Tessy频率 tetra频谱图

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mob6454cc67e023 2024-04-14 16:20:44

文章标签 Tessy频率四舍五入傅里叶变换采样率 文章分类 架构后端开发

spectrogram-翻译为频谱图
matlab原文档中的介绍如下：
该频谱图用于短时傅里叶画频谱图。
[S,F,T,P]=spectrogram(x,window,noverlap,nfft,fs)
[S,F,T,P]=spectrogram(x,window,noverlap,F,fs)

spectrogram(x)
s = spectrogram(x)
s = spectrogram(x, window)
s = spectrogram(x, window, noverlap)
s = spectrogram(x, window, noverlap, nfft)
s = spectrogram(x, window, noverlap, nfft, fs)
[S,F,T,P] = spectrogram(x, window, noverlap, nfft, fs)
[S,F,T,P] = spectrogram(x, window, noverlap, f, fs)
[S,F,T,P] = spectrogram(x, window, noverlap, f, fs)

参数：

x表示输入信号；
window表示窗函数，如果window的值是一个整数，那么被分段的x的每一段的长度都等于window，并采用默认的Hamming窗；如果window是一个向量，那么被分段后每一段的长度都等于length(window)，且输入的向量即为所要加的窗函数；
noverlap表示两段之间的重合点数，window-overlap=步长。overlap的值必须要小于窗长，如果没有指定overlap，默认是窗长的一半，即50%的overlap；
nfft表示fft的点数，fft的点数跟窗长可以是不同的，当没有指定该参数时，Matlab会取max(256,2^(ceil(log2(length(window)))))，即当窗长小于256时，fft的点数是256；当窗长大于256时，fft的点数取大于窗长的最小的2的整数次幂；这个数值应该是double或者single，不是向量。区分函数中nfft（离散点大小）和f（频率区间）的使用不同
f 表示显示的频谱范围，f是一个向量 (eg:f=1:30;%1-30hz的stft)，长度跟s的行数相同；

当x是实信号且nfft为偶数时，s的行数为(nfft/2+1)
当x是实信号且nfft为奇数时，s的行数为(nfft+1)/2
当x是复信号时，s的行数为nfft
当在输入的参数列表中指定f后，函数会在f指定的频率处计算频谱图，返回的f跟输入的f是相同的；

fs表示采样率，用来归一化显示使用；

%输出变量

S—输入信号x的短时傅里叶变换。它的每一列包含一个短期局部时间的频率成分估计，时间沿列增加，频率沿行增加。如果x是长度为Nx的复信号，则S为nfft行k列的复矩阵，其中k取决于window，如果window为一个标量，则k = fix((Nx-noverlap)/(window-noverlap)).如果window为向量，则k = fix((Nx-noverlap)/(length(window)-noverlap))
F—在输入变量中使用F频率向量，函数会使用Goertzel方法计算在F指定的频率处计算频谱图。
对于实信号x，如果nfft为偶数，则S的行数为(nfft/2+1)，如果nfft为奇数，则行数为(nfft+1)/2，列数同上。
指定的频率被四舍五入到与信号分辨率相关的最近的DFT容器(bin)中。而在其他的使用nfft语法中，短时傅里叶变换方法将被使用。对于返回值中的F向量，为四舍五入的频率，其长度等于S的行数。
T—频谱图计算的时刻点，其长度等于上面定义的k，值为所分各段的中点。
P—能量谱密度PSD(Power Spectral
Density)，对于实信号，P是各段PSD的单边周期估计；对于复信号，当指定F频率向量时，P为双边PSD。

