Digital Signal Processing LAB 3 solved

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Objectives:
Understand different concepts of convolution along with its applications.
Prerequisites:
 Linear Convolution
 2D – Convolution
 Circular Convolution
Problems
1. Explore command conv2 in Matlab. Take input of 2 Matrix from user and Find 2D
convolution of the same. Also explore the properties of conv2 command and analyze the
result.
For an example
A
[

 

 

 

]

 

B = [

 

]
2. Application of 2D convolution on image processing applications
a) Take a standard test image “Lenna.png” from shared folder. Explore following
commands and apply for given image.
 imread
 rgb2gray
 imshow
b) Now in order to perform 2D convolution, Given image becomes first input as matrix
and second input will be a sets of kernel matrix performing different operations on
image which are mentioned below:
SEAS Winter 2020
2
List of different kernels:
In image processing, a kernel, convolution matrix, or mask is a small matrix useful for
averaging, sharpening, embossing, edge-detection, and more. This is accomplished by
means of convolution between a kernel and an image.
 Average (blur, smooth) 3×3 convolution kernel
A = [

 

]
 Sharpen 3×3 convolution kernel
S = [

 

]
 Edge detection 3×3 convolution kernel
E= [

 

] EH = [

 

] EV= [

 

]
 Gradient detection 3×3 convolution kernel
GH = [

 

] GV = [

 

]
 Sobel Operator 3×3 convolution kernel
SH = [

 

] SV = [

 

]
3
3. Develop a MATLAB function to obtain circular convolution of two sequences. Verify the
function for following sequence. Write a script file to use the developed function.

1. x1(n) = {1,-1,-2,3,-1} and x2(n) = {1,2,3}

2. x1(n) = {1, 2, 1, 2} and x2(n)= {3,2,1,4}
3. x1(n)= (

) and x2(n)= (

), .for N=8

4. Write a MATLAB program to find circular convolution of two sequences using Matrix
Multiplication method.
1. x1(n) = {1,-1,-2,3,-1} and x2(n) = {1,2,3}

2. x1(n) = {1, 2, 1, 2} and x2(n)= {3,2,1,4}
3. x1(n)= (

) and x2(n)= (

), .for N=8