EE435 HW #2

Due: 04 November 2011, 17:30 Problem-1) We have a voice file “chimes.wav” which we use to make an AM wave (Listen to it by double clicking the file). The file contains stereo voice, but we’ll use only one channel of it. To process it we’ll use MATLAB and the following script is used to read one of its channels: u=wavread(‘chimes.wav’); m=u(:,1); The signal will be used to amplitude modulate a high frequency carrier but with an ambiguity in its sign (i.e., both m(t) and –m(t) can be used).

i. Find the maximum power efficiency max of the resulting AM as a function of the

modulating wave’s parameters (i.e., its power, peak value). (Note this part refers to a general AM behaviour, not specific to this problem only.)

ii. Determine max for the signal in the file provided.

Explain each step clearly. Note: some MATLAB functions that may be useful:

max(x) : returns the maximum of the vector x. mean(x .* x) : returns the mean square value of vector x.

Problem-2) An upper sideband SSB signal is obtained from a message signal m(t) = a(t) cos(2 π fm t) where a(t) is a waveform bandlimited to Wa=600 Hz, and fm=1000 Hz. The SSB carrier frequency is fc=100 Khz.

i. Write an expression for the SSB signal. ii. Sketch the magnitude spectrum of the SSB waveform. iii. Express the Fourier transform of the SSB signal in terms of A(f), fm and fc. iv. Assume that this SSB signal is fed to an envelope detector. Obtain a simplified expression for

the envelope detector output signal.

Problem-3)

Noncoherent demodulation of SSB signals, utilizing the envelope detection via carrier signal addition at the receiver side, is possible. For the receiver architecture given in the figure, a carrier signal with phase- and frequency-offset is added to the received LSB signal. It is assumed that m(t) is a real signal bandlimited to “W”, and fc >> W. Answer the following questions:

i. Obtain the output signal y(t) as simple as possible using the assumption that Ac >> |m(t)|. ii. Plot the magnitude spectra for Y(f) using the result of (i), and comment on the modulation

type of this approximate output signal y(t). iii. Comment on the effects of small and large frequency and phase errors (Δw and Ф) on the

output signal assuming that m(t) is a sound signal. Hint: You may try to observe the effects using the MATLAB script “SSB_envelope_det.m” of DEMO-1 at METU-Online. You should simply set A_const to a large enough value (e.g., 1 or 5) when compared to the speech signal levels. Also you may experiment with different values of delta_f and delta_phi parameters to modify frequency and phase offsets respectively.