Friday, October 14, 2011
FFT dari Sinyal Sinus di Matlab/Octave
Seharusnya, bila kita membuat sinyal sinusoidal dengan frekuensi 20 Hz, maka kalau kita fft-kan (fourrier transform-kan) sinyal tersebut memiliki frekuensi tunggal pada sumbu X=20. Bila tidak, atau plotnya menunjukkan spektrum yang tidak beraturan, maka gambar dan teknik yang kita gunakan tersebut salah.
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| Sinyal Sin 20 Hz dan FFT -nya |
% Sampling frequency Fs = 1024; % Time vector of 1 second t = 0:1/Fs:1; % Create a sine wave of 20 Hz. x = sin(2*pi*t*20); % Use next highest power of 2 greater than or equal to length(x) to calculate FFT.Source: Mathwork
nfft= 2^(nextpow2(length(x)));
% Take fft, padding with zeros so that length(fftx) is equal to nfft
fftx = fft(x,nfft);
% Calculate the numberof unique points
NumUniquePts = ceil((nfft+1)/2);
% FFT is symmetric, throw away second half
fftx = fftx(1:NumUniquePts);
% Take the magnitude of fft of x and scale the fft so that it is not a function of the length of x
mx = abs(fftx)/length(x);
% Take the square of the magnitude of fft of x.
mx = mx.^2;
% Since we dropped half the FFT, we multiply mx by 2 to keep the same energy.
% The DC component and Nyquist component, if it exists, are unique and should not be multiplied by 2.
if rem(nfft, 2) % odd nfft excludes Nyquist point
mx(2:end) = mx(2:end)*2;
else
mx(2:end -1) = mx(2:end -1)*2;
end
% This is an evenly spaced frequency vector with NumUniquePts points.
f = (0:NumUniquePts-1)*Fs/nfft;
% Generate the plot, title and labels.
subplot(211); plot(x);
title('Waveform of a 20Hz Sine Wave');
xlabel('Time');
ylabel('Amplitude');
subplot(212); plot(f,mx);
title('Power Spectrum of a 20Hz Sine Wave');
xlabel('Frequency (Hz)');
ylabel('Power');