matlab例子：

x=[7.40000000000000e-05;6.50000000000000e-05;8.20000000000000e-05;0.000104000000000000;9.00000000000000e-05;8.70000000000000e-05;6.30000000000000e-05;4.80000000000000e-05;4.70000000000000e-05;2.60000000000000e-05;1.40000000000000e-05;2.20000000000000e-05;4.30000000000000e-05;2.00000000000000e-05;2.60000000000000e-05;2.40000000000000e-05;8.00000000000000e-06;4.00000000000000e-06;1.40000000000000e-05;1.70000000000000e-05;1.60000000000000e-05;2.30000000000000e-05;3.90000000000000e-05;4.10000000000000e-05;2.90000000000000e-05;2.10000000000000e-05;1.70000000000000e-05;1.20000000000000e-05;9.00000000000000e-06;1.80000000000000e-05;2.10000000000000e-05;2.10000000000000e-05;2.40000000000000e-05;1.40000000000000e-05;3.00000000000000e-05;5.30000000000000e-05;7.00000000000000e-05;4.40000000000000e-05;5.40000000000000e-05;9.10000000000000e-05;3.00000000000000e-06;-1.50000000000000e-05;-7.00000000000000e-06;-4.00000000000000e-05;-6.10000000000000e-05;-5.90000000000000e-05;-8.60000000000000e-05;-0.000108000000000000;-0.000102000000000000;-9.10000000000000e-05;-9.10000000000000e-05;-8.20000000000000e-05;-6.40000000000000e-05;-5.90000000000000e-05;-5.40000000000000e-05;-6.10000000000000e-05;-5.50000000000000e-05;-5.80000000000000e-05;-6.20000000000000e-05;-6.40000000000000e-05;-5.60000000000000e-05;-6.00000000000000e-05;-6.00000000000000e-05;-6.50000000000000e-05;-7.10000000000000e-05;-7.30000000000000e-05;-7.10000000000000e-05;-6.30000000000000e-05;-5.20000000000000e-05;-5.80000000000000e-05;-5.10000000000000e-05;-4.80000000000000e-05;-4.30000000000000e-05;-6.40000000000000e-05;-9.20000000000000e-05;-0.000106000000000000;-9.90000000000000e-05;-0.000112000000000000;-0.000117000000000000;-0.000112000000000000;-0.000106000000000000;-8.10000000000000e-05;-8.30000000000000e-05;-9.40000000000000e-05;-0.000101000000000000;-9.30000000000000e-05;-9.20000000000000e-05;-8.70000000000000e-05;-0.000114000000000000;-0.000117000000000000;-7.10000000000000e-05;-3.50000000000000e-05;-1.10000000000000e-05;1.10000000000000e-05;2.40000000000000e-05;1.50000000000000e-05;-2.60000000000000e-05;-0.000103000000000000;-0.000152000000000000;-7.60000000000000e-05;-4.90000000000000e-05;-8.10000000000000e-05;-4.70000000000000e-05;-1.10000000000000e-05;-7.00000000000000e-06;-1.20000000000000e-05;-1.00000000000000e-05;-2.30000000000000e-05;-3.90000000000000e-05;-2.60000000000000e-05;-1.20000000000000e-05;-2.50000000000000e-05;-3.00000000000000e-05;-1.10000000000000e-05;-3.00000000000000e-06;-2.00000000000000e-06;-8.00000000000000e-06;-3.50000000000000e-05;-3.70000000000000e-05;-2.50000000000000e-05;-2.00000000000000e-06;-1.10000000000000e-05;-1.40000000000000e-05;-2.70000000000000e-05;-3.10000000000000e-05;-1.10000000000000e-05;2.00000000000000e-06;1.00000000000