Can Somebody explain how to do this problem step by step what formulas did you u

Question

Can Somebody explain how to do this problem step by step what formulas did you use, what do they mean please step by step with explanations

What is the sampling aud the What is the Nyquist rate for the signal x a(t)? What are the frequencies in the resulting discrete-time signal x(n)? What is the resolution delta? Consider the simple signal processing system shown in Fig. P1.11. The sampling periods of the A/D and D/A converters are T = 5 ms and T' = 1 ms. respectively. Determine the output y a (t) of the system. if the input is x a(t) = 3 cos 100 pi t + 2 sin 250 pi t (t in seconds) The postfilter removes any frequency component above F s/2. Figure P1.11 Derive the expression for the discrete-time signal x (n) in Example 1.4.2 using the periodicity properties of sinusoidal functions. What is the analog signal we can obtain from x(n) if in the reconstruction process we assume that F s = 10 kHz?

Explanation / Answer

T = 5*10^-3 ms

X(n) =3cos(100*pi*nT) +2sin(250*pi*nT)

       =3cos(100*pi*n*5*10^-3) +2sin(250*pi*5*10^-3*n)

as T = 5*10^-3 s , then Fs = sampling frequency = 1/T = 200 HZ ,

hence Fs>2*50 , so   output   contains 3cos(100*pi*t)

hence ya(t) = 3*cos(100*pi*t)

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