Matlab谱图函数的手动实现

Question

我正在尝试实现我自己的函数，它提供与 Matlab 频谱图函数相同的结果。到目前为止，我已经完成了这样的功能：

function out = manulaSpectogram(x, win, noverlap, nfft)
x = x(:);
n = length(x);
wlen = length(win);
nUnique = ceil((1+nfft)/2); % number of uniqure points
L = fix((n-noverlap)/(wlen-noverlap)); % number of signal frames
out = zeros(L, nUnique);
index = 1:wlen;
    for i = 0:L-1
        xw = win.*x(index);
        X = fft(xw, nfft);
        out(i+1, :) = X(1:nUnique);
        index = index + (wlen - noverlap);
    end
end

在我的测试中，当参数 nfft 大于或等于 window.

的长度时，它可以完美运行并给出与频谱图函数相同的结果

% first test (nnft = window length):
A = [1,2,3,4,5,6];
window = 6;
overlap = 2;
nfft = 6;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
   9.7300 + 0.0000i  -5.2936 + 0.9205i   0.7279 - 0.3737i  -0.1186 + 0.0000i
s2 =
   9.7300 + 0.0000i  -5.2936 - 0.9205i   0.7279 + 0.3737i  -0.1186 + 0.0000i
   
% second test (nfft > window length):
A = [1,2,3,4,5,6];
window = 3;
overlap = 2;
nfft = 6;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
   2.3200 + 0.0000i   0.9600 + 1.9399i  -1.0400 + 1.5242i  -1.6800 + 0.0000i
   3.4800 + 0.0000i   1.5000 + 2.8752i  -1.5000 + 2.3209i  -2.5200 + 0.0000i
   4.6400 + 0.0000i   2.0400 + 3.8105i  -1.9600 + 3.1177i  -3.3600 + 0.0000i
   5.8000 + 0.0000i   2.5800 + 4.7458i  -2.4200 + 3.9144i  -4.2000 + 0.0000i
   
s2 =
   2.3200 + 0.0000i   0.9600 - 1.9399i  -1.0400 - 1.5242i  -1.6800 + 0.0000i
   3.4800 + 0.0000i   1.5000 - 2.8752i  -1.5000 - 2.3209i  -2.5200 + 0.0000i
   4.6400 + 0.0000i   2.0400 - 3.8105i  -1.9600 - 3.1177i  -3.3600 + 0.0000i
   5.8000 + 0.0000i   2.5800 - 4.7458i  -2.4200 - 3.9144i  -4.2000 + 0.0000i

如果window的长度小于nfft，则结果不同。

% third test (nfft < window length):
A = [1,2,3,4,5,6];
window = 6;
overlap = 2;
nfft = 3;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
   9.7300 + 0.0000i   0.7279 - 0.3737i
 
s2 =
   3.6121 + 0.0000i  -1.6861 + 1.6807i

那么，即使在 nnft 小于 window 长度的情况下，我如何改进我的函数以接收相同的结果？ Matlab的spectogram是如何计算这种情况的？

我正在尝试实现我自己的函数，因为频谱图函数是我需要从 Matlab 到 C# 语言实现的大型算法的一部分，所以我想知道频谱图“黑匣子”的作用..

Answer 1

我注意到当 window 大小大于 nfft 标量数时，必须以某种方式转换数据。最后我找到了一个可能在原始 spectogram Matlab 函数中调用的内部 Matlab 函数。它被命名为 datawrap 并包装输入数据模 nfft.

所以在我的函数中，我必须在调用 fft 之前转换数据段（与 datawrap 函数的处理方式相同）。改进功能：

function out = manulaSpectogram(x, win, noverlap, nfft)
x = x(:);
n = length(x);
wlen = length(win);
nUnique = ceil((1+nfft)/2); % number of uniqure points
L = fix((n-noverlap)/(wlen-noverlap)); % number of signal frames
out = zeros(L, nUnique);
index = 1:wlen;
    for i = 0:L-1
        xw = win.*x(index);
        % added transformation
        if length(xw) > nfft
            xw = sum(buffer(xw, nfft), 2);
        end
        % end of added transformation
        X = fft(xw, nfft);
        out(i+1, :) = X(1:nUnique);
        index = index + (wlen - noverlap);
    end
end

我相信它工作正常，因为它给出了与 Matlab spectogram 函数相同的结果。

Answer 2

使用 window 计算块的末端为零。这需要作为强制性要求，window 和 FFT-Block 的矢量长度相同。 Matlab 允许使用默认参数不相等的值：nsc 不等于 nff（请参阅默认的 Matlab docu 频谱图）。如果 window 和 nff 的块长度不同，则需要一条错误消息。我认为默认参数的 Matlab 频谱图是错误的。与 LabView、Dasylab、Hewlett-Packard 和 http://www.schmid-werren.ch/hanspeter/publications/2012fftnoise.pdf

比较

Matlab谱图函数的手动实现

Manual implementation of Matlab spectogram function

matlab

fft