lab2
a) find the FT [F(w)] of f(t) = exp(-(t^2)/Z) where Z = 4
hint multiply f(t) by exp(-w^2)*exp(w^2) = 1
plot this function.[w:rad/s][t:s]
%%%%ans = F(w) = 2*exp(-w^2)
b) f[n] = f(Ts*n) where n is an integer and Ts is a constant.
write an equation for the DTFT of f[n] in terms of F(w);
c) g(t) = f(t-50) for 0<=t<=100
write a progam to sample g(t) in the range of 0<=t<=100
with the sampling rate Fs = 3 Hz to get gs[n]
calculate the DFT of this vector. Gs[k] = DFT(gs[n])
To do this use the octave command Gs = fft(gs)
plot Gs (the magnitude of Gs).
Explain (in words) how F(w) and Gs[k] and the DTFT of f[n} are related. be sure to address the complex nature
Gs and include concepts of aliasing in time and frequency in your discussion.
try varying the function f(t) by varying Z (try values ranging from
0.1 to 100). what do you observe?
d)Zero Padding in time: write a script to generate:
gszt[n] = gs[n] 0<=n<=300; 0 for 300 < n <= 900
compare the magnitude of Gszt[k] = fft(gsz) to that of Gs[k].
what is the effect of zero paddingin time?
f) Zero Padding in Frequency: write a script to generate:
Gszf[n] = Gs[n} for 0<=n<=150; 0 for 150 < n <=750; Gs[n-600] for 750