Matlab Project

Matlab Project

MATH IN SIGNALS AND SYSTEMS, ART GRIGORYAN,
MATLAB-Based Project: Convolution of Signals and FFT 1

1For this project you will be given maximum of 10 points which will be added to

your final score, MATH IN SIGNALS AND SYSTEMS, ART GRIGORYAN, UTSA-2015 2
Speech signal and linear convolution
The speech signal for this project was posted on our web page in BB. Write your

code2
to calculate the
convolution of the speech signal by performing the following steps.
1. Read the speech signal {fn} from the file ’mike.wav’ (see Figure 1); for that

the command “wavread”
can be used. (To sound this signal f, use the command “sound(f,Fs)”. This signal is

of 38.7360 seconds
0 5 10 15 20 25 30 35
−0.5
0
0.5
speech signal
time (seconds)
Fig. 1. Original 1-D signal.
duration.
2. Consider the triangle filter
{hn} = {1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2,

2}/K
with the center h0 = 8; note the filter is not symmetric. Define value of K from

the condition
X
12
n=−12
hn = 1.
3. Calculate and sketch the convolution of the signal with this filter.
4. Divide the signal fn by parts of 8 seconds each; add zeros to the last part to

complete it to 8 seconds.
5. Perform the linear convolution of each part of the signal by this filter, by

using the direct method of
convolution.
6. Compose one new signal from these convoluted parts; this signal, gn, should be

of the same length as
the original speech signal.
7. Repeat steps 3-6 by calculating the convolutions in steps 3 and 5 by the method

of fast Fourier
transform.
Provide your code(s) and report for this project in hard copy with illustrations,

as well as in electronic
form (in one zip-file). Functions form MATLAB calculating the convolution and

filters cannot be used, only
”fft” and ”ifft” can be used for the DFT. Plot the signals, convolutions, Fourier

transforms of the signals
and filter in absolute scale. Explain clearly your work in the project, and write

how fast your program(s)
work.
A.M.G. (e-mail: amgrigoryan@utsa.edu)
2No MATLAB commands “conv”, “filter”,… can be used.

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