000e-05;2.10000000000000e-05;4.20000000000000e-05;3.10000000000000e-05;3.10000000000000e-05;4.40000000000000e-05;3.10000000000000e-05;2.90000000000000e-05;3.20000000000000e-05;3.20000000000000e-05;4.50000000000000e-05;4.00000000000000e-05;4.40000000000000e-05;5.30000000000000e-05;3.60000000000000e-05;4.00000000000000e-05;4.20000000000000e-05;4.30000000000000e-05;4.10000000000000e-05;5.40000000000000e-05;9.70000000000000e-05;8.10000000000000e-05;6.10000000000000e-05;5.60000000000000e-05;7.00000000000000e-05;7.40000000000000e-05;6.10000000000000e-05;7.80000000000000e-05;9.10000000000000e-05;7.30000000000000e-05;6.20000000000000e-05;4.80000000000000e-05;4.50000000000000e-05;5.30000000000000e-05;5.20000000000000e-05;2.50000000000000e-05;1.90000000000000e-05;1.10000000000000e-05;2.00000000000000e-05;4.40000000000000e-05;3.00000000000000e-05;1.70000000000000e-05;1.80000000000000e-05;3.00000000000000e-05;3.00000000000000e-05;3.30000000000000e-05;4.50000000000000e-05;1.80000000000000e-05;8.00000000000000e-06;2.30000000000000e-05;3.00000000000000e-05;1.50000000000000e-05;2.80000000000000e-05;2.10000000000000e-05;4.10000000000000e-05;4.30000000000000e-05;4.60000000000000e-05;5.90000000000000e-05;3.70000000000000e-05;2.60000000000000e-05;2.60000000000000e-05;9.00000000000000e-06;1.30000000000000e-05;2.10000000000000e-05;2.90000000000000e-05;3.70000000000000e-05;5.30000000000000e-05;5.00000000000000e-05;3.90000000000000e-05;2.50000000000000e-05;2.60000000000000e-05;3.00000000000000e-05;4.40000000000000e-05;5.80000000000000e-05;5.20000000000000e-05;5.40000000000000e-05;8.00000000000000e-05;9.20000000000000e-05;9.20000000000000e-05;7.50000000000000e-05;4.20000000000000e-05;3.20000000000000e-05;3.60000000000000e-05;3.20000000000000e-05;4.20000000000000e-05;3.30000000000000e-05;3.90000000000000e-05;6.10000000000000e-05;7.30000000000000e-05;7.70000000000000e-05;5.60000000000000e-05;7.30000000000000e-05;6.40000000000000e-05;4.50000000000000e-05;5.30000000000000e-05;4.10000000000000e-05;5.30000000000000e-05;4.20000000000000e-05;1.00000000000000e-05;2.20000000000000e-05;2.70000000000000e-05;3.10000000000000e-05;4.50000000000000e-05;5.50000000000000e-05;6.10000000000000e-05;6.20000000000000e-05;4.70000000000000e-05;4.80000000000000e-05;4.80000000000000e-05;3.50000000000000e-05;2.90000000000000e-05;3.70000000000000e-05;3.90000000000000e-05;2.00000000000000e-05;-2.20000000000000e-05;-4.20000000000000e-05;-3.70000000000000e-05;5.00000000000000e-06;1.50000000000000e-05;1.90000000000000e-05;3.50000000000000e-05;4.60000000000000e-05;1.20000000000000e-05;-3.60000000000000e-05;-3.90000000000000e-05;-4.80000000000000e-05;-5.00000000000000e-05;-4.50000000000000e-05;-4.80000000000000e-05;-3.30000000000000e-05;-3.00000000000000e-05;-4.40000000000000e-05;-2.70