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  • 本代码是一个 Matlab 函数,它提供给定频谱图 STFT(k, l) 的逆短时傅立叶变换 ... 关于 STFT 分析和 ISTFT 合成例程的开发及其实际实现。 TEM 期刊,ISSN:2217-8309,DOI:10.18421/TEM81-07,卷。 8,第 1 期,第
  • 注意:这个函数现在可以从 IoSR Matlab 工具箱作为 iosr.dsp.stft 和 iosr.dsp.istft 使用。 ------------------------- 计算信号的短时傅立叶变换及其逆变换。 STFT 被归一化,使其满足恒定重叠相加 (COLA) 标准。 ...
  • 三种短时傅里叶变换的逆变换,可以正常使用
  • STFT(短时傅立叶变换),ISTFT(逆-短时傅立叶变换),用于音频,麦克风输入 提供25%,50%的重叠STFTCraft.io。 笔记 git clone --recursive https://github.com/kooBH/STFT.git 要构建测试代码,您需要克隆--...
  • librosa的stft和istft

    2021-07-22 11:06:25
    n_fft = 111 hop_length = 111 win_length = 111 noisy_mag, noisy_phase = librosa.magphase(librosa.stft(noisy, n_fft=n_fft, hop_length=hop_length, win_length=win_length)) enhanced = librosa.istft(noisy_...
    n_fft = 111
    hop_length = 111
    win_length = 111
    noisy_mag, noisy_phase = librosa.magphase(librosa.stft(noisy, n_fft=n_fft, hop_length=hop_length, win_length=win_length))
    enhanced = librosa.istft(noisy_mag * noisy_phase, hop_length=hop_length, win_length=win_length, length=len(noisy))
    
    展开全文
  • ISTFT

    2021-01-02 10:47:52
    <p>It works, but I'...s written in Python (<code>torch.stft</code> is written in C). Just for a future reference/usage. </p><p>该提问来源于开源项目:keunwoochoi/torchaudio-contrib</p></div>
  • C语言版本STFT/ISTFT

    千次阅读 2019-09-29 17:40:15
    改了这个错误后竟然可以跑的通STFT与ISTFT了,不得不说C还是6,同样1024点,C只需3ms,java30ms,这差别真大。 冻死了,空调开得太冷了,我回去穿个衣服,就住附近。   另外有相关问题可以加入QQ群讨论,...

    接上一篇:https://blog.csdn.net/SPESEG/article/details/101672559

    注意:寡人的stft是有前提条件的,并不是完全与librosa.stft一一对应【我的版本参数是固定的,不可变,其他是一样的】,因为我的hop_length是固定为nfft的1/4,而nfft与波形长度完全相同,有人说,你这nfft长度和波形长度一样还有短时谱?SB,你先看看librosa中的定义再BB,别特么啥都不了解就凭主观臆断或者以往认知下结论。

    我先去吃个饭再说。头文件如下:

    float *get_hanning(int n);
    float *np_pad(float *y, int n_fft);
    float **util_frame(float *y2, int n_fft);
    float get_angle(float imag, float real);
    cmplx *rfft(float *rin, int n_fft);
    void reverse(float *x,int n_fft);
    float *irfft(cmplx *mp, int n_fft);
    cmplx **stft(float *y, int n_fft);
    float *win_sums(float *ifft_window, int n_frames, int n_fft, int hop_length);
    float *istft(cmplx **spec, int n_fft);

    昨天写的函数测试结果有问题,我挨个测试下。因为cpp中有了complex类型(应该有),我定义同样的结构体结果告诉我重定义,不同基类型,结果我定义成cmplx,另外我将mag和angle的结构用同样的东西了。两者混用。

    STFT有问题。待我解决。

    python的结果如下:1~16作为输入信号验证

    array([ 0.0000000e+00,  3.1415927e+00, -3.1415927e+00,  5.4828723e-16,
            3.1415927e+00,  1.2280696e-15, -3.1415927e+00,  6.4078058e-16,
            3.1415927e+00], dtype=float32)
    
    array([ 0.        ,  2.5029557 , -1.630843  , -2.200605  ,  3.040559  ,
            1.3331858 , -0.31469315, -1.689683  ,  3.1415927 ], dtype=float32)
    
    array([ 0.       ,  2.7401707, -1.5707964, -1.5707964, -1.5707964,
           -1.5707964, -1.5707964, -1.5707964,  0.       ], dtype=float32)
    
    array([ 0.        ,  2.9132805 , -1.2707483 , -0.16391452,  1.7701185 ,
           -2.435899  , -0.6977143 ,  1.1905247 ,  3.1415927 ], dtype=float32)
    
    array([ 0.       , -3.0581887,  0.4727274, -1.9634954,  1.4135916,
           -1.1780972,  2.2885025, -0.3926991,  3.1415927], dtype=float32)

    下面的C的结果,只有第一行的第三个数相差个符号,这让我懵逼啊。。。。。。。要是这个位置都出现,那就是有问题

    我特么服了,当波形为1~32时,结果仍旧是第一行有问题,不只一个地方。

    array([ 0.0000000e+00, -3.1415927e+00, -3.1415927e+00,  3.3679136e-16,
            3.1415927e+00,  2.9604969e-16, -3.1415927e+00,  6.0319980e-16,
           -3.1415927e+00,  6.3023799e-16,  3.1415927e+00, -3.1086539e-15,
           -3.1415927e+00, -1.2200039e-15,  3.1415927e+00, -2.8588476e-15,
            3.1415927e+00], dtype=float32)

