Consider the signal x(t) x(t) = sinc (a) Find the Fourier transform of x(t) (b) Determine the bandwidth of the signal (c) Determine the Nyquist rate

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Consider the signal x(t)
x(t) = sinc
(a) Find the Fourier transform of x(t)
(b) Determine the bandwidth of the signal
(c) Determine the Nyquist rate
(d) Sketch the spectrum of the sampled signal xs(t) when:
a. fs = 1.5 Nyquist rate
b. f = 0.25 Nyquist rate
and comment on the result. Which case is corresponding to oversampling? Which case is
corresponding to undersampling? When does aliasing occur?
P,(t)
TW
OT sinc
2T
Tt
+2mp,(w)
T sinc
2|t|
1 -
TW
sinc
sinc
Tt
+27 1
cos(@t) T[8(@ + wo) + 8(@ – w)]
Transcribed Image Text:Consider the signal x(t) x(t) = sinc (a) Find the Fourier transform of x(t) (b) Determine the bandwidth of the signal (c) Determine the Nyquist rate (d) Sketch the spectrum of the sampled signal xs(t) when: a. fs = 1.5 Nyquist rate b. f = 0.25 Nyquist rate and comment on the result. Which case is corresponding to oversampling? Which case is corresponding to undersampling? When does aliasing occur? P,(t) TW OT sinc 2T Tt +2mp,(w) T sinc 2|t| 1 - TW sinc sinc Tt +27 1 cos(@t) T[8(@ + wo) + 8(@ – w)]
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