000000000000e-05;-2.50000000000000e-05;-1.00000000000000e-05;-1.20000000000000e-05;-1.80000000000000e-05;-3.10000000000000e-05;-1.70000000000000e-05;3.70000000000000e-05;2.40000000000000e-05;0;7.00000000000000e-06;3.40000000000000e-05;1.10000000000000e-05;-7.00000000000000e-06;-1.40000000000000e-05;-2.30000000000000e-05;-7.00000000000000e-06;1.70000000000000e-05;3.40000000000000e-05;3.50000000000000e-05;1.80000000000000e-05;1.80000000000000e-05;4.10000000000000e-05;4.00000000000000e-05;4.60000000000000e-05;4.40000000000000e-05;4.60000000000000e-05;3.50000000000000e-05;2.60000000000000e-05;2.20000000000000e-05;2.40000000000000e-05;9.00000000000000e-06;-3.00000000000000e-06;-4.00000000000000e-06;7.00000000000000e-06;-1.30000000000000e-05;-3.50000000000000e-05;-3.20000000000000e-05;-3.40000000000000e-05;-4.00000000000000e-06;-1.40000000000000e-05;-3.90000000000000e-05;-9.00000000000000e-06;2.00000000000000e-06;-1.00000000000000e-05;1.80000000000000e-05;2.10000000000000e-05;2.00000000000000e-06;2.20000000000000e-05;3.30000000000000e-05;4.10000000000000e-05;3.90000000000000e-05;2.90000000000000e-05;1.70000000000000e-05;2.10000000000000e-05;2.20000000000000e-05;2.30000000000000e-05;2.10000000000000e-05;2.20000000000000e-05;1.50000000000000e-05;1.40000000000000e-05;3.80000000000000e-05;2.80000000000000e-05;4.10000000000000e-05;4.10000000000000e-05;4.30000000000000e-05;4.20000000000000e-05;3.90000000000000e-05;3.00000000000000e-05;3.40000000000000e-05;3.40000000000000e-05;5.70000000000000e-05;4.10000000000000e-05;2.10000000000000e-05;3.00000000000000e-05;2.10000000000000e-05;5.00000000000000e-05;4.80000000000000e-05;4.50000000000000e-05;7.00000000000000e-05;3.50000000000000e-05;2.70000000000000e-05;4.20000000000000e-05;5.00000000000000e-05;2.40000000000000e-05;1.80000000000000e-05;7.00000000000000e-06;2.00000000000000e-05;3.20000000000000e-05;2.40000000000000e-05;3.30000000000000e-05;1.00000000000000e-05;7.00000000000000e-06;1.90000000000000e-05;1.70000000000000e-05;6.00000000000000e-06;-5.00000000000000e-06;1.00000000000000e-05;2.00000000000000e-05;3.10000000000000e-05;2.00000000000000e-05;2.10000000000000e-05;-1.00000000000000e-06;-1.80000000000000e-05;-2.20000000000000e-05;-4.00000000000000e-06;9.00000000000000e-06;3.00000000000000e-06;-1.00000000000000e-06;-1.60000000000000e-05;-2.60000000000000e-05;-2.10000000000000e-05;1.00000000000000e-06;1.20000000000000e-05;2.00000000000000e-05;2.00000000000000e-06;2.00000000000000e-06;2.50000000000000e-05;5.00000000000000e-06;4.00000000000000e-06;3.00000000000000e-06;1.20000000000000e-05;-2.00000000000000e-06;7.00000000000000e-06;1.60000000000000e-05;1.00000000000000e-05;-5.00000000000000e-06;-1.90000000000000e-05;-3.50000000000000e-05;-3.70000000000000e-05;-2.30000000000000e-05;-3.30000000