EE416 Homework 5 Spring 2015

4.1 The signal X(t), whose pdf is shown in Fig. 1, amplitude modulates a carrier with m = 0.5.Calculate (S/N)d in terms of Sr/fx for envelope demodulation, assuming white noise with a psdof /2 watt/Hz at the input.

Figure 1:

4.2 Assume that the baseband message signal in an AM system has a bandwidth of 4 kHz and theamplitude distribution shown in Fig. 1. The AM signal is accompanied by thermal noise witha psd /2 = 1012 watt/Hz. The signal is demodulated by envelope detection and appropriatepostdetection filtering. It is required that the output signal-to-noise ratio be greater than 40 dB.Assume m = 1.

(a) Find the minimum value of the carrier amplitude that will yield (S/N)d 40 dB.(b) Find the threshold value of ac.

4.3 A carrier of amplitude 1 mv is 50% amplitude modulated by a sinusoidal waveform of frequencyfx < 1000 Hz. The signal is accompanied by thermal noise of twosided spectral density /2 =1012 watt/Hz. The signal plus noise is passed through a predetection filter having the responseshown in Fig. 2. The signal is demodulated by multiplication with a local carrier of amplitude 2volts and filtering the product with an ideal lowpass filter having a bandwidth of 1 kHz.

Figure 2:

(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 is 103

watt per Hertz. The modulating wave is sinusoidal, with a carrier power of 80 kw, and a sidebandpower of 10 kw per sideband. The message bandwidth is 4 kHz. Assuming the use of an envelopedetector in the receiver, determine the output signaltonoise ratio of the system.

4.5 Let a message signal X(t) be transmitted using single-sideband modulation. The power spectraldensity of X(t) is

Gx(f) =

{ |f |fx , for |f | fx

0, elsewhere

where and fx are constants. White Gaussian noise of zero mean and power spectral density of/2 is added to the SSB modulated wave at the receiver input. Find an expression for the outputsignal-to-noise ratio of the receiver.

1