The impulse train p(t) = -co 8(t-nT) can be used for sampling continuous time signals. Its Fourier Transform is: 2πT P(j

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The impulse train p(t) = -co 8(t-nT) can be used for sampling continuous time signals. Its Fourier Transform is: 2πT P(jw) = ²-8 (w — kwc), where we = T T (a) Sketch P(jw) for the sampling period T = 7 (b) Sketch the Spectrum of the sampled signal y(t) = x(t)p(t) for T = where the spectrum of x (t) is: X(jw) Hint: Multiplication in the time domain results in convolution in the frequency domain as follows: x(t)p(t) ¹ X(jw) * P(jw) 2πT (c) Sketch the Spectrum of the sampled signal y(t) for the sampling period 2πt T = 3 (d) Explain whether you can recover the signal x(t) from the sampled signal in parts (b) and (c). FIM π