EE416 Homework 4 Fall 2014

4.1 Consider a baseband system with the following characteristics:

Hc(f) = [1 + j2f/fx]1 ; Gni(f) = N0/2 watt/Hz

Gx(f) =

{0.5 fx, for |f | < fx

0, elsewhere

Heq(f) =

{1 + j(2f/fx), for |f | < fx

0, elsewhere

(No preemphasis filter.) Calculate (S/N)d for this system.

4.2 Design optimum preemphasis/deemphasis filters for the system described in problem 4.1 andcompute (S/N)d for the optimum system. Assume ST to be the same and compare the results.

4.3 A carrier of amplitude 1 mv is 50% amplitude modulated by a sinusoidal waveform of fre-quency fx < 1000 Hz. The signal is accompanied by thermal noise of twosided spectraldensity N0/2 = 10

12 watt/Hz. The signal plus noise is passed through a predetection filterhaving the response shown in Fig. 1. The signal is demodulated by multiplication with alocal carrier of amplitude 2 volts and filtering the product with an ideal lowpass filter havinga bandwidth of 1 kHz.

Figure 1:

(a) Find the output signal power.

(b) Find the output noise power.

(c) Find (S/N) at the demodulator input and (S/N)d.

4.4 The average noise power per unit bandwidth measured at the front end of an AM receiver is103 watt per Hertz. The modulating wave is sinusoidal, with a carrier power of 80 kw, anda sideband power of 10 kw per sideband. The message bandwidth is 4 kHz. Assuming theuse of an envelope detector in the receiver, determine the output signaltonoise ratio of thesystem.

1