    烦死了,从头开始测试函数。幅度谱都没毛病,就是角度有问题。这个暂时没有发现哪里错误,烦恼。

    后面发现了java在new时可能已经初始化为0了,而C中的malloc是没有初始化的,只是分配了空间。

    所以如果要在堆中开辟空间必须手动初始化为0,所以这是C中普遍存在的问题,先解决这个。改了这个错误后竟然可以跑的通STFT与ISTFT了,不得不说C还是6,同样1024点,C只需3ms,java30ms,这差别真大。

    冻死了,空调开得太冷了,我回去穿个衣服,就住附近。

     

    另外有相关问题可以加入QQ群讨论,不设微信群

    QQ群:868373192 

    语音深度学习群

     

     

    展开全文
  • istft_傅里叶变换_istft_matlab.zip
  • istft_傅里叶变换_istft_matlab_源码.zip
  • ISTFT和STFT是否可逆的问题

    千次阅读 2018-03-22 13:28:56
    ,如果以上的关系不成立,则现在绝大多数的音频增强算法的套路:对幅度谱进行修正,利用带噪信号相位谱进行istft变换获得修正时域语音,会存在一定的风险。下面对这一问题进行讲解。 代码: realData = rand...
    引言:

    前几天听了汪德亮老师的讲座,碰到一个奇怪的问题:在低信噪比、高混响下对原始信号时频幅度谱进行修正后,再进行 istft i s t f t stft s t f t 的转换,此时的时频谱和修正后的原始时频谱不一样,而且 istft i s t f t 后获得的时域信号并没有起到去混响的效果反而是十分奇怪的声音。当时同事们对此现象都感到疑惑。按照我的理解,对于任意的复数域元素 H H ,HCMN, M M 表示数据的帧数,N表示数据的频点数,存在如下的关系: stft(istft(H))=H s t f t ( i s t f t ( H ) ) = H ,如果以上的关系不成立,则现在绝大多数的音频增强算法的套路:对幅度谱进行修正,利用带噪信号相位谱进行istft变换获得修正时域语音,会存在一定的风险。下面对这一问题进行讲解。

    代码:

    realData = rand(257,100);
    %realData = [realData;realData(end-1:-1:2,:)];
    imgData = rand(257,100);
    %imgData = [imgData;-imgData(end-1:-1:2,:)];
    comData = realData + 1i*imgData;
    overLap = 0.5;
    frameSize = 512;
    y = ISTFT(comData, frameSize, overLap);
    [ftbin,Nframe,Nbin,Lspeech,speechFrame] = STFT((y), frameSize, overLap, frameSize);
    error = squeeze(ftbin) - comData ;

    data = ones(10240,1);
    overLap =0.5;
    [ftbin1,Nframe,Nbin,Lspeech,speechFrame]= STFT(data, frameSize, overLap, frameSize);
    y1 = ISTFT(squeeze(ftbin1), frameSize, overLap);
    [ftbin2,Nframe,Nbin,Lspeech,speechFrame]= STFT(y1, frameSize, overLap, frameSize);
    error1 = data - y1;
    error2 = squeeze(ftbin1) - squeeze(ftbin2) ;

    image
    HCMN H ∈ C M N :任意的复数矩阵
    F F :运算符
    H:运算符

    F(H)=G(H)H F ( H ) = G ( H ) − H

    G(H)=STFT(iSTFT(H)) G ( H ) = S T F T ( i S T F T ( H ) )

    按照一般的理解, F(H)=0 F ( H ) = 0 成立,然而根据前文的介绍,该等式并非恒成立。

    直接粘贴论文的定义吧:
    The set of ==consistent spectrograms== can thus be described as the kernel (or null space) of the R-linear operator from
    CMN C M N to itself defined by

    F(H)=G(H)H F ( H ) = G ( H ) − H

    G(H)=STFT(iSTFT(H)) G ( H ) = S T F T ( i S T F T ( H ) )

    Let H(m,n) H ( m , n ) be a set of complex numbers, where m m will correspond to the frame index and n to the frequency band index, and W W and S be analysis and synthesis
    windows verifying the perfect reconstruction conditions for
    a frame shift S S . For the set H to be a consistent STFT spectrogram, it needs to be the STFT S T F T spectrogram of a signal X(t) X ( t ) . But by consistency, this signal can be none other than the result of the inverse STFT of the set H(m,n) H ( m , n ) . A necessary and sufficient condition for H H to be a consistent spectrogram is thus for it to be equal to the STFT of its inverse STFT S T F T . The point here is that, for a given window length N N and a given frame shift, if we denote the inverse STFT by iSTFT i S T F T , the operation iSTFTSTFT i S T F T – S T F T from the space of real signals to itself is the identity, while STFTiSTFT S T F T – i S T F T from CMN C M N to itself is not.

    这个问题对我们的启示是,在进行语音增强后通过得到的频域幅度谱恢复出的时域信号再返回到时谱幅度谱时两者并不相同,前端信号处理在频域完成处理后输出时域信号给识别器时,其提取的MFCC特征可能并不是最优的。对于该问题更严格的推导,可参考论文。

    参考论文:

    1.Explicit consistency constraints for STFT spectrograms and their application to phase reconstruction.
    2.FAST SIGNAL RECONSTRUCTION FROM MAGNITUDE STFT SPECTROGRAM
    BASED ON SPECTROGRAM CONSISTENCY.

    author:longtaochen
    email:1440935236@qq.com

    展开全文
  • 老子今天将FFT改成ifft,说实话我也是一脸懵逼啊,这特么不就差个系数的问题吗?我特么不知道系数啊。 IFFT和FFT设置成一样可以不?我和python对比下就知道了。人生艰难啊。 看了下python版本的fft和ifft,这特么不...

