- a) Consider a time domain signal, x=[1 1 1 1];
Construct a plot of the magnitude of the Discrete
Time Fourier Series (DTFS) of this signal, x.
This can be done using the DFT (FFT) function in Octave:
x=[1 1 1 1];
plot(abs(fft(x)));
Explain this plot.
- b) Consider a discrete time signal: x[n]=1, 0<=n<=3; x[n]=0, otherwise.
Determine the Discrete Time Fourier Transform (DTFT) for this signal.
Sketch a graph of this function.
- c) Zero padding:
Consider a discrete time periodic signal, constructed by periodizing
the above signal: y[n]=sum(x[n-lN]), for integer l, and integer period N.
Suppose N=1000. Construct a plot of the magnitude of the Discrete
Time Fourier Series (DTFS). This can be done using the DFT (FFT)
function in Octave:
y=[1 1 1 1 zeros(1,N-4)];
plot(abs(fft(y)));
How does this plot relate to the plots in parts (a) and (b).
- d) Repeat part (c) above, with N=8 (e.g. padding with 4 zeros
instead of 996 zeros):
y=[1 1 1 1 zeros(1,4)];
plot(abs(fft(y)));
How does this plot relate to the plots in parts (a), (b), and (c).
- e) In (c) and (d) above, you were padding the signal, in the time domain,
with zeros.
Explain the effect this time-domain zero padding has in the frequency
domain.