SLAAEH6 September   2024 TAA5212 , TAA5412-Q1 , TAC5111 , TAC5111-Q1 , TAC5112 , TAC5211 , TAC5212 , TAC5212-Q1 , TAC5311-Q1 , TAC5312-Q1 , TAC5411-Q1 , TAC5412-Q1 , TAD5112 , TAD5112-Q1 , TAD5212 , TAD5212-Q1

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Infinite Impulse Response Filters
    1. 2.1 Digital Biquad Filter
  6. 3TAC5x1x and TAC5x1x-Q1 Digital Biquad Filters
    1. 3.1 Filter Design using PurePath™ Console
      1. 3.1.1 Example of Programming Biquad Filters Using PurePath™ Console
    2. 3.2 Generating Coefficients N0, N1, N2, D1, D2 using a Digital Filter Design Package
    3. 3.3 Avoiding Overflow Conditions
    4. 3.4 Biquad Filter Allocation on Recording Channel
    5. 3.5 Biquad Filter Allocation on Playback Channel
    6. 3.6 Biquad Filter Programming Example on the TAC5x1x
  7. 4Typical Audio Applications of Biquad Filters
    1. 4.1 Parametric Equalizers
    2. 4.2 Crossover Networks
    3. 4.3 Voice Boost
    4. 4.4 Bass Boost
    5. 4.5 Removing 50Hz–60Hz Hum With Notch Filters
  8. 5Summary
  9. 6References

2.1 Digital Biquad Filter

A digital biquad filter is a second-order IIR digital filter. The filter is represented is a ratio of two quadratic equations, hence called biquad (or bi-quadratic). The transfer function of a biquad filter is specified in Equation 2, and Figure 2-1 shows the Direct Form II block diagram implementation for the same. In this equation, the coefficients are normalized so that a0 = 1 through the division of all the coefficients by a0.
Equation 2. H ( z )   =   b 0   +   b 1 z - 1   +   b 2 z - 2 1   +   a 1 z - 1   +   a 2 z - 2

Direct Form II Biquad Filter

Figure 2-1 Direct Form II Biquad Filter

Different values of the filter coefficients a1, a2, b0, b1 and b2 result in different filter frequency responses.