    老子今天将FFT改成ifft,说实话我也是一脸懵逼啊,这特么不就差个系数的问题吗?我特么不知道系数啊。

    IFFT和FFT设置成一样可以不?我和python对比下就知道了。人生艰难啊。
    看了下python版本的fft和ifft,这特么不只是系数的问题吧。如下,

    >>> import numpy as np
    >>> x=np.arange(1,17)
    >>> np.fft.fft(x,16)
    array([136. +0.j        ,  -8.+40.21871594j,  -8.+19.3137085j ,
            -8.+11.9728461j ,  -8. +8.j        ,  -8. +5.3454291j ,
            -8. +3.3137085j ,  -8. +1.59129894j,  -8. +0.j        ,
            -8. -1.59129894j,  -8. -3.3137085j ,  -8. -5.3454291j ,
            -8. -8.j        ,  -8.-11.9728461j ,  -8.-19.3137085j ,
            -8.-40.21871594j])
    >>> np.fft.fft(np.fft.fft(x,16),16)
    array([ 16.+0.j, 256.+0.j, 240.+0.j, 224.+0.j, 208.+0.j, 192.+0.j,
           176.+0.j, 160.+0.j, 144.+0.j, 128.+0.j, 112.+0.j,  96.+0.j,
            80.+0.j,  64.+0.j,  48.+0.j,  32.+0.j])
    >>> np.fft.ifft(np.fft.fft(x,16),16)
    array([ 1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  5.+0.j,  6.+0.j,  7.+0.j,
            8.+0.j,  9.+0.j, 10.+0.j, 11.+0.j, 12.+0.j, 13.+0.j, 14.+0.j,
           15.+0.j, 16.+0.j])

    我看看源码是啥情况。

    #FFT
    def fft(a, n=None, axis=-1, norm=None):
    
        a = asarray(a).astype(complex, copy=False)
        if n is None:
            n = a.shape[axis]
        output = _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftf, _fft_cache)
        if _unitary(norm):
            output *= 1 / sqrt(n)
        return output
    
    #IFFT
    def ifft(a, n=None, axis=-1, norm=None):
       
        # The copy may be required for multithreading.
        a = array(a, copy=True, dtype=complex)
        if n is None:
            n = a.shape[axis]
        unitary = _unitary(norm)
        output = _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftb, _fft_cache)
        return output * (1 / (sqrt(n) if unitary else n))
    

    这特么很明显都是函数里面套函数,但不过都是用的_raw_fft,其他的就是系数问题了。

    不过我突然发现_raw_fft中具体的参数有个差别,fftpack.cfftf和fftpack.cfftb,卧槽。看源码,我估计应该是类似于matlab那种fftshift那种,应该是排列或者说是前后移动的问题。老子综合认为直接移动就好,然后除以个系数nfft结果差不多,虚部可以直接忽略,因为得到的必然应该是实数,而实际上虚部也在1e-14级别,可以忽略,寡人试了16/32/64/128结果都是如此。

    [ 1.-8.88178420e-16j  2.+4.44089210e-16j  3.-4.44089210e-16j
      4.+1.77635684e-15j  5.-8.88178420e-16j  6.+8.88178420e-16j
      7.-8.88178420e-16j  8.+8.88178420e-16j  9.+0.00000000e+00j
     10.-8.88178420e-16j 11.+8.88178420e-16j 12.-1.77635684e-15j
     13.+8.88178420e-16j 14.-4.44089210e-16j 15.+4.44089210e-16j
     16.-4.44089210e-16j 17.+8.88178420e-16j 18.-4.44089210e-16j
     19.+4.44089210e-16j 20.-1.77635684e-15j 21.+8.88178420e-16j
     22.-8.88178420e-16j 23.+8.88178420e-16j 24.-8.88178420e-16j
     25.+0.00000000e+00j 26.+8.88178420e-16j 27.-8.88178420e-16j
     28.+1.77635684e-15j 29.-8.88178420e-16j 30.+4.44089210e-16j
     31.-4.44089210e-16j 32.+4.44089210e-16j]
    
    [ 1.-1.77635684e-15j  2.-8.88178420e-16j  3.-8.88178420e-16j
      4.+0.00000000e+00j  5.-8.88178420e-16j  6.-8.88178420e-16j
      7.+8.88178420e-16j  8.+8.88178420e-16j  9.+1.77635684e-15j
     10.-1.33226763e-15j 11.+2.22044605e-15j 12.-1.77635684e-15j
     13.+8.88178420e-16j 14.-8.88178420e-16j 15.+4.44089210e-16j
     16.+1.33226763e-15j 17.+8.88178420e-16j 18.-1.77635684e-15j
     19.-8.88178420e-16j 20.-1.77635684e-15j 21.+8.88178420e-16j
     22.-8.88178420e-16j 23.-8.88178420e-16j 24.-8.88178420e-16j
     25.-1.77635684e-15j 26.+1.33226763e-15j 27.-4.44089210e-16j
     28.+4.44089210e-15j 29.-8.88178420e-16j 30.+1.77635684e-15j
     31.+1.33226763e-15j 32.-1.33226763e-15j 33.+0.00000000e+00j
     34.+8.88178420e-16j 35.+8.88178420e-16j 36.+3.55271368e-15j
     37.-8.88178420e-16j 38.+8.88178420e-16j 39.-2.66453526e-15j
     40.+8.88178420e-16j 41.-1.77635684e-15j 42.-1.33226763e-15j
     43.+4.44089210e-16j 44.-1.77635684e-15j 45.+8.88178420e-16j
     46.-8.88178420e-16j 47.+4.44089210e-16j 48.-2.22044605e-15j
     49.+8.88178420e-16j 50.+1.77635684e-15j 51.+8.88178420e-16j
     52.-1.77635684e-15j 53.+8.88178420e-16j 54.+8.88178420e-16j
     55.+2.66453526e-15j 56.-8.88178420e-16j 57.+1.77635684e-15j
     58.+1.33226763e-15j 59.-2.22044605e-15j 60.-8.88178420e-16j
     61.-8.88178420e-16j 62.+0.00000000e+00j 63.-2.22044605e-15j
     64.+2.22044605e-15j]
    
