Digital Filters Part 2


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Introduction of infinite impulse response filters and adaptive filters

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Digital Filters Part 2

  1. 1. DIGITAL FILTERS <ul><li>Source: ANALOG DEVICES </li></ul>Part 2: Infinite Impulse Response (IIR) Filters
  2. 2. Introduction <ul><li>Purpose </li></ul><ul><ul><li>This module introduce the technology of Infinite Impulse Response (IIR) Filters, Multirate Filters and Adaptive Filters. </li></ul></ul><ul><li>Outline </li></ul><ul><ul><li>Introduce the technology of Infinite Impulse Response (IIR) Filters </li></ul></ul><ul><ul><li>Introduce the technology of Multirate Filters. </li></ul></ul><ul><ul><li>Introduce the technology of Adaptive Filters. </li></ul></ul><ul><li>Contents </li></ul><ul><ul><li>23 pages </li></ul></ul><ul><li>Duration </li></ul><ul><ul><li>15 Minutes </li></ul></ul>
  3. 3. Bandpass and Bandstop Filters Designed from Lowpass And Highpass Filters
  4. 4. Infinite Impulse Response (IIR) Filters <ul><li>Uses Feedback (Recursion) </li></ul><ul><li>Impulse Response has an Infinite Duration </li></ul><ul><li>Potentially Unstable </li></ul><ul><li>Non-Linear Phase </li></ul><ul><li>More Efficient than FIR Filters </li></ul><ul><li>No Computational Advantage when Decimating Output </li></ul><ul><li>Usually Designed to Duplicate Analog Filter Response </li></ul><ul><li>Usually Implemented as Cascaded Second-Order Sections (Biquads) </li></ul>
  5. 5. Hardware Implementation Of Second-order IIR Filter (Biquad) Direct Form 1
  6. 6. IIR Biquad Filter Direct Form 2
  7. 7. IIR Biquad Filter Simplified Notations
  8. 8. Review Of Popular Analog Filters <ul><li>Butterworth </li></ul><ul><ul><li>All Pole, No Ripples in Passband or Stopband </li></ul></ul><ul><ul><li>Maximally Flat Response (Fastest Roll-off with No Ripple) </li></ul></ul><ul><li>Chebyshev (Type 1) </li></ul><ul><ul><li>All Pole, Ripple in Passband, No Ripple in Stopband </li></ul></ul><ul><ul><li>Shorter Transition Region than Butterworth for Given Number of Poles </li></ul></ul><ul><ul><li>Type 2 has Ripple in Stopband, No Ripple in Passband </li></ul></ul><ul><li>Elliptical (Cauer) </li></ul><ul><ul><li>Has Poles and Zeros, Ripple in Both Passband and Stopband </li></ul></ul><ul><ul><li>Shorter Transition Region than Chebyshev for Given Number of Poles </li></ul></ul><ul><ul><li>Degraded Phase Response </li></ul></ul><ul><li>Bessel (Thompson) </li></ul><ul><ul><li>All Pole, No Ripples in Passband or Stopband </li></ul></ul><ul><ul><li>Optimized for Linear Phase and Pulse Response </li></ul></ul><ul><ul><li>Longest Transition Region of All for Given Number of Poles </li></ul></ul>
  9. 9. IIR Filter Design Techniques <ul><li>Impulse Invarient Transformation Method </li></ul><ul><ul><li>Start with H(s) for Analog Filter </li></ul></ul><ul><ul><li>Take Inverse Laplace Transform to get Impulse Response </li></ul></ul><ul><ul><li>Obtain z-Transform H(z) from Sampled Impulse Response </li></ul></ul><ul><ul><li>z-Transform Yields Filter Coefficients </li></ul></ul><ul><ul><li>Aliasing Effects Must be Considered </li></ul></ul><ul><li>Bilinear Transformation Method </li></ul><ul><ul><li>Another Method for Transforming H(s) into H(z) </li></ul></ul><ul><ul><li>Performance Determined by the Analog System’s Differential Equation </li></ul></ul><ul><ul><li>Aliasing Effects do not Occur </li></ul></ul><ul><li>Matched z-Transform Method </li></ul><ul><ul><li>Maps H(s) into H(z) for filters with both poles and zeros </li></ul></ul><ul><li>CAD Methods </li></ul><ul><ul><li>Fletcher-Powell Algorithm </li></ul></ul><ul><ul><li>Implements Cascaded Biquad Sections </li></ul></ul>
  10. 10. Throughput Considerations For IIR Filters <ul><li>Determine How Many Biquad Sections (N) are Required to Realize the Desired Frequency Response </li></ul><ul><li>Multiply this by the number of instruction cycles per Biquad for the DSP and add overhead cycles (5N + 2 cycles for the ADSP-21xx series, for example). </li></ul><ul><li>The Result (plus overhead) is the Minimum Allowable Sampling Period (1 / fs) for Real-Time Operation </li></ul>
  11. 11. Comparison Between FIR and IIR Filters
  12. 12. Decimation Of a Sampled Signal By a Factor of M
  13. 13. Decimation Combined With FIR Filtering
  14. 14. Interpolation by a Factor Of L
  15. 15. Effects of Interpolation on Frequency Spectrum
  16. 16. Typical Interpolation Implementation <ul><li>Efficient DSP algorithms take advantage of: </li></ul><ul><li>Multiplications by zero </li></ul><ul><li>Circular Buffers </li></ul><ul><li>Zero-Overhead Looping </li></ul>
  17. 17. Sample Rate Converters
  18. 18. Adaptive Filter
  19. 19. Digital Transmission using Adaptive Equalization
  20. 20. Linear Predictive Coding (LPC) Model of Speech Production
  21. 21. LPC Speech Companding System
  22. 22. All Pole Lattice Filter
  23. 23. Estimation of Lattice Filter Coefficients in Transmitting DSP
  24. 24. Additional Resource <ul><li>For ordering the ADSP-21xx, please click the part list or </li></ul><ul><li>Call our sales hotline </li></ul><ul><li>For additional inquires contact our technical service hotline </li></ul><ul><li>For more product information go to </li></ul><ul><li> </li></ul>