Created
May 31, 2012 17:00
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Illustration of sinusoid in time and frequency domain (Octave script)
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function freqtime(f) | |
% The fourier transform below assumes that y is a periodic signal which it is if 'f' is an integer (i.e we don't do any windowing) | |
if 0==nargin | |
f = 2; | |
end | |
A = 1; | |
fs = 100; | |
T = 20; % Longer signal -> higher frequency resolution | |
t = linspace(0,T,T*fs+1); | |
y0 = A*sin(t*f*2*pi); | |
hz = (0:length(y0)-1)/T; | |
noise=[0 3*A]; | |
for ni=1:length(noise) | |
y = y0 - noise(ni).*(rand(size(y0))-0.5); | |
F = fft(y)*2/numel(t); | |
subplot(4,2,ni); | |
time_to_plot=min(2,T); | |
ti = 1:time_to_plot*fs; | |
plot(t(ti),y(ti)); | |
title(['Time domain of y_' num2str(ni) ]); | |
ylabel('y'); | |
xlabel('t [s]'); | |
ylim([-1 1]*max(noise)); | |
subplot(4,2,2+ni); | |
fi = 1:ceil(length(F)/2); % Plot the entire spectra but skip the redundant part | |
plot(hz(fi),abs(F(fi))); | |
title('Frequency domain'); | |
ylabel(['|F\{y_' num2str(ni) '\}|']); | |
xlabel('f [Hz]'); | |
ylim([0 .5]*max(noise)); | |
subplot(4,2,4+ni); | |
max_hz = 6; % Just plot the first 6 Hz | |
fi = 1+ (0:max_hz*T); | |
plot(hz(fi),abs(F(fi))); | |
title(['Frequency domain from 0 Hz to ' num2str(max_hz) ' Hz']); | |
ylabel(['|F\{y_' num2str(ni) '\}|']); | |
xlabel('f [Hz]'); | |
ylim([0 .5]*max(noise)); | |
subplot(4,2,6+ni); | |
spectraLines = 40; | |
spectra = zeros(spectraLines,numel(t)); | |
spectra(1,:) = F; | |
for li = 2:spectraLines | |
% Create more signal data similiar to the first part | |
y = y0 - noise(ni).*(rand(size(y0))-0.5); | |
spectra(li,:) = fft(y)*2/numel(t); | |
end | |
max_hz = 6; % Just plot the first 6 Hz | |
fi = 1+ (0:max_hz*T); | |
spectra = abs(spectra(:,fi)); | |
C = zeros(256,3); | |
C(:,2) = linspace(0,1,256); | |
colormap( C ); | |
imagesc(hz(fi),((1:spectraLines)*T-0.5*T)/60,(spectra./max(spectra(:))).^0.25); | |
title('Spectrogram of continued signal'); | |
ylabel('t [min]'); | |
xlabel('f [Hz]'); | |
end |
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