    [  1.+0.00000000e+00j   2.+9.32587341e-15j   3.+1.33226763e-15j
       4.-5.32907052e-15j   5.+2.66453526e-15j   6.-6.21724894e-15j
       7.-9.76996262e-15j   8.+8.88178420e-16j   9.+8.88178420e-15j
      10.+7.99360578e-15j  11.-6.21724894e-15j  12.-8.88178420e-15j
      13.+6.21724894e-15j  14.-7.54951657e-15j  15.-3.10862447e-15j
      16.+4.88498131e-15j  17.+8.88178420e-16j  18.+6.66133815e-15j
      19.+4.44089210e-16j  20.+0.00000000e+00j  21.+8.88178420e-16j
      22.-4.44089210e-15j  23.-4.44089210e-15j  24.+2.66453526e-15j
      25.-5.32907052e-15j  26.+2.66453526e-15j  27.+7.99360578e-15j
      28.-8.88178420e-16j  29.+2.66453526e-15j  30.+4.44089210e-16j
      31.+1.33226763e-15j  32.-1.33226763e-15j  33.+0.00000000e+00j
      34.-3.10862447e-15j  35.+1.33226763e-15j  36.+8.88178420e-15j
      37.-8.88178420e-16j  38.+4.44089210e-15j  39.-2.66453526e-15j
      40.+8.88178420e-16j  41.+1.77635684e-15j  42.-4.44089210e-15j
      43.+6.21724894e-15j  44.-8.88178420e-15j  45.+8.88178420e-16j
      46.-4.44089210e-16j  47.+3.99680289e-15j  48.-5.77315973e-15j
      49.+8.88178420e-16j  50.-2.22044605e-15j  51.-6.66133815e-15j
      52.+1.77635684e-15j  53.-2.66453526e-15j  54.+6.21724894e-15j
      55.+1.33226763e-14j  56.-9.76996262e-15j  57.-5.32907052e-15j
      58.-6.21724894e-15j  59.+9.76996262e-15j  60.+2.66453526e-15j
      61.-6.21724894e-15j  62.+7.54951657e-15j  63.-5.77315973e-15j
      64.+4.44089210e-16j  65.-3.55271368e-15j  66.-8.43769499e-15j
      67.-5.77315973e-15j  68.+1.77635684e-15j  69.-4.44089210e-15j
      70.+7.99360578e-15j  71.+1.15463195e-14j  72.+8.88178420e-16j
      73.-5.32907052e-15j  74.-2.66453526e-15j  75.+1.15463195e-14j
      76.+5.32907052e-15j  77.-4.44089210e-15j  78.+6.66133815e-15j
      79.+3.99680289e-15j  80.-2.22044605e-15j  81.+8.88178420e-16j
      82.-1.11022302e-14j  83.+4.44089210e-16j  84.+0.00000000e+00j
      85.+8.88178420e-16j  86.+2.66453526e-15j  87.+2.66453526e-15j
      88.-4.44089210e-15j  89.+1.77635684e-15j  90.-4.44089210e-15j
      91.-6.21724894e-15j  92.+6.21724894e-15j  93.-4.44089210e-15j
      94.+7.54951657e-15j  95.+1.33226763e-15j  96.-1.33226763e-15j
      97.+0.00000000e+00j  98.+3.99680289e-15j  99.+1.33226763e-15j
     100.+1.77635684e-15j 101.-8.88178420e-16j 102.-2.66453526e-15j
     103.-2.66453526e-15j 104.+8.88178420e-16j 105.-5.32907052e-15j
     106.-4.44089210e-15j 107.-7.99360578e-15j 108.+5.32907052e-15j
     109.+8.88178420e-16j 110.-4.44089210e-16j 111.-3.10862447e-15j
     112.+1.33226763e-15j 113.+8.88178420e-16j 114.+4.88498131e-15j
     115.+7.54951657e-15j 116.-8.88178420e-15j 117.+4.44089210e-15j
     118.-7.99360578e-15j 119.-7.99360578e-15j 120.+7.99360578e-15j
     121.+8.88178420e-15j 122.+1.15463195e-14j 123.-1.50990331e-14j
     124.-8.88178420e-16j 125.+4.44089210e-15j 126.-1.37667655e-14j
     127.+1.33226763e-15j 128.+3.99680289e-15j]
    

    当然也要试试随机的数,这些数都是1~nfft的数。对于随机数的结果如下:nfft分别为16/32/64/128/256

    The Error 
     [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j
     0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
    