000000e-05;-4.20000000000000e-05;-4.50000000000000e-05;-3.50000000000000e-05;-2.90000000000000e-05;-5.00000000000000e-06;1.00000000000000e-05;2.70000000000000e-05;4.70000000000000e-05;7.40000000000000e-05;6.70000000000000e-05;2.00000000000000e-05;-1.10000000000000e-05;-1.60000000000000e-05;-2.00000000000000e-05;-2.60000000000000e-05;-2.70000000000000e-05;-3.70000000000000e-05;-3.90000000000000e-05;-5.30000000000000e-05;-7.70000000000000e-05;-4.40000000000000e-05;-3.40000000000000e-05;-4.30000000000000e-05;-5.70000000000000e-05;-5.50000000000000e-05;-5.90000000000000e-05;-6.90000000000000e-05;-5.30000000000000e-05;-4.30000000000000e-05;-5.30000000000000e-05;-4.50000000000000e-05;-4.20000000000000e-05;-3.30000000000000e-05;-4.30000000000000e-05;-6.90000000000000e-05;-6.90000000000000e-05;-5.20000000000000e-05;-5.20000000000000e-05;-7.90000000000000e-05;-8.80000000000000e-05;-5.40000000000000e-05;-4.20000000000000e-05;-1.70000000000000e-05;-1.20000000000000e-05;-2.00000000000000e-05;-1.90000000000000e-05;-2.00000000000000e-06;3.00000000000000e-06;-5.00000000000000e-06;-1.60000000000000e-05;-3.00000000000000e-05;-2.00000000000000e-05;-8.00000000000000e-06;-2.30000000000000e-05;-2.10000000000000e-05;-2.60000000000000e-05;-1.80000000000000e-05;8.00000000000000e-06;2.30000000000000e-05;3.50000000000000e-05;2.50000000000000e-05;-2.30000000000000e-05;-9.00000000000000e-06;-5.00000000000000e-06;-1.00000000000000e-05;-4.50000000000000e-05;-6.80000000000000e-05;-7.30000000000000e-05;-6.70000000000000e-05;-5.00000000000000e-05;-3.70000000000000e-05;-5.10000000000000e-05;-5.60000000000000e-05;-7.70000000000000e-05;-9.30000000000000e-05;-9.30000000000000e-05;-0.000106000000000000;-0.000118000000000000;-0.000130000000000000;-9.10000000000000e-05;-8.40000000000000e-05;-0.000107000000000000;-9.10000000000000e-05;-9.00000000000000e-05;-0.000113000000000000;-0.000124000000000000;-0.000147000000000000;-0.000139000000000000;-0.000142000000000000;-0.000137000000000000;-0.000152000000000000;-0.000148000000000000;-0.000143000000000000;-0.000152000000000000;-0.000139000000000000;-0.000133000000000000;-0.000152000000000000;-0.000159000000000000;-0.000145000000000000;-0.000144000000000000;-0.000145000000000000;-0.000101000000000000;-0.000130000000000000;-0.000153000000000000;-0.000146000000000000;-0.000177000000000000;-0.000218000000000000;-0.000223000000000000;-0.000223000000000000];%x是一个500*1的输入向量
    ;
    %x是一个500*1的输入向量
    %%%
    window=100;%滑动窗大小
    noverlap=99;%重叠样本数为100重叠99平移样本,每隔1个单位画一个框计算
    %%%
    f=1:30;%1-30hz变换
    Fs=250;%采样频率
	[B,F, T, P] = spectrogram(x',window,noverlap,f,Fs);  
    % B是F大小行T大小列的频率峰值，P是对应的能量谱密度
	figure
	imagesc(T,F,P);
	set(gca,'YDir','normal')
	colorbar;
	xlabel('时间 t/s');
	ylabel('频率 f/Hz');
	title('短时傅里叶时频图');

