Question

2: (a) Consider a discrete-time sequence x[n] = cos(n+3). Find the fundamental period(N). (b) Consider the sinusodal signal x(t) = 10 sin(21 Fot) with analog frequency F. Write an equa- tion for the discrete time signal n. (c) In part(b) if Fe = 400Hz and the sampling frequency F. = 4kHz, determine the fundamen- tal period of x[n].

Answer 1

2 : a) consider a discrete-time sequence x[n] = cos(nT/+T/s). Find the fundamental period (N). ANS:- In a discrete -time, fundamental period (N) is given as : ware here > OOOC N = 20 = 8 IN=87 b) consides the sinusoidal signal xct) = losin (211 fats with analog frequency fa. write an equation for the discrete time signal x[n]. ANS; Here, for converting continuous time signal into the discrete time signal then t = nis & n/fs x(n) = 20 sin [20 x fax inch) = losin [ 2 hinta] is a discrete time signal of given.

a c In part(b) is fa = 600 HZ and the sampling Frequency fs = 4kHz determine the fundamental period of ecn). ANS: From part [b ] discrete time signal is x(0) = 10 sin[arn ta] but here given that sa = 400HZ x (n) = 10 sinalinx 4007 = losin [21n XI ] (n) = lo sin [m/s] In discrete time, fundamental period is given by 20 =10 & fs = 4kHZ. FOOO N = 20 = 1 N=10