    The Error 
     [ 0.00000000e+00+0.00000000e+00j  0.00000000e+00+5.55111512e-17j
      0.00000000e+00+0.00000000e+00j  1.66533454e-16+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-3.46944695e-17j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16-5.55111512e-17j
      0.00000000e+00+0.00000000e+00j -5.55111512e-17+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j -3.88578059e-16-1.11022302e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+6.93889390e-18j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-5.55111512e-17j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+3.46944695e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+5.55111512e-17j
      0.00000000e+00+0.00000000e+00j  5.55111512e-17+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+1.11022302e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-6.93889390e-18j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16+0.00000000e+00j]
    
    The Error 
     [ 0.00000000e+00+0.00000000e+00j -5.55111512e-17+0.00000000e+00j
      0.00000000e+00+1.38777878e-16j -2.22044605e-16+2.77555756e-17j
      0.00000000e+00+0.00000000e+00j  4.44089210e-16+5.55111512e-17j
     -2.22044605e-16-8.32667268e-17j -1.11022302e-16+2.08166817e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j
     -4.44089210e-16+1.38777878e-17j  0.00000000e+00-2.22044605e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j
     -2.22044605e-16+0.00000000e+00j  2.77555756e-17+1.24900090e-16j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16-1.38777878e-16j
      2.49800181e-16-8.32667268e-17j  0.00000000e+00+5.55111512e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-5.55111512e-17j
     -4.44089210e-16+1.38777878e-16j  0.00000000e+00-2.08166817e-17j
      0.00000000e+00+0.00000000e+00j  5.55111512e-17+5.55111512e-17j
     -2.22044605e-16+2.08166817e-16j  0.00000000e+00+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+1.11022302e-16j
     -1.11022302e-16-5.55111512e-17j  4.44089210e-16-1.38777878e-17j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16+0.00000000e+00j
     -1.66533454e-16-8.32667268e-17j  0.00000000e+00-2.77555756e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+5.55111512e-17j
      2.22044605e-16-8.32667268e-17j  2.22044605e-16+2.08166817e-17j
      0.00000000e+00+0.00000000e+00j -1.66533454e-16-5.55111512e-17j
      4.44089210e-16+1.38777878e-17j  0.00000000e+00+0.00000000e+00j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+0.00000000e+00j
      3.33066907e-16+0.00000000e+00j  8.32667268e-17-9.71445147e-17j
      0.00000000e+00+0.00000000e+00j  2.77555756e-16+1.38777878e-16j
     -1.66533454e-16+2.77555756e-17j  0.00000000e+00-5.55111512e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-5.55111512e-17j
      4.44089210e-16+2.77555756e-17j  0.00000000e+00-2.08166817e-17j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+0.00000000e+00j
     -1.11022302e-16-2.35922393e-16j  0.00000000e+00+2.22044605e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-1.11022302e-16j
     -2.22044605e-16+5.55111512e-17j -4.44089210e-16-1.38777878e-17j]
    
