EE-3TR4 Mid Term Exam 2008

Duration of examination: 1 hour and 30 minutes

All the questions are of equal weights.

Answer all the questions.

1. The input of a filter is given by

, (1)

where is the bit interval. The filter output is

. (2)

Find a transfer function of the filter. Sketch the magnitude and phase frequency responses of the filter. Would it be possible to have two or more transfer functions of the filter that lead to the output given by Eq. (2) for the input of Eq. (1)? Comment on the uniqueness of the transfer function.

2. Find the Fourier transform of the following signal:

.

Sketch the magnitude and phase spectra. Assume t₀ < 0.

3. The message signal is given by

.

Find the spectrum of the standard AM signal. Sketch the standard AM signal in time and frequency domains for (a) 50% modulation and (b) 125% modulation. Calculate the locations of phase reversal, if any. Assume carrier amplitude 1 V and carrier frequency KHz.

Useful Information:

1. Fourier transform pairs:

2. Trigonometric relations: