DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 335

Task 4
Design an analog 9th-order Butterworth LPF with cutoff frequency of 50 Hz and
filter the sampled signal. Plot the output signal and its spectrum and compare with
the original analog signal for sampling frequency of 50, 100, and 500 Hz and
check for aliasing.
Task 5
Now generate a LFM signal of initial frequency 10 Hz and modulation index of
0.7. Note that the sinusoid is a periodic function (hence, its spectrum is impulses)
while the LFM is non-periodic (hence, its spectrum is a continuous function of
frequency). From the spectrum we see that the maximum frequency in the LFM is
about 50 Hz, hence, we expect the sampling frequency to be at least 100 Hz to
avoid aliasing. Try fs = 50, 100 , and 500 Hz then compare the results.
Task 6
In this task we study the audio effect of aliasing. Download and listen to an audio
signal such as Ohno.wav which was used before in Experiment 4. On MATLAB use
[x,fs,bits] = wavread('Ohno') to convert the audio file Ohno.wav to a
vector of numerical values (and know its original sampling frequency and number
of quantization bits). The sampling frequency of Ohno can be read fs = 22 kHz.
Try downsampling Ohno to fk = fs/k (k integer) then re-write the signal on
another file using the statement wavwrite(x,fs1,'Ohno1.wav') . Now
listen to Ohno1.wav . At what value of k does aliasing start to occur? Why?
Experiment # 7: Binary Signal Transmission
Introduction
In binary communication systems, binary data (which is a sequence of 0's and 1's)
are often transmitted through a channel using two orthogonal signals, s 0 (t) and s 1
(t). One possible signal configuration is shown in Fig. D.10 .
If data is large, then 0's and 1's are equally probable (p(1) = p(0) = 1/2) and
statistically independent. The AWGN channel adds Gaussian noise (wideband,
approximately white) with power spectral density (PSD) = g/2 (W/Hz). Hence, the
received signal will be in the following form:
r ð t Þ¼ s i ð t Þþ n ð t Þ; i 2f 0 ; 1 g; 0 t T :