1 / 20

BIEN425 – Lecture 13

BIEN425 – Lecture 13. By the end of the lecture, you should be able to: Outline the general framework of designing an IIR filter using frequency transform and bilinear transform

jin-garrison
Download Presentation

BIEN425 – Lecture 13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BIEN425 – Lecture 13 • By the end of the lecture, you should be able to: • Outline the general framework of designing an IIR filter using frequency transform and bilinear transform • Describe the differences between various classical analog filter (Butterworth, Chebyshev-I, Chebyshev-II and Elliptic) characteristics • Design classical analog filters (Butterworth, Chebyshev-I, Chebyshev-II and Elliptic)

  2. Design IIR filters by prototype filters • Most widely used design procedure • Filter design parameters obtained from filter design specifications • Recall: Fp, Fs, dp, ds

  3. Selectivity and Discrimination • Selectivity factor (r) • Discrimination factor (d) • Ideal filter (r = 1, d = 0)

  4. Analog filter 1 - Butterworth

  5. Butterworth • Magnitude response – Aa(f) • Fc is called 3-dB cut-off frequency • The poles of Ha(s) are:

  6. Butterworth • Laplace transform Ha(s) • The passband and stopband constraints are:

  7. Butterworth • Selecting the order (n) and the cutoff frequency (Fc)

  8. Analog filter 2 - Chebyshev-I

  9. Chebyshev-I • Magnitude response – Aa(f) • Where Tk+1(x) is called Chebyshev polynomial which is expressed recursively • Because Tn(1)=1, we can define the ripple factor e

  10. Chebyshev-I • The poles are on a ellipse • Laplace transform Ha(s) • Where b is defined as (-1)np0p1p2…pn-1 • Aa(0) is the DC gain • Order (n) is determined by

  11. Analog filter 3 - Chebyshev-II

  12. Chebyshev-II • Magnitude response – Aa(f) • Ripple factor

  13. Chebyshev-II • Laplace transform Ha(s) • Where b = sum of poles / sum of zeros • Poles are located at the reciprocals of the poles of Chebyshev-I • Zeros are located along the imaginary axis • Order (n) is computed the same way as Chebyshev-I

  14. Analog filter 4 - Elliptic

  15. Elliptic • Magnitude response – Aa(f) • Un is n-th order Jacobian elliptic function

  16. Elliptic • Finding the poles and zeros of elliptic filter requires iterative solution of nonlinear algebraic equations • Order (n)

  17. Comparison

  18. General method 1

  19. General method 2

  20. Using frequency + bilinear transform • We will cover this in the next lecture • Method 1: • Normalized lowpass (analog) • Frequency transformation to LP,HP,BP,BS (analog) • Bilinear transformation (digital) • Method 2: • Normalized lowpass (analog) • Bilinear transformation lowpass (digital) • Frequency transform to LP,HP,BP,BS (digital)

More Related