    The Error 
     [ 0.00000000e+00+0.00000000e+00j -4.16333634e-17-5.55111512e-17j
     -2.22044605e-16-1.66533454e-16j -1.11022302e-16+0.00000000e+00j
      2.22044605e-16-5.55111512e-17j -4.44089210e-16+2.77555756e-17j
      2.22044605e-16+1.11022302e-16j -5.55111512e-17-1.11022302e-16j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16-2.08166817e-17j
      0.00000000e+00-2.30718222e-16j  2.77555756e-16+1.52655666e-16j
     -4.44089210e-16+5.55111512e-17j  1.11022302e-16-4.16333634e-17j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+1.04083409e-17j
      0.00000000e+00+0.00000000e+00j  5.55111512e-17-8.32667268e-17j
     -1.66533454e-16+9.71445147e-17j -1.11022302e-16+1.38777878e-17j
      0.00000000e+00+4.16333634e-17j  1.11022302e-16+5.55111512e-17j
     -4.44089210e-16-2.49800181e-16j -1.11022302e-16+1.38777878e-16j
      0.00000000e+00+0.00000000e+00j -4.44089210e-16+6.93889390e-17j
      0.00000000e+00-2.77555756e-17j  0.00000000e+00-6.93889390e-18j
      2.22044605e-16+0.00000000e+00j  1.66533454e-16+1.11022302e-16j
      2.22044605e-16-1.38777878e-17j  0.00000000e+00+1.73472348e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-4.51028104e-17j
      0.00000000e+00+1.11022302e-16j  2.22044605e-16+0.00000000e+00j
      0.00000000e+00+1.38777878e-17j -1.11022302e-16+1.11022302e-16j
      4.44089210e-16-5.55111512e-17j  0.00000000e+00-1.94289029e-16j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16-1.31838984e-16j
      4.44089210e-16-2.13370988e-16j  1.11022302e-16-1.38777878e-17j
      2.22044605e-16+2.77555756e-17j  0.00000000e+00+5.55111512e-17j
      2.22044605e-16-1.66533454e-16j -1.11022302e-16-1.73472348e-17j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16+2.77555756e-17j
     -1.66533454e-16+1.38777878e-17j  1.11022302e-16+2.77555756e-17j
      1.66533454e-16-2.77555756e-17j  2.22044605e-16-5.55111512e-17j
      0.00000000e+00-8.32667268e-17j  1.11022302e-16-2.22044605e-16j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16-8.32667268e-17j
      2.22044605e-16+1.52655666e-16j -1.11022302e-16+6.24500451e-17j
     -1.11022302e-16+1.11022302e-16j  0.00000000e+00+1.11022302e-16j
      1.11022302e-16+6.93889390e-17j  5.55111512e-17+7.28583860e-17j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16-5.55111512e-17j
      2.22044605e-16+5.55111512e-17j  3.05311332e-16+5.55111512e-17j
      0.00000000e+00+5.55111512e-17j  0.00000000e+00-2.77555756e-17j
      2.22044605e-16-1.11022302e-16j -1.11022302e-16+2.22044605e-16j
      0.00000000e+00+0.00000000e+00j  5.55111512e-17+6.24500451e-17j
      0.00000000e+00+2.13370988e-16j -1.11022302e-16-1.38777878e-17j
      0.00000000e+00-5.55111512e-17j  5.55111512e-17-4.16333634e-17j
      0.00000000e+00-1.11022302e-16j -1.11022302e-16-1.00613962e-16j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16+1.38777878e-16j
      2.77555756e-16-1.38777878e-17j  1.11022302e-16-9.71445147e-17j
      0.00000000e+00-4.16333634e-17j  2.22044605e-16-1.66533454e-16j
      4.44089210e-16+1.94289029e-16j -2.22044605e-16-2.77555756e-17j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16+1.52655666e-16j
     -1.11022302e-16-5.55111512e-17j  0.00000000e+00-6.93889390e-18j
     -2.22044605e-16+0.00000000e+00j  2.77555756e-16+0.00000000e+00j
     -1.66533454e-16-1.38777878e-17j  0.00000000e+00-9.36750677e-17j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+1.56125113e-16j
      0.00000000e+00+0.00000000e+00j -9.71445147e-17+0.00000000e+00j
     -2.22044605e-16-1.38777878e-17j  0.00000000e+00-1.11022302e-16j
     -4.44089210e-16+5.55111512e-17j  2.22044605e-16-2.77555756e-17j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+9.02056208e-17j
      0.00000000e+00+2.30718222e-16j -3.33066907e-16-1.38777878e-17j
      0.00000000e+00-2.77555756e-17j  0.00000000e+00+2.77555756e-17j
     -2.22044605e-16+2.77555756e-16j  2.22044605e-16+3.81639165e-17j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16-8.32667268e-17j
      1.11022302e-16-9.71445147e-17j -1.66533454e-16+0.00000000e+00j
      5.55111512e-17+2.77555756e-17j  3.33066907e-16+1.66533454e-16j
      0.00000000e+00+1.38777878e-16j  1.11022302e-16+2.22044605e-16j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16-1.38777878e-16j
      2.22044605e-16-6.93889390e-17j -1.11022302e-16-1.59594560e-16j
      2.22044605e-16-1.11022302e-16j -2.22044605e-16-2.22044605e-16j
      1.11022302e-16-4.16333634e-17j -5.55111512e-17+7.28583860e-17j]
    
