Sampling of sinusoidal signal aliasing consider the following continuous time sinusoidal signal xa(t) sin2 F01, t Since xa (t) is described mathematically, its sampled version can be described by values every T seconds The sampled signal is described by the formula Where F s 1 T is the sampling frequency (a) Plot the signal x(n), 0 n 99 for F s 5 kHz and F 0 0 5, 2, 3, and 4 5 kHz Explain the similarities and differences among the various plots (b) Suppose that F 0 2 kHz and F s 50 kHz (1) Plot the signal x(n) What is the frequency f 0 of the signal x(n) (2) Plot the signal y(n) created by taking the even numbered samples of x(n) Is this a sinusoidal signal Why If so, what is its frequency Fo x(nT) sin 27 F, 0 n 0 x(n) 3D

Question: Sampling of sinusoidal signal: aliasing consider the following continuous-time sinusoidal signal xa(t) = sin2?F01, - ???? t ??? ? Since xa (t) is described mathematically,

Sampling of sinusoidal signal: aliasing consider the following continuous-time sinusoidal signal xa(t) = sin2?F01, - ???? t ??? ?

Since xa (t) is described mathematically, its sampled version can be described by values every T seconds. The sampled signal is described by the formula

Fo x(nT) = sin 27 F, -0 < n < 0 x(n):

Where F_s = 1/T is the sampling frequency.

(a) Plot the signal x(n), 0 ? n ? 99 for F_s = 5 kHz and F₀ = 0.5, 2, 3, and 4.5 kHz. Explain the similarities and differences among the various plots.

(b) Suppose that F₀ = 2 kHz and F_s = 50 kHz.

(1) Plot the signal x(n). What is the frequency f₀ of the signal x(n)?

(2) Plot the signal y(n) created by taking the even-numbered samples of x(n). Is this a sinusoidal signal? Why? If so, what is its frequency??

Fo x(nT) = sin 27 F, -0 < n < 0 x(n): %3D

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