2.45. Using a computer program*, calculate the discrete Fourier transform of a unit amplitude rectangular pulse of duration one second. Take 64 samples of the pulse and pad it with 96 zero-valued samples on either side so that a Fast ...

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2.44. Write a computer program* to calculate the discrete exponential Fourier series (Equation (2.61)) of the waveform shown in Figure 2.20. Sketch the amplitude spectrum. (Use 64 sample points/period.) Compare the coefficient values with the values obtained in Problem 2.9.

2.43. Assume that y(t) described in Problem 2.42 is such that x(t)<1 y(t) is passed through a nonlinearity whose output z(t) is given by z{t) = 2y2(t) (a) Find Z(f) (assume that x2(t) < |x(t)|). (b) If z(t) is passed through an ideal lowpass filter ...

2.42. Let y(t) = [1 + x(t)) cos 2nfot, where x(t) is a lowpass signal with a bandwidth fx having a Fourier transform X(f) shown in Figure 2.30c. Assuming fo> fx, sketch the transform of y(t).

2.41. A signal x(t) with a Fourier transform X(f) is passed through a nonlinearity whose output y(t) is given by Find Y(f) and sketch it.

2.40. The signal x(t) = cos 200nt +0.2 cos 700nt is sampled (ideally) at a rate of 400 samples per second. The sampled waveform is then passed through an ideal lowpass filter with a bandwidth of 200 Hz. Write an ...

2.39. In Figure 2.30 assume that the sampling function consists of a sequence of impulses with a period To and that the filter is ideal bandpass with a center frequency fo and a bandwidth of 2fx, Show that y(t)=kx(t) cos ,,,,, where ...

2.38. Consider the system shown in Figure 2.30. Show that y(t)= kx(t) where k is a scale factor, when the filter is ideal lowpass with a cut-of frequency fx (i.e., show that it is possible to reconstruct a signal x(t) from its ...

2.37. A symmetrical square wave of zero DC value, peak to peak amplitude of 10 volts, and period 10 /3 is applied to an ideal lowpass filter with a transfer

2.36. Repeat Problem 2.35 with a highpass filter with a cutoff frequency of 5 kHz.