    The Error 
     [ 0.00000000e+00+0.00000000e+00j  1.11022302e-16+4.16333634e-17j
      1.11022302e-16-6.93889390e-18j  5.55111512e-17-5.72458747e-17j
      2.22044605e-16-1.94289029e-16j -3.33066907e-16-1.38777878e-16j
     -4.44089210e-16+1.04083409e-16j  2.22044605e-16-1.35308431e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00-3.29597460e-17j
      4.44089210e-16-1.24900090e-16j -2.22044605e-16+6.93889390e-17j
      0.00000000e+00+1.04083409e-17j  0.00000000e+00+4.44089210e-16j
      4.44089210e-16-1.38777878e-16j -1.66533454e-16-3.33934269e-17j
      0.00000000e+00+0.00000000e+00j -3.33066907e-16-3.46944695e-17j
      0.00000000e+00+1.87350135e-16j  1.11022302e-16+0.00000000e+00j
     -1.11022302e-16+0.00000000e+00j  2.22044605e-16+1.24900090e-16j
     -5.55111512e-17-3.46944695e-17j  2.22044605e-16-2.77555756e-17j
     -3.33066907e-16+4.16333634e-17j -2.22044605e-16-5.55111512e-17j
      1.11022302e-16+1.38777878e-17j  0.00000000e+00-1.87350135e-16j
      0.00000000e+00-6.93889390e-17j  0.00000000e+00-6.93889390e-17j
      5.55111512e-17-6.59194921e-17j -2.22044605e-16+1.70002901e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+6.24500451e-17j
      0.00000000e+00+1.45716772e-16j -3.33066907e-16+2.49800181e-16j
      0.00000000e+00-2.77555756e-17j -1.11022302e-16-5.55111512e-17j
     -2.22044605e-16-3.46944695e-17j  2.22044605e-16+1.73472348e-17j
      0.00000000e+00-4.51028104e-17j -1.11022302e-16-6.24500451e-17j
     -1.11022302e-16+0.00000000e+00j  2.22044605e-16-1.24900090e-16j
      0.00000000e+00+1.73472348e-17j  4.44089210e-16-1.38777878e-16j
     -1.11022302e-16+1.04083409e-16j  5.55111512e-16+1.21430643e-16j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16+2.08166817e-17j
      2.22044605e-16+1.59594560e-16j -2.22044605e-16-2.49800181e-16j
     -2.22044605e-16+1.45716772e-16j  0.00000000e+00+4.16333634e-17j
     -1.11022302e-16-2.08166817e-17j  1.11022302e-16+9.02056208e-17j
      0.00000000e+00-1.38777878e-17j  6.66133815e-16+4.85722573e-17j
      2.22044605e-16+0.00000000e+00j -1.11022302e-16+1.17961196e-16j
      0.00000000e+00-1.38777878e-17j -1.11022302e-16+0.00000000e+00j
      1.11022302e-16+1.66533454e-16j  2.22044605e-16-1.90819582e-16j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16-1.04083409e-16j
      5.55111512e-17-1.04083409e-16j -2.22044605e-16-2.60208521e-17j
      2.22044605e-16+8.32667268e-17j  4.44089210e-16+8.32667268e-17j
     -2.22044605e-16-2.56739074e-16j -2.22044605e-16+3.46944695e-18j
      1.11022302e-16+0.00000000e+00j  0.00000000e+00+1.61329283e-16j
     -2.77555756e-16+1.66533454e-16j  2.22044605e-16+1.38777878e-17j
      0.00000000e+00+4.51028104e-17j -5.55111512e-17-1.24900090e-16j
      0.00000000e+00-1.38777878e-17j -5.55111512e-17+1.09721260e-16j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16+4.85722573e-17j
      2.22044605e-16-1.45716772e-16j -2.22044605e-16-6.93889390e-17j
      6.66133815e-16+1.11022302e-16j -2.22044605e-16+9.71445147e-17j
      2.22044605e-16+2.08166817e-17j  2.22044605e-16+1.94289029e-16j
      4.44089210e-16-6.93889390e-18j  0.00000000e+00+1.04083409e-16j
     -3.88578059e-16-4.16333634e-17j  0.00000000e+00-1.59594560e-16j
      0.00000000e+00+2.77555756e-17j -2.22044605e-16-8.32667268e-17j
     -5.55111512e-17-1.70002901e-16j  0.00000000e+00-9.36750677e-17j
      0.00000000e+00+0.00000000e+00j -1.11022302e-16-1.59594560e-16j
      2.22044605e-16+1.17961196e-16j  0.00000000e+00+0.00000000e+00j
      1.11022302e-16-1.11022302e-16j  2.77555756e-16-2.49800181e-16j
      5.55111512e-17+2.08166817e-17j -2.22044605e-16+7.28583860e-17j
      0.00000000e+00-2.77555756e-17j  1.11022302e-16-9.02056208e-17j
     -2.22044605e-16+1.38777878e-17j  0.00000000e+00-1.24900090e-16j
      1.11022302e-16-4.51028104e-17j  2.77555756e-16+1.94289029e-16j
      0.00000000e+00-3.67761377e-16j -4.44089210e-16-4.51028104e-17j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16+1.17961196e-16j
     -1.11022302e-16+7.63278329e-17j  1.11022302e-16-2.77555756e-17j
      0.00000000e+00-3.46944695e-17j -2.22044605e-16-1.24900090e-16j
     -5.55111512e-17-2.08166817e-17j  0.00000000e+00-2.98372438e-16j
     -5.55111512e-17+4.16333634e-17j  2.22044605e-16+1.31838984e-16j
      2.22044605e-16+8.32667268e-17j  2.22044605e-16-4.85722573e-17j
      0.00000000e+00+2.77555756e-17j  2.22044605e-16-5.55111512e-17j
      1.11022302e-16+1.38777878e-17j -4.44089210e-16+3.46944695e-18j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+8.32667268e-17j
      1.11022302e-16+7.63278329e-17j -3.33066907e-16+1.64798730e-16j
      0.00000000e+00+1.38777878e-16j -5.55111512e-16-1.38777878e-16j
      4.44089210e-16+1.04083409e-16j  4.44089210e-16+3.12250226e-17j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16-1.57859836e-16j
      0.00000000e+00-2.08166817e-16j  0.00000000e+00+6.93889390e-17j
      0.00000000e+00+1.04083409e-17j -2.22044605e-16-3.33066907e-16j
     -2.22044605e-16+3.05311332e-16j  0.00000000e+00-1.44415729e-16j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16-9.02056208e-17j
      0.00000000e+00-3.46944695e-17j  5.55111512e-17+5.55111512e-17j
     -3.33066907e-16-1.11022302e-16j  2.77555756e-16+1.38777878e-17j
      5.55111512e-16+1.59594560e-16j -6.66133815e-16+8.32667268e-17j
     -1.11022302e-16-6.93889390e-17j  1.11022302e-16-1.24900090e-16j
      2.22044605e-16+1.38777878e-17j  0.00000000e+00+2.56739074e-16j
      0.00000000e+00+1.38777878e-17j -2.22044605e-16-6.93889390e-17j
      0.00000000e+00-1.04083409e-17j -2.22044605e-16+5.89805982e-17j
      0.00000000e+00+0.00000000e+00j -5.55111512e-17-4.85722573e-17j
      3.33066907e-16-1.87350135e-16j -2.22044605e-16-8.32667268e-17j
     -3.33066907e-16+2.77555756e-17j -4.44089210e-16+5.55111512e-17j
      4.44089210e-16-1.45716772e-16j  2.22044605e-16-9.36750677e-17j
      0.00000000e+00+4.51028104e-17j  1.11022302e-16+4.85722573e-17j
      1.11022302e-16+5.55111512e-17j  1.11022302e-16+9.71445147e-17j
      4.16333634e-17-3.81639165e-17j -4.44089210e-16+8.32667268e-17j
      2.22044605e-16-6.93889390e-18j  0.00000000e+00+1.21430643e-16j
      0.00000000e+00+0.00000000e+00j -9.71445147e-17+2.08166817e-17j
      2.22044605e-16-6.93889390e-18j  0.00000000e+00+1.94289029e-16j
     -1.11022302e-16-7.63278329e-17j  2.22044605e-16+4.16333634e-17j
      0.00000000e+00-2.08166817e-17j -1.11022302e-16+2.01227923e-16j
      0.00000000e+00-6.93889390e-17j  0.00000000e+00+4.85722573e-17j
     -2.22044605e-16-1.11022302e-16j -4.44089210e-16+6.93889390e-18j
      0.00000000e+00-1.38777878e-17j  0.00000000e+00-2.22044605e-16j
     -1.11022302e-16-5.55111512e-17j  0.00000000e+00+1.42247325e-16j
      0.00000000e+00+0.00000000e+00j  5.55111512e-17+1.17961196e-16j
      1.66533454e-16-1.04083409e-16j  3.33066907e-16-2.60208521e-17j
     -2.22044605e-16-2.77555756e-17j  4.44089210e-16+8.32667268e-17j
      4.44089210e-16+2.42861287e-16j -2.22044605e-16+1.14491749e-16j
      0.00000000e+00+0.00000000e+00j  1.11022302e-16+1.73472348e-18j
     -1.11022302e-16+1.66533454e-16j  1.11022302e-16-9.71445147e-17j
      0.00000000e+00-6.59194921e-17j  1.66533454e-16+2.35922393e-16j
      0.00000000e+00-1.38777878e-17j  2.22044605e-16-1.30104261e-18j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16-1.73472348e-16j
      0.00000000e+00+7.63278329e-17j -5.55111512e-17+1.38777878e-17j
      2.22044605e-16+0.00000000e+00j  0.00000000e+00+1.52655666e-16j
      2.22044605e-16-6.93889390e-18j  2.22044605e-16-2.49800181e-16j
      0.00000000e+00+3.46944695e-17j  0.00000000e+00-6.24500451e-17j
      4.44089210e-16-4.16333634e-17j  0.00000000e+00+6.24500451e-17j
      0.00000000e+00+2.77555756e-17j  1.11022302e-16+2.22044605e-16j
      0.00000000e+00+5.20417043e-17j  5.55111512e-17+1.00613962e-16j
      0.00000000e+00+0.00000000e+00j  0.00000000e+00+6.24500451e-17j
      0.00000000e+00-1.04083409e-16j  2.22044605e-16+0.00000000e+00j
      0.00000000e+00+1.11022302e-16j  2.22044605e-16+2.77555756e-17j
      2.77555756e-16-9.02056208e-17j  3.88578059e-16+7.28583860e-17j
      0.00000000e+00+2.77555756e-17j -1.11022302e-16-3.46944695e-17j
      2.22044605e-16-6.93889390e-17j  2.22044605e-16+9.71445147e-17j
     -1.11022302e-16+6.59194921e-17j -2.22044605e-16-2.49800181e-16j
      0.00000000e+00+1.87350135e-16j -4.44089210e-16-1.56125113e-16j
      0.00000000e+00+0.00000000e+00j  2.22044605e-16+3.46944695e-17j
     -4.44089210e-16-1.45716772e-16j  0.00000000e+00-1.38777878e-16j
      1.66533454e-16-3.46944695e-17j  0.00000000e+00-1.38777878e-17j
     -1.66533454e-16-2.08166817e-17j  0.00000000e+00-7.63278329e-17j
      5.55111512e-17+4.16333634e-17j -2.22044605e-16+7.63278329e-17j
     -4.44089210e-16+8.32667268e-17j  2.22044605e-16-4.85722573e-17j
      0.00000000e+00+0.00000000e+00j -2.22044605e-16+1.66533454e-16j
     -4.44089210e-16+1.38777878e-17j  0.00000000e+00-1.63064007e-16j]
    

