1 - What does the spectrum tell you about the frequency content of chirp signals
ID: 2304839 • Letter: 1
Question
1 - What does the spectrum tell you about the frequency content of chirp signals?
2- Repeat this task for the case where the frequency is decreasing from 2000 to 200 Hz. Does the spectrum make it easy to see that the chirp is decreasing or increasing in frequency?
3- Think about ways we could make it clearer to see that a chirp’s frequency is increasing or decreasing. Have a look at ‘time-frequency analysis’ and the ‘spectrogram’ to get an idea on how we can improve Fourier analysis in the case of non-stationary signals.
0.5 0.5 -1 0.08 0.09 0.1 0.03 0.04 0.05 0.06 0.07 0 0.01 0.02 0.5 0.5 -1 4.95 4.97 4.98 4.99 4.9 4.91 4.92 4.93 4.94 4.96 0.03 0.02 0.01 0 800 1200 1400 1600 1800 2000 200 400 600 1000Explanation / Answer
The frequency content of chirp signals from the given chatrs as fallows,
The frequencies were calculated for the plots indexed from top to bottom.
i. 200/0.1 = 2000Hz
ii. 22/ 0.1 = 220 Hz
iii chirp signal spectrum
iv. 400/0.1 = 400 Hz
v. 100/ 0.1 = 1000Hz
A chirp is a sinusoid with time varying frequency. In particular a linear chirp has a
frequency which varies linearly with time between two frequencies. The expression is
given by
X(t ) = A cos (2?F(t)t+ ?)
For example in matlab, the following code generates a chirp with frequency varying
between 100Hz and 4,000Hz in 1/10 sec:
Fs=10000;
% sampling frequency in Hz
Ts=1/Fs;
% sampling interval in seconds
t=(0:999)*Ts;
% time axis
y=chirp(t, 100, t(1000), 4000);
% chirp signal
plot(t(1:300), y(1:300))
% plot of first 300 samples
spectrogram
The Short-time Fourier transform is complex valued and its real part and imaginary part are highly
oscillatory and adequate visualization is given by the squared magnitude is the Spectrogram
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.