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 |
Source: Mathwork
- % 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.
- 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');