结果：

Tessy频率 tetra频谱图_采样率

那么有人要问了。为什么我选取信号时间长度和频谱图中时间长度不同。

原因是短时傅里叶变化选取的框的大小会把时间点长度给覆盖，不满足框大小的时间段。

所以上面的程序中。

原始为500个采样点（250hz，2秒），matlab使用了间隔为1个步长的100大小的框。那么（500-100）/1=400计算区间。转换到时间就是400/250hz=1.6秒，

matlab原始时间是0-2s，现在成了0.2-1.8s。实际上就是1.6s，matlab将时间中点作为舍取中心。于是左右就合并了50个采样点也就是说50/250=0.2s的单位。

如果希望解决这个问题，那么避免时间框选择太大，（选择小框缺点是计算损失一些低频信息，如1hz的信号分辨精度下降）

我修改窗函数大小的结果，

window=60；

noverlap=59;%滑动间隔依旧保持1个步长

x=[7.40000000000000e-05;6.50000000000000e-05;8.20000000000000e-05;0.000104000000000000;9.00000000000000e-05;8.70000000000000e-05;6.30000000000000e-05;4.80000000000000e-05;4.70000000000000e-05;2.60000000000000e-05;1.40000000000000e-05;2.20000000000000e-05;4.30000000000000e-05;2.00000000000000e-05;2.60000000000000e-05;2.40000000000000e-05;8.00000000000000e-06;4.00000000000000e-06;1.40000000000000e-05;1.70000000000000e-05;1.60000000000000e-05;2.30000000000000e-05;3.90000000000000e-05;4.10000000000000e-05;2.90000000000000e-05;2.10000000000000e-05;1.70000000000000e-05;1.20000000000000e-05;9.00000000000000e-06;1.80000000000000e-05;2.10000000000000e-05;2.10000000000000e-05;2.40000000000000e-05;1.40000000000000e-05;3.00000000000000e-05;5.30000000000000e-05;7.00000000000000e-05;4.40000000000000e-05;5.40000000000000e-05;9.10000000000000e-05;3.00000000000000e-06;-1.50000000000000e-05;-7.00000000000000e-06;-4.00000000000000e-05;-6.10000000000000e-05;-5.90000000000000e-05;-8.60000000000000e-05;-0.000108000000000000;-0.000102000000000000;-9.10000000000000e-05;-9.10000000000000e-05;-8.20000000000000e-05;-6.40000000000000e-05;-5.90000000000000e-05;-5.40000000000000e-05;-6.10000000000000e-05;-5.50000000000000e-05;-5.80000000000000e-05;-6.20000000000000e-05;-6.40000000000000e-05;-5.60000000000000e-05;-6.00000000000000e-05;-6.00000000000000e-05;-6.50000000000000e-05;-7.10000000000000e-05;-7.30000000000000e-05;-7.10000000000000e-05;-6.30000000000000e-05;-5.20000000000000e-05;-5.80000000000000e-05;-5.10000000000000e-05;-4.80000000000000e-05;-4.30000000000000e-05;-6.40000000000000e-05;-9.20000000000000e-05;-0.000106000000000000;-9.90000000000000e-05;-0.000112000000000000;-0.000117000000000000;-0.000112000000000000;-0.000106000000000000;-8.10000000000000e-05;-8.30000000000000e-05;-9.40000000000000e-05;-0.000101000000000000;-9.30000000000000e-05;-9.20000000000000e-05;-8.70000000000000e-05;-0.000114000000000000;-0.000117000000000000;-7.10000000000000e-05;-3.50000000000000e-05;-1.10000000000000e-05;1.10000000000000e-05;2.40000000000000e-05;1.50000000000000e-05;-2.60000000000000e-05;-0.000103000000000000;-0.000152000000000000;-7.60000000000000e-05;-4.90000000000000e-05;-8.10000000000000e-05;-4.70000000000000e-05;-1.10000000000000e-05;-7.00000000000000e-06;-1.20000000000000e-05;-1.00000000000000e-05;-2.30000000000000e-05;-3.90000000000000e-05;-2.60000000000000e-05;-1.20000000000000e-05;-2.50000000000000e-05;-3.00000000000000e-05;-1.10000000000000e-05;-3.00000000000000e-06;-2.00000000000000e-06;-8.00000000000000e-06;-3.50000000000000e-05;-3.70000000000000e-05;-2.50000000000000e-05;-2.00000000000000e-06;-1.10000000000000e-05;-1.40000000000000e-05;-2.70000000000000e-05;-3.10000000000000e-05;-1.10000000000000e-05;2.00000000000000e-06;1.00000000000000e-05;2.10000000000000e-05;4.20000000000000e-05;3.10000000000000e-05;3.10000000000000e-05;4.40000000000000e-05;3.10000