График показывает время по горизонтальной оси и частоту по вертикальной оси.Цвет пикселя показывает интенсивность каждой частоты в каждый момент времени.
Спектрограмма генерируется путем взятия сигнала и разбиения его на маленькие сегменты времени, выполняя ряд Фурье для каждого сегмента.
здесьэто некоторый код Matlab для его генерации.
Обратите внимание, как при прямом изображении сигнала это выглядит как мусор , но при построении спектрограммы мы можем четко видеть частоты компонентных сигналов.
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%% setup
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%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,:));
Обратное преобразование Фурье матрицы fourierResult вернет исходный сигнал.