = t_stft.astype(stft_win.dtype)
+            t_spec = kaldi.powspec(t_stft)[0]
+
+            self.assertEqual(t_nframe.item(), stft_win.shape[0])
+            
+            self.assertLess(np.sum(t_spec.numpy() - stft_win), 5e4)
+            self.assertTrue(np.allclose(t_spec.numpy(), stft_win, atol=1e2))
+
+
+# from python_speech_features import mfcc
+# from python_speech_features import delta
+# from python_speech_features import logfbank
+# import scipy.io.wavfile as wav
+
+# (rate,sig) = wav.read("english.wav")
+
+# # note that generally nfilt=40 is used for speech recognition
+# fbank_feat = logfbank(sig,nfilt=23,lowfreq=20,dither=0,wintype='povey')
+
+# # the computed fbank coefficents of english.wav with dimension [110,23]
+# # [ 12.2865	12.6906	13.1765	15.714	16.064	15.7553	16.5746	16.9205	16.6472	16.1302	16.4576	16.7326	16.8864	17.7215	18.88	19.1377	19.1495	18.6683	18.3886	20.3506	20.2772	18.8248	18.1899
+# # 11.9198	13.146	14.7215	15.8642	17.4288	16.394	16.8238	16.1095	16.4297	16.6331	16.3163	16.5093	17.4981	18.3429	19.6555	19.6263	19.8435	19.0534	19.001	20.0287	19.7707	19.5852	19.1112
+# # ...
+# # ...
+# # the same with that using kaldi commands: compute-fbank-feats --dither=0.0
+
+
+# mfcc_feat = mfcc(sig,dither=0,useEnergy=True,wintype='povey')
+
+# # the computed mfcc coefficents of english.wav with dimension [110,13]
+# # [ 17.1337	-23.3651	-7.41751	-7.73686	-21.3682	-8.93884	-3.70843	4.68346	-16.0676	12.782	-7.24054	8.25089	10.7292
+# # 17.1692	-23.3028	-5.61872	-4.0075	-23.287	-20.6101	-5.51584	-6.15273	-14.4333	8.13052	-0.0345329	2.06274	-0.564298
+# # ...
+# # ...
+# # the same with that using kaldi commands: compute-mfcc-feats --dither=0.0
+
+
+
+if __name__ == '__main__':
+    unittest.main()
\ No newline at end of file