000000000e-05;2.90000000000000e-05;3.20000000000000e-05;3.20000000000000e-05;4.50000000000000e-05;4.00000000000000e-05;4.40000000000000e-05;5.30000000000000e-05;3.60000000000000e-05;4.00000000000000e-05;4.20000000000000e-05;4.30000000000000e-05;4.10000000000000e-05;5.40000000000000e-05;9.70000000000000e-05;8.10000000000000e-05;6.10000000000000e-05;5.60000000000000e-05;7.00000000000000e-05;7.40000000000000e-05;6.10000000000000e-05;7.80000000000000e-05;9.10000000000000e-05;7.30000000000000e-05;6.20000000000000e-05;4.80000000000000e-05;4.50000000000000e-05;5.30000000000000e-05;5.20000000000000e-05;2.50000000000000e-05;1.90000000000000e-05;1.10000000000000e-05;2.00000000000000e-05;4.40000000000000e-05;3.00000000000000e-05;1.70000000000000e-05;1.80000000000000e-05;3.00000000000000e-05;3.00000000000000e-05;3.30000000000000e-05;4.50000000000000e-05;1.80000000000000e-05;8.00000000000000e-06;2.30000000000000e-05;3.00000000000000e-05;1.50000000000000e-05;2.80000000000000e-05;2.10000000000000e-05;4.10000000000000e-05;4.30000000000000e-05;4.60000000000000e-05;5.90000000000000e-05;3.70000000000000e-05;2.60000000000000e-05;2.60000000000000e-05;9.00000000000000e-06;1.30000000000000e-05;2.10000000000000e-05;2.90000000000000e-05;3.70000000000000e-05;5.30000000000000e-05;5.00000000000000e-05;3.90000000000000e-05;2.50000000000000e-05;2.60000000000000e-05;3.00000000000000e-05;4.40000000000000e-05;5.80000000000000e-05;5.20000000000000e-05;5.40000000000000e-05;8.00000000000000e-05;9.20000000000000e-05;9.20000000000000e-05;7.50000000000000e-05;4.20000000000000e-05;3.20000000000000e-05;3.60000000000000e-05;3.20000000000000e-05;4.20000000000000e-05;3.30000000000000e-05;3.90000000000000e-05;6.10000000000000e-05;7.30000000000000e-05;7.70000000000000e-05;5.60000000000000e-05;7.30000000000000e-05;6.40000000000000e-05;4.50000000000000e-05;5.30000000000000e-05;4.10000000000000e-05;5.30000000000000e-05;4.20000000000000e-05;1.00000000000000e-05;2.20000000000000e-05;2.70000000000000e-05;3.10000000000000e-05;4.50000000000000e-05;5.50000000000000e-05;6.10000000000000e-05;6.20000000000000e-05;4.70000000000000e-05;4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000000000;-0.000118000000000000;-0.000130000000000000;-9.10000000000000e-05;-8.40000000000000e-05;-0.000107000000000000;-9.10000000000000e-05;-9.00000000000000e-05;-0.000113000000000000;-0.000124000000000000;-0.000147000000000000;-0.000139000000000000;-0.000142000000000000;-0.000137000000000000;-0.000152000000000000;-0.000148000000000000;-0.000143000000000000;-0.000152000000000000;-0.000139000000000000;-0.000133000000000000;-0.000152000000000000;-0.000159000000000000;-0.000145000000000000;-0.000144000000000000;-0.000145000000000000;-0.000101000000000000;-0.000130000000000000;-0.000153000000000000;-0.000146000000000000;-0.000177000000000000;-0.000218000000000000;-0.000223000000000000;-0.000223000000000000];%x是一个500*1的输入向量
    ;%x是一个500*1的输入向量
    %%%
    window=60;%滑动窗大小
    noverlap=59;%重叠样本数为250重叠249平移样本,每隔1个单位画一个框计算
    %%%
    f=1:30;%1-30hz变换
    Fs=250;%采样频率
	[B,F, T, P] = spectrogram(x',window,noverlap,f,Fs);  
    % B是F大小行T大小列的频率峰值，P是对应的能量谱密度
	figure
	imagesc(T,F,P);
	set(gca,'YDir','normal')
	colorbar;
	xlabel('时间 t/s');
	ylabel('频率 f/Hz');
	title('短时傅里叶时频图');

采样损失好了很多。

Tessy频率 tetra频谱图_傅里叶变换_02