presentation on overlap add for signal system project. MUMBAI UNIVERSITY

1. OVERLAP-ADD METHOD
USING CONVOLUTION
GUIDED BY ASST.PROF PRAMOD KACHARE
PROJECT BY:
Megha Thakur- 17ET2004
Kiran Prashanth- 17ET2025
Anushka Pokle- 17ET1065
Aishwarya Zope- 17ET1016

2. CONTENTS:
2
1. What overlap add method ?
2. Steps to perform overlap add method.
3. Example of overlap add method.
4. Reference

3. 3
OVERLAP ADD
METHOD

4. In signal processing the overlap–add method is an
efficient way to evaluate the discrete convolution of
a very long signal
Convolution is a mathematical operation
used to express the relation between input
and output of an LTI system
WHAT IS OVERLAP ADD?
WHAT IS CONVOLUTION?

5. STEPS FOR OVERLAP ADD
METHOD
5
STEP-1:
Determine length ‘M’, which is the length of the
impulse response data sequences i.e. h[n] &
determine ‘M-1’.
STEP-2:
Given input sequence x[n] size is ‘N’. let assume,
N=5

6. 6
STEP-3:
Determine the length of the new data,
‘L’
STEP-4:
Pad ‘M-1’ zeros to xk[n]
Pad ‘L-1’ zeros to h[n]
xk[n] ‘M-1’ zeros
h[n] ‘L-1’ zeros

7. 7
Input Data Sequence x[n]
x1[n]
x2[n]
x4[n]
x3[n]
M-1 zeros
M-1 zeros
M-1 zeros
M-1 zeros
L L L L

8. 8
STEP-4:
Perform Convolution of h[n] & blocks of x[n]
i.e. y1[n]= x1[n]
y2[n]= x2[n]
y3[n]= x3[n]
y4[n]= x4[n]
N
N
h[n]
h[n]
N h[n]
h[n]
N

9. 9
y1[n]
y2[n]
y4[n]
y3[n]
M-1 data
M-1 data
M-1 data
Final Output Data Sequence y[n]
M-1 data
add
add
add

10. 10
& h[n]={1,1,1}Ques. Given x[n]={3,-1,0,1,3,2,0,1,2,1}
 Let, N=5
Length of h[n], M= 3
Therefore, M-1= 2
We know,
 N=(L+M-1)
 5=L+3-1
 L=3
∴Pad L-1=2 zeros with h[n] i.e. h[n]={1,1,1,0,0}
SOLVED EXAMPLE

11. 11
3 -1 0 1 3 2 0 1 2 1
0 1 2
x2[n]
x4[n]
x3[n]
M-1(=2) no. of zeros
L(=3) no. of new data
3 -1 0 0 0
1 3 2 0 0
Input sequence x[n]
x1[n]
1 0 0 0 0
0 0

12. 12
Performing yk[n]= xk[n] h[n], where k=1,2,3,4
1. y1[n]=
2. y2[n]=
3. y3[n]=
4. y4[n]=
{3,2,2,-1,0}
{1,4,6,5,2}
{0,1,3,3,2}
{1,1,1,0,0}
N

13. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2
30

14. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2 0 4 6
31

15. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2 0 4 6 5 3 3
32

16. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2 0 4 6 5 3 3 4 3
33

17. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2 0 4 6 5 3 3 4 3 1 0 0
34

18. 1 4 6 5 2
0 1
1 1 1 0 0
+=> add
n- 0 1 2 3 4 5 6 7 8 9 10 11 12 13
y1[n]
y1[n]
y1[n]
y1[n]
3 2 2 -1 0
+ +
++
3 3 2
+ +
y[n] 3 2 2 0 4 6 5 3 3 4 3 1 0 0
35

19. REFERENCE:
19
 Digital Signal Processing - P. Rameshbabu
 Discrete Time Signal Processing - Oppenheim & Schafer