1. Signals and Systems Filter Design

2. Part III Design

3. Filter Design Techniques

4. Discrete-time filters

5. Discrete-time IIR filter

6. Specifications for DT filters

7. Specifications for DT filters in Log domain

8. A Design Example

9.  Discrete-time IIR filter design is done using analog filter techniques: 1.Analog IIR filter design methods have simple closed form solutions; 2.Design examples have existed for years. 3.Direct design of IIR filters has traditionally been avoided 4.Direct design of FIR filters is possible. Discrete-time IIR filter

10. Discrete-time IIR filter Design Flow

11. Discrete-time IIR filter Design 1. Poles on the jΩ axis in the s-plane correspond to poles on the unit circle in the z-plane. 2. Poles in the left half of the s-plane correspond to poles inside the unit circle in the z-plane. Hence stable and causal continuous-time filters will produce stable and causal discrete-time filters.

12. Traditional Analog Filter Design

14. Butterworth Design

16. Chebyshev filters

19. Elliptic filters

20. Example

21. Filter Design Techniques Impulse Invariance Bilinear Transformation

23.  The design technique is as follows:  (1) Perform a partial fractions expansion on H(s).  (2) Transform each pole into its - transform equivalent.  (3) Combine the terms into a single polynomial.

28. Impulse Invariance

29. Butterworth Design To get a stable and causal filter, choose H c (s) to implement the poles in the left-hand plane.

31. Butterworth Filter

32. Butterworth Filter-Impulse Invariance

34. Example: Impulse Invariance Take T = 1, value of T will not change the discrete-time filter results.)

35. Bilinear Transformation

36. Bilinear Transform To avoid aliasing, we need a one-to-one mapping from the s-plane to the z-plane.

37. Bilinear Transform: Freq axis

38. Bilinear Transformation  Transformation is unaffected by scaling. Consider inverse transformation with scale factor equal to unity  For  and so

39. Bilinear Transformation  Mapping of s-plane into the z-plane

40. Bilinear Transformation  Nonlinear mapping introduces a distortion in the frequency axis called frequency warping  Effect of warping shown below

41. Bilinear Transformation (Graphical Translation)

42. 1.Perform frequency prewarp to obtain the corresponding analog filter specs (pick any T) 2.Design the analog filter H c (s) using any one of the analog filter prototypes. 3.Transform H c (s) to H(z). Bilinear Transform: Design Procedure

43. Example

44. Bilinear Transform: Ex.

45. Bilinear Transform

46. FIR Filter Design

47. Windowing Principal

48. Windowing: Frequency Interpretation

49. Windowing Effects

53. Rectangular Window

54. Common Windows

55. Common window

56. Effect of Windowing

57. Windows Freq Domain

58. Other Windows in Feq Domain

59. Comparison

65. Kaiser Method

66. Kaiser

70. Marks McClellan Algo

71. Parks McClellan Algorithm

72. Butterworth Approx. in MATLAB

73. Butterworth Approximation

74. Chebyshev Approximation

75. Elliptic Approximation in MATLAB

76. Elliptic Approximation