# Spectrogram of a chirp and its FFT

This question follows from an answer to this other question: Conceptual question on FFT and chirp signal

I wrote a code starting from the spectrogram to compare it with the FFT result.

% Chirp generation
t = [0 0.5 1.0 1.5 2.0]; % time breakpoints
f = [0 200 100 150 300];  % instantaneous frequency breakpoints
p = polyfit(t,f,4);
dt = 0.001;
t = 0:dt:2;
y = chirp(t,p);
L = length(y);

% FFT
NFFT = 2^nextpow2(L);
Y = fft(y,NFFT)/L;
Fs = 1/dt;
f_plot = Fs/2*linspace(0,1,NFFT/2+1);

% Spectrogram
figure()
specgram(y,128,Fs,128,120); % 2D time-freqency display

[S,F,T,P]=spectrogram(y,128,120,128,1E3);
figure()
surf(T,F,10*log10(P),'edgecolor','none')
axis tight


This is what I obtain.   My qyestion is: shouldn't the spectrogram and the FFT have the same amplitude variation? Whereas the spectrogram does not seem to have amplitude variation (the red line is red at the same way everywhere).

Second question, why in the FFT I have high peaks at $100$ and $200 Hz$ only?

• This is just a guess, but it seems like the signal stays at 100 Hz and 200 Hz longer than at other frequencies. For instance, the frequency is very close to 100 Hz in the interval from 1 s to 1.2 s. The FFT reflects this. – MBaz Jan 12 '15 at 20:20