DSP Lab Experiments - Digital Signal Processing: An Introduction with MATLAB and Applications - page 329

then we can reduce this power by applying a filter (LPF or BPF) to extract only the
area of interest in the spectrum.
MATLAB Simulation
In this experiment we will design filters for the purpose of noise reduction in
narrowband signals.
Task 1
Consider a signal x(t) corrupted by additive Gaussian noise n(t), where x(t) = asin
(x o t), with a ¼ 1 ; f o ¼ 1Hz ; 0 t 10 s ; and SNR = 2 dB. Plot the time signals
x(t) and s(t) = x(t)+n(t) with their spectra. Design a LPF (Butterworth and
Chebychev 3 dB ripple) of minimum possible order K such that the attenuation is
less than -80 dB for f [ 10 Hz. You should carefully specify the appropriate cut-
off frequency f c . Plot the filter transfer function given by
H ð f Þ dB ¼ 20 log 10 j H ð f Þj;
and vary K until you reach the proper order. Then filter s(t) and plot the time
output signal y(t) with its spectrum and compare with s(t).
Task 2
In this task we study the effect of the sampling frequency on a recorded signal, and
we conclude that if we want to process a recorded signal, we should know its
sampling frequency. Listen to any test audio signal, e.g., Ohno.wav (can be
downloaded from http://free-loops.com/download-free-loop-3022.html ), using a
media player (just double-click on the file icon). On MATLAB use x = wav-
read('Ohno') to convert the audio file to a vector of numerical values (volt-
ages) suitable for mathematical processing. The sampling frequency of Ohno can
be read from the media player; it is fs = 22 kHz . Try changing fs to 35 kHz then
re-write the signal on another file using the statement
Ohno1 ¼ wavwrite ð x ; fs ; 'Ohno1 : wav 0 Þ ;
Now listen to the new file. Change the sampling frequency to 15 kHz and repeat
the process.
Task 3
In this task we consider audio effects as explained in the lecture notes. Implement
an FIR filter with 4 coefficients to simulate echoes, and then listen to the resulting
audio signal. Change the magnitude of the coefficients and listen again.