Digital signal process

EE-4643, DIGITAL SIGNAL PROCESSING, ART GRIGORYAN 1

II. Exam-Project: Digital Signal Processing

[Due April 6, UTSA-2018]

Test for 100 points

Provide your code(s) and report for this project in hard copy with illustrations, as well as in electronic form (in one zip file) with the codes and signals. Explain clearly your project.

Instructor: Dr. Artyom Grigoryan

Student name:

EE-4643, DIGITAL SIGNAL PROCESSING, ART GRIGORYAN 2

[100pts]. 1-D Optimal Wiener Filtration

The signal for this project can be found on the BB web page. It is in the file ”boli.sig”.

Consider only the first 512 values of the signal. Case N = 512.

1. Process this signal o(n) by the following smooth filter:

h = [· · · , 0, 1, 2, 3, 3, 2, 1, 1, · · ·]/13, (h(0) = 3),

i.e., calculate the circular convolution b(n) = o(n) ∗ h(n), where n = 0 : N − 1.

2. Generate a normal distribution noise-signal, n1(n) with mean 0 and standard deviation 2. 1

3. Add this noise-signal to the blur signal, to compose the noisy signal

i1(n) = b(n) + n1(n) = (o ∗ h)(n) + n1(n), n = 0 : N − 1.

4. Design the Wiener filter YWin(ω) to process the degraded signal i1(n).

5. Apply the Wiener filter YWin(ω) to the signal i1(n) and calculate the mean-square-root error of estimation of the signal o(n).

6. Display the results and print errors of the signal reconstruction, and filter characteristics in the frequency and time domain, i.e., |H(ω)|, |YWin(ω)|, and signal-noise ratio.

2

1you can use: no = 0 + 2.*randn(1,N); 2The results of the optimal filtration should be similar to the results given in the notes.