Question

我很想知道右上角的人物：http：//en.wikipedia.org/wiki/Spectrogram 是生成（脚本）以及如何分析它，它传达了什么信息？我会很感激简化的答案与最小的数学术语。谢谢。

Answer 1

该图显示沿水平轴的时间和沿垂直轴的频率。像素颜色显示每次每个频率的强度。

通过采集信号并将其斩波成小时段来生成频谱图，在每个段上执行傅里叶级数。

这里有一些生成一个的matlab代码。

注意如何直接绘制信号，它看起来像 garbage ，但是绘制谱图，我们可以清楚地看到分量信号的频率。

%%%%%%%%
%% setup
%%%%%%%%

%signal length in seconds
signalLength = 60+10*randn();

%100Hz sampling rate
sampleRate = 100;
dt = 1/sampleRate;

%total number of samples, and all time tags
Nsamples = round(sampleRate*signalLength);
time = linspace(0,signalLength,Nsamples);

%%%%%%%%%%%%%%%%%%%%%
%create a test signal
%%%%%%%%%%%%%%%%%%%%%

%function for converting from time to frequency in this test signal
F1 = @(T)0+40*T/signalLength; #frequency increasing with time
M1 = @(T)1-T/signalLength;    #amplitude decreasing with time

F2 = @(T)20+10*sin(2*pi()*T/signalLength); #oscilating frequenct over time
M2 = @(T)1/2;                              #constant low amplitude

%Signal frequency as a function of time
signal1Frequency = F1(time);
signal1Mag = M1(time);

signal2Frequency = F2(time);
signal2Mag = M2(time);

%integrate frequency to get angle
signal1Angle = 2*pi()*dt*cumsum(signal1Frequency);
signal2Angle = 2*pi()*dt*cumsum(signal2Frequency);

%sin of the angle to get the signal value
signal = signal1Mag.*sin(signal1Angle+randn()) + signal2Mag.*sin(signal2Angle+randn());

figure();
plot(time,signal)


%%%%%%%%%%%%%%%%%%%%%%%
%processing starts here
%%%%%%%%%%%%%%%%%%%%%%%

frequencyResolution = 1
%time resolution, binWidth, is inversly proportional to frequency resolution
binWidth = 1/frequencyResolution;

%number of resulting samples per bin
binSize = sampleRate*binWidth;

%number of bins
Nbins = ceil(Nsamples/binSize);

%pad the data with zeros so that it fills Nbins
signal(Nbins*binSize+1)=0;
signal(end) = [];

%reshape the data to binSize by Nbins
signal = reshape(signal,[binSize,Nbins]);

%calculate the fourier transform
fourierResult = fft(signal);

%convert the cos+j*sin, encoded in the complex numbers into magnitude.^2
mags= fourierResult.*conj(fourierResult);

binTimes = linspace(0,signalLength,Nbins);
frequencies = (0:frequencyResolution:binSize*frequencyResolution);
frequencies = frequencies(1:end-1);

%the upper frequencies are just aliasing, you can ignore them in this example.
slice = frequencies<max(frequencies)/2;

%plot the spectrogram
figure();
pcolor(binTimes,frequencies(slice),mags(slice,:));

fourierResult矩阵的逆傅立叶变换将返回原始信号。

Answer 2

只是为了补充Suki的答案，这是一个很棒的教程，它将引导您逐步阅读Matlab谱图，只触及足够的数学和物理来直观地解释主要概念：

http://www.caam.rice.edu/~yad1/data/EEG_Rice/Literature/Spectrograms.pdf

谱图及其含义

2 个答案: