what is fft code?

Hi all,

I'm new to FFT and I want to ask about calculating FFT in Matlab. The following is my coding guidance from Matlab help:-

clc;
Fs = 512;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 8100;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
x = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t); 
y = x + 2*randn(size(t));     % Sinusoids plus noise
plot(Fs*t(1:50),y(1:50));
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('time (milliseconds)');

NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2);

% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2))); 
title('Single-Sided Amplitude Spectrum of y(t)');
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');

Can someone verify my code because the fft graph unconvincing. Here the figure of the graph

Thank you.

[Walter Roberson]

What features of the plot are you seeing as "unconvincing" ?

[nur yusof]

the peak.looks not relevant.

[Walter Roberson]

I am not sure why you say that? You coded

0.7*sin(2*pi*50*t) + sin(2*pi*120*t);

which calls for a 0.7 peak at 50 Hz and a 1.0 peak at 120 Hz. The peaks are visually shown at the correct place, 50 Hz and 120 Hz. When I extract the value of the peak locations I get 0.683776526075202 and 0.986050681728091 . Why not exactly 0.7 and 1.0? Because of the normally distributed random noise with standard deviation 2 that you added, a standard deviation that exceeds the maximum value of the two sines added together (0.7+1). The peaks look relevant to me.

[Sag]

Why to multiply by 2 in step: plot(f,2*abs(Y(1:NFFT/2)));

[Afshin Loghmani M Toussi]

Because you are plotting half of the frequency range( because of the symmetry). However, to show the same amount of energy you are multiplying the values by 2.

Answer 1

[Andreas Goser]

Frequent puzzlese with interpreting FFT:

2 peaks instead of 1 peak

Frequency "off" by a factor of 6.

Both effects are in the nature of the algorithm and "6" is actually "2*Pi". Next steps depend on whether you want to just use the results, then this will help. If you want to understand, read a text book about signal processing.

[nur yusof]

thank you so much