    不管是实部还是虚部,误差都比较小,可以忽略,即使是16bit的音频,3万多,误差也在10亿分之一级别,可以忽略。

    确定了方案,我试试java版本的如何。等会哈

    寡人解决了ifft问题,将fft中的参数修改即可得到,另外由半个谱恢复整个谱,参数mag和phase要用到欧拉公式。

    注意:另一半虚部是反相的。

    测试结果误差在10万分之一级别,别问我为啥这么大,因为我用的float,不是double。这个误差就是float的误差。

    将ifft整合到istft中,得到结果,测试结果如下:

    1024点求STFT及ISTFT一共用时44ms,一般般吧,先不考虑时间问题了。下一步实现C版本的。

    从1~1024【波形数据1~1024】的STFT及ISTFT得到的波形误差大于0.01的个数为12个,基本上可以忽略,完全能用。

     

    另外有相关问题可以加入QQ群讨论,不设微信群

    QQ群:868373192 

    语音深度学习群

     

     

    展开全文
  • istft.rar的程序

    2019-05-28 11:17:43
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  • matlab时频分析之短时傅里叶变换 spectrogram

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  • STFT使用overlap-add重建信号

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  • Librosa音频处理(三)

    千次阅读 2019-05-18 13:43:17
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  • 语音合成概述

    千次阅读 2020-01-12 14:16:15
    在Tacotron中,作者使用Griffin-Lim算法,从Linear-Spectrum中恢复相位,再通过短时傅里叶变换ISTFT还原出波形。Griffin-Lim算法简单, 但是速度慢, 很难做到实时。而且通过Griffin-Lim生成波形过于平滑,空洞较多...
  • matlab tftstft和tftistft的使用

    千次阅读 2018-12-28 22:48:00
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  • 时频分析学习

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  • pytorch求STFT

    2020-10-19 10:23:11
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