Calculation of common second-order IIR filter systems

Original address: http://home.eeworld.com.cn/my/space.php? Uid = 210489 & Do = Blog & id = 52787

 

The IIR filter is an infinite Impact Response filter. Its advantages are as follows: 1. It is easy to understand with the standard design of simulated prototype filter. 2. Low-level design can be used for implementation and high-speed operation. 3. For a design scheme with the same tolerances, the order number is shorter than that of FIR. 4. Closed-Loop design can be used. Disadvantages: 1. Non-Linear Phase 2. Limitation cycles may occur. 3. Multi-channel design is difficult. Low-pass, high-pass, and band-pass can only be designed. 4. Instability will be introduced in feedback.

5. It is very difficult to obtain high-speed Pipeline Design

 

The IIR filter can simulate four types of prototype filters: Butterworth, chebyshevi, chebyshevii, and elliptic. Typical Second-order filter function formula: H (z) = (b0 + B1 * Z ^-1 + B2 * Z ^-2) /(A0 + A1 * Z ^-1 + A2 * Z ^-2); typical ideal IIR output formula: Y (n) = {b0x (n) + b1x (n-1) +... + BMX (n-m)}-{a1x (n-1) + a2x (n-2) +... + AMX (n-m)} output formula for second-order IIR filter

Y (n) = b0xn + b1xn-1 + b2xn-2-(a1xn-1 + a2xn-2) Type 1

In Formula 1, A1, A2, B0, B1, and b2 are the two-order filter IIR coefficients, which determine the frequency response curve and gain of the filter. How to obtain A0, A1, A2, B0, B1, B2? For a second-order IIR filter, the standard technical indicators are as follows: 1. center frequency f0; 2. sampling frequency fs; 3. Gain dB; 4. quality factor;

Based on the above technical indicators, we can determine the low-pass, band-pass or high-pass coefficients of the second-order IIR filter.

Based on the above technical indicators, we can determine the following general calculation workload: A = SQRT [10 ^ (dB/20)]; Omega = 2 * pI * f0/Fs; sin = sin (OMEGA); cons = cos (OMEGA); alpha = sin (2 * q); therefore, the second-order IIR high-pass filter coefficient calculation: b0 = (1 + cos) /2; b1 =-(1 + cos); b2 = (1 + cos