Using the FFT and plotting results

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Oliver
Oliver 2014-2-13
Hi,
I'm using the FFT to compute the FT of some data, and follow the example code used on the Mathworks FFT help page (shown below):
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sample time
L = 1000; % 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+1);
% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1)))
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')
I just have a couple of queries:
1) where does the factor of 1/2 in the declaration of frequency come from? (f = Fs/2*linspace(0,1,NFFT/2+1);)/
2) when plotting why is the amplitude of the absolute value of Y(f) doubled? (plot(f,2*abs(Y(1:NFFT/2+1))))
Thanks in advance. Olie

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