2. FILTER DESIGN

3. Ideal Filter Magnitude Response NumericLogaritmic

4. StopbandPassband Transition Band Non Ideal Filter Magnitude Response In Numeric

5. N Order Filter Design Infinite Impulse ResponseFinite Impulse Response Difference Equation Transfer Function/ Frequency Response Difference Equation Transfer Function/ Frequency Response Impulse Response

7. Type of IIR Digital Filter Butterworth Chebyschev 1 Chebyschev 2Elliptic

8. Steps to Design IIR Digital Filter 1. Sketch Magnitude Response of Digital Filter as the specification needed 2. Determine Digital Frequency of Required Filter 3. Convert digital frequency to analogue frequency 4. Backward Process : Determine Cut off Frequency of Normalized LPF 5. Determine Filter Order 6. Design Normalized LPF Analogue Filter 7. Forward Process : Design Analogue Filter as needed specification via analog to analog transformation 8. Design digital filter from analogue filter via analog to digital transformation (bilinear/impulse invarian)

9. IIR Design Steps Prewarp Backward Forward/Analog to Analog Transformation Analog to Digital Transformation Analog Domain

10. StopbandPassband Transition Band Steps 1

11. Steps 2 and 3 Steps 2 (Digital Frequency) rad/sample Steps 2 (Digital Frequency) rad/sample Steps 3 (Analog Frequency /Prewarping) rad/s Steps 3 (Analog Frequency /Prewarping) rad/s

12. Remember ! Digital Freq. Analog Freq.

13. Steps 4 : Backward LPF

14. Steps 4 : Backward HPF

15. Steps 4 : Backward BPF

16. Steps 4 : Backward BSF

17. Steps 5 : Filter Order Remember !!! R p & R s must be in dB

18. Steps 5 : Filter Order Remember !!! R p & R s must be in dB

19. Steps 6 : LPF Normalized N order At page 127, Fundamental DSP, Ludeman

20. Steps 6 : LPF Normalized N order b 0 could be found at page 140, Fundamental DSP, Ludeman, Next Slide

21. Steps 6 : LPF Normalized N order

23. Steps 7 : LPF Required / Analog to Analog Transformation FILTERFORWARD LPF HPF BPF BSF

24. Steps 8 : Digital Filter Required / Analog to Digital Transformation Bilinear Transformation Impulse Invariance Transformation Can be removed, and must be removed if from step 2 2Fs was already removed

25. Problem 1 Digital Filter has Specification : – Pass the signal more than 2 kHz and less than 6 kHz with passband attenuation more than -3 dB – Stop the signal less than 100 Hz and more than 9 kHz with stopband attenuation less than -10 dB – There is no ripple either in passband area or stopband area – Bilinear Transformation – Sampling Frequency is 20 kHz

26. Problem 2 Digital Filter has Specification : – Pass the signal below 200 Hz and more than 8 kHz with passband attenuation more than 3 dB – Stop the signal between 2 kHz and 6 kHz with stopband attenuation less than 6 dB – There is no ripple at all band – Bilinear Transformation – Sampling Frequency is 20 kHz Design the digital filter ! Check the filter !

27. Problem 3 Digital Filter has Specification : – Stop the signal below 1 kHz and more than 8 kHz with stopband attenuation more than 10 dB – Pass the signal between 4 kHz and 6 kHz with passband attenuation less than 3 dB – There is no ripple at all band – Bilinear Transformation – Sampling Frequency is 20 kHz Design the digital filter ! Check the filter !

28. Problem Digital Filter has Specification : – Pass the signal below 1 kHz with passband attenuation more than -3 dB – Stop the signal above 9 kHz with stopband attenuation less than -14 dB – There is ripple in passband area – Bilinear Transformation – Sampling Frequency is 20 kHz Design the digital filter ! Check the filter !

29. Question 1.Design the digital Filter with explained steps ! 2.Determine the magnitude when f=0, f=5 kHz, and f=10 kHz, make a conclusion ! 3.Realize the filter !

30. 1. Gambarkan respon magnituda filter digital sesuai spesifikasi yang diketahui 2. Ubah parameter frekuensi ke domain analog 3. Hitung orde filter 4. Rancang Filter Analog LPF Ternormalisasi 5. Rancang Filter Analog Sesuai Spesifikasi yang Diinginkan 6. Rancang Filter digital dari filter analog sebelumnya dengan transformasi digital (Impulse Invarian / Bilinier)

32. 2 Methods FIR Filter Design Windowing MethodFrequency Sampling Method Inverse Discrete Time Fourier Transform / ITFWD Windowing Sampling Inverse Discrete Fourier Transform/IDFT/IFFT

33. FIR FILTER DESIGN

34. Steps 1.Sketch Magnitude Response of Digital Filter as the specification needed 2.Determine the ideal impulse response h i (n) from Magnitude Response 1 st step by Inverse DTFT (look up the table) 3.Determine the delay /symmetrical axis (  ), filter order (N), Filter length (M) 4.Determine and calculate the delayed impulse response in which the delay was determined from 3 rd step, from 0 to N (N-filter order with N+1 filter length) 5.Calculate the coefficient of the window used from 0 to N (N-filter order with N+1 filter length) (given) 6.Multiply the result of 4 th and 5 th step to determine the overall filter coefficient

35. N-order Windowing Methods FIR Filter Design Inverse Discrete Time Fourier Transform / ITFWD Windowing Filter length : N+1

36. Steps 1-2 (Several Ideal Magnitude Response) LPF

37. Steps 1-2 (Several Ideal Magnitude Response) HPF

38. Steps 1-2 (Several Ideal Magnitude Response) BPF

39. Steps 1-2 (Several Ideal Magnitude Response) BSF

40. Steps 1-2 (Several Ideal Magnitude Response) All Pass Filter/Hilbert Transform

41. Steps 1-2 (Several Ideal Magnitude Response) Differensiator

42. Steps 3 Determining , N (Filter Order), M (Filter length)

43. Steps 4 Calculating h i (n-  )

44. Steps 5 Calculating w(n)

45. Steps 6 Calculating h(n)=h i (n)w(n)

46. Latihan  Diketahui suatu filter dengan respon berikut 1. Rancanglah filter tsb ! 2. Ceklah filter hasil perancangan

47. FIR FILTER DESIGN

48. 47 Desired real-valued frequency response: Frequency-Sampling Method: Basic Principle Approximation error: Samples of Approximation of ideal frequency response:

49. 48 Example: magnitude responses (linear scale) Task of a): transition region width= Task of b): transition region width= k=0k=1k=2k=3 k=5 k=6k=7 a) k=4 b) k=4

50. 2 Methods FIR Filter Design Windowing MethodFrequency Sampling Method Inverse Discrete Time Fourier Transform / ITFWD Windowing Sampling Inverse Discrete Fourier Transform/IDFT/IFFT

51. Sampling Frequency Formula 50 N = Length of FIR filter

52. Latihan D