matlab - 频谱图及其含义

我很想知道右上角的数字是如何出现在：http://en.wikipedia.org/wiki/Spectrogram
是生成的（脚本）以及如何分析它，即它传达了什么信息？我希望用最少的数学术语给出一个简单的答案谢谢您。

最佳答案

该图显示水平轴上的时间，以及沿垂直轴的频率。像素颜色显示每个频率在每个时间的强度。
一个谱图是通过把一个信号分成几个小的时间段，在每个时间段上做一个傅里叶级数来生成的。
下面是一些生成的matlab代码。
注意如何直接绘制信号，它看起来像垃圾，但是绘制频谱图，我们可以清楚地看到组成信号的频率。

%%%%%%%%
%% 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矩阵的逆傅里叶变换将返回原始信号。

关于matlab - 频谱图及其含义，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/8781556/