Consider a discrete time periodic signal x n cos ( 0 7 n ) (1) D...

Consider a discrete-time periodic signal x [ n ]Â Â Â =Â Â Â cos ( 0 . 7 Ï€n ) (1) Determine...

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Programming

Consider a discrete-time periodic signal
x [ n ]Â Â Â =Â Â Â cos ( 0 . 7 Ï€n )
(1) Determine the fundamental period of x[n].
(2) Suppose x[n] is obtained by sampling the continuous-timesignalÂ Â x ( t)Â Â Â =Â Â Â cosÂ Â Â ( Ï€t ),by letting the sampling period to be T s =Â Â Â 0 . 7and considering the sample values at each n. Is the Nyquistsampling conditions satisfied in this case? Explain and relate thisto the answer given before.
(3) Under that conditions would sampling a continuous-timesignal x ( t )Â Â Â =Â Â Â cos ( Î© 0 t )give a discrete-time sinusoid x[n] that resembles x(t)? Explain andgive an example.

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3.9 Ratings (736 Votes)

1 It is given that xn cos07 n So first we will have to check whether the signal is a periodic one or an aperiodic one For this let us check the conditon of periodicity Condition of periodic function 2 W Rational number R Here W 07 So 2 07 Rational value See Answer

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