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.

Sinyal Sin 20 Hz dan FFT -nya

Cek dan run listing code matlab di bawah untuk menghasilkan FFT dari sinyal sinus yang match dengan frekuensinya.

% 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;


  mx(2:end -1) = mx(2:end -1)*2;


% 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');



subplot(212); plot(f,mx);

title('Power Spectrum of a 20Hz Sine Wave');

xlabel('Frequency (Hz)');


Source: Mathwork


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