Question

Q1) The spectrum of a signal m() is shown in Fig.Q1. This signal is ideally sampled using train of impulses. MIn -3k 3 f Fig.Q1 a) Sketch the spectrum of the sampled signal gs() when i) f, = 7 kHz. ii) f, equals the Nyquist rate b) The sampled signal is passed through an ideal low-pass filter LPF which is band-limited to 3 kHz. Sketch the spectrum of the output signal for each of the three sampling rates given above.

Answer 1

Let us rewind some properties - x (t) * y (t) rightarrow [x (w) . y (w)] or x (f) . y (f) x (t) . y (t) rightarrow [x (f) (*) y (f)] freq domain freq components plusminus f_1 f_s - f_! f_s + f_1 2 f_3 - f_1 2f_s + f_1 fm = 3k H_2 when sampled at f_s = 7k Hz rightarrow spectrum of sampled signal \r\n f_s = Nyquist rate = 2 times fm = 2 times 3k = 6k Hz f_s = 5kHz we have a lif - (i) fs = 7 kHz: - sampled passes through H (t) - it extract the 1^st square - so out put will be f_3 = 6k Hz - same output will be recovered - as for all f greaterthanorequalto 3k - out put will be 0 - \r\n when fs = 5kHz rightarrow over lapping place - so when fs = 5 kHz rightarrow msg will not be recovered.