頻譜圖和它是什麼

Question

我非常有興趣知道如何生成右上圖：http：//en.wikipedia.org/wiki/Spectrogram （腳本），以及如何分析它，即什麼信息它表達了什麼？我會很感激最簡單的答案，用最少的數學術語。謝謝。

Answer 1

該圖顯示沿着水平軸的時間以及沿着垂直軸的頻率。像素顏色顯示每個時間每個頻率的強度。

通過獲取信號並將其切分爲小時間段，在每個段上執行傅立葉級數，生成譜圖。

這裏有一些matlab代碼來生成一個。

注意如何直接繪製信號，看起來像垃圾，但繪製譜圖，我們可以清楚地看到分量信號的頻率。

%%%%%%%% 
%% 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,:)); 

矩陣fourierResult的逆傅里葉變換將返回原始信號。

Answer 2

只需添加到蘇基的答案，這裏是一個偉大的教程，通過走你，一步一步，閱讀Matlab的譜圖，觸及只夠數學和物理直觀地解釋主要概念：

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