circular convolution and Linear convolution

circular convolution and Linear convolution

1. DIGITAL SIGNAL
PROCESSING
MODULE- 2
Circular Convolution,
Linear Filtering
By
Ms.J.Shiny Christobel, AP/ECE,
Sri Ramakrishna Institute of Technology, Coimbatore
1

2. X1(n) is fixed & marked in Anti Clockwise Direction
X2(n) is marked in clockwise direction . But
Rotation in Anti Clockwise Direction
Solution:
2 9-May-24

3. X1(n)
3
X2(n)
1
-1
3
-2
1
-1
2
3
0
0
y(0) = [1x1] + [-1x0] + [-2x0] + [3x3] + [2x-1]

= 1 + 0 + 0 + 9 - 2 = 8
Rotate x
2(n) in anti-
clockwise direction
9-May-24

4. X1(n)
4
X2(n)
1
-1
3
-2
2
-1
3
0
0
1
y(1) = [1x2] + [-1x1] + [-2x0] + [3x0] + [3x-1]

= 2 - 1 + 0 + 0 - 3 = -2
9-May-24

5. X1(n)
5
X2(n)
1
-1
3
-2
3
-1
0
0
1
2
y(2) = [1x3] + [-1x2] + [-2x1] + [3x0] + [0x-1]

= 3 - 2 - 2 + 0 + 0 = -1
9-May-24

6. X1(n)
6
X2(n)
1
-1
3
-2
0
-1
0
1
2
3
y(3) = [1x0] + [-1x3] + [-2x2] + [3x1] + [0x-1]

= 0 - 3 - 4 + 3 + 0 = -4
9-May-24

7. X1(n)
7
X2(n)
1
-1
-2
0
-1
1
2
3
0
3
y(4) = [1x0] + [-1x0] + [-2x3] + [3x2] + [1x-1]
= 0 + 0 - 6 + 6 - 1 = -1
Ans:
y(n) = { 8, -2, -1, -4, -1 }
9-May-24

8. 8 9-May-24

9. 9 9-May-24

10. 10 9-May-24

11. 11 9-May-24

12. 12 9-May-24

13. 13 9-May-24

14. Linear Convolution
14 9-May-24

15. Circular Convolution without zero padding
15 9-May-24

16. Circular Convolution with zero padding
x(n) = {1,2,3,1} , length of x(n) is L = 4
h(n) = {1,1,1} , length of h(n) is M = 3
if
append (L-1) zeroes at the end of x(n)
append (M-1) zeroes at the end of h(n)
then the given sequence will be
x(n) = {1,2,3,1,0,0}
h(n) = {1,1,1,0,0,0}
16 9-May-24

17. 17 9-May-24

18. 18 9-May-24

19. 19 9-May-24

20. Use of FFT in Linear Filtering
Methods:
(1)Overlap Add Method
(2)Overlap Save Method

Fast Convolution
Linear filtering Long Sequences
20 9-May-24

21. 21 9-May-24

22. 22 9-May-24

23. 23 9-May-24

24. 24 9-May-24

25. 25 9-May-24

26. 26 9-May-24

27. 27 9-May-24

28. 28 9-May-24

29. 29 9-May-24

30. 30 9-May-24

31. 31 9-May-24

32. 32 9-May-24

33. 33 9-May-24

34. 34 9-May-24

35. 35 9-May-24

36. 36 9-May-24

37. 37 9-May-24

38. 38 9-May-24

39. 39 9-May-24