DSP Group Activity

1. Submitted By:
1DA19EC428- Rajath R Navalgi
1DA19EC433- Sachin Ramachandra Achari
1DA19EC434- Sachin Subrahmanya Shet
1DA19EC436- Vijay Kumar N
1DA19EC438- Vinay Kumar HS
1DA19EC439- Vinod
Group Activity for:
Digital Signal Processing (18EC52)
BACHELOR OF ENGINEERING
In
ELECTRONIC AND COMMUNICATION ENGINEERING

2. CONTENTS
 Introduction to Scilab
 Linear Convolution
 Algorithm
 Scilab Code:
 Convolution using Direct formula
 Convolution using inbuilt function

3. INTRODUCTION TO SCILAB
 Scilab is a free and open-source, cross-platform numerical computational package and a high-level,
numerically oriented programming language. It can be used for signal processing, statistical analysis,
image enhancement, fluid dynamics simulations, numerical optimization, and modeling, simulation of
explicit and implicit dynamical systems and (if the corresponding toolbox is installed) symbolic
manipulations.
 Scilab is one of the two major open-source alternatives to MATLAB, the other one being GNU
Octave.Scilab puts less emphasis on syntactic compatibility with MATLAB than Octave does, but it is
similar enough that some authors suggest that it is easy to transfer skills between the two systems.

4. LINEAR CONVOLUTION
 Convolution is a mathematical operation used to express the relation between input and
output of an LTI system.
 It relates input, output and impulse response of an LTI system as
 y(n)=x(n)∗h(n)
Where y (n) = output of LTI
x (n) = input of LTI
h (n) = impulse response of LTI

5. Discrete Convolution
y(n)=x(n)∗h(n)
=
𝑘−∞
∞
𝑥 𝑘 ℎ(𝑛 − 𝑘)
By using convolution we can find zero state response of the system.

6. ALGORITHM
 Give input sequence x[n].
 Give impulse response sequence h(n)
 Find the convolution y[n] using the Formula method or using Scilab convol() function
 Plot x[n],h[n],y[n]

7. SCILAB CODE:
 Using Direct formula method:

8. EXAMPLE-1:
 enter x seq[1,2,3,4]
 enter h seq[1,1,1]

 y=
1.
3.
6.
9.
7.
4.

9. RESULT WAVEFORM FOR EXAMPLE-1:

10. SCILAB CODE:
 Using convol() function.
 Syntax
[y]=convol(h,x)
[y,e1]=convol(h,x,e0)
 Description
Calculates the convolution y= h*x of two discrete sequences by using the fft. The convolution is defined as follows:
Overlap add method can be used.

11. SCILAB CODE:

12. EXAMPLE-2:
 enter x sequence[1,2]
 enter h sequence[1,2,5]
 y=
1. 4. 9. 10.

13. RESULT WAVEFORM FOR EXAMPLE-2: