A Sequence \(x\left[ n \right] = \cos \left[ {\frac{{\pi n}}{4}}

$A Sequence \(x\left[ n \right] = \cos \left[ {\frac{{\pi n}}{4}}$

| A Sequence $x\left[ n \right] = \cos \left[ {\frac{{\pi n}}{4}} \right]$ was obtained by sampling a continuous signal x(t) = cos (Ω₀t) at a sampling rate of 1000 Hz. The two possible values of Ω₀that have resulted in sequence x[n] are

A. 250 π and 2250 π

B. 125 π and 2250 π

C. 250 π and 1125 π

D. 125 π and 1125 π

Please scroll down to see the correct answer and solution guide.

Right Answer is: A

SOLUTION

Digital frequency can be obtained from Analog frequency using

ω = Ω T_s [Ω is analog frequency]

${\rm{\Omega }} = \frac{{\omega \;}}{{{T_s}}} = \omega {f_s}$

$ = \frac{{\rm{\pi }}}{4} \times 1000 = 250\pi $

For discrete signals frequency is repeated after every 2π radians.

Other possible frequency.

$\Rightarrow \left[ {\frac{\pi }{4} + 2\pi } \right] \times 1000$

= 2250 π