- 4 A Consider An Analog Filter That Has The Following Frequency Response 1200 H A A Be Ce Where A B And C Are Real 1 (56.87 KiB) Viewed 28 times
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4. (a) Consider an analog filter that has the following frequency response -1200 H(a)=a+be+ce where a, b, and c are real numbers. (i) Find the impulse response of the filter for a = b = c = 1. (ii) Find the frequency spectrum of the filter's output in part (i) given the input signal of cos (t). (iii) If the DC value of H() is 10, and the amplitude response of 2√2 and the phase response of 135° are measured at the angular frequency of 7/2 radians/second, determine the values of a, b, and c that meet these specifications. (b) An analog signal x(t) is over-sampled using the sampling rate of f = 48 kHz, and the resulted discrete-time signal x[n] is derived as follows: x[n] = cc Sna 16 (i) Determine the digital frequency of x[n] and the fundamental frequency of x(1). (ii) Is x[n] periodic? Justify your answer. (iii) How long does it take to acquire twelve periods of x[n] samples? (iv) Find another two analog signals that would produce the same x[n] when sampled at the sampling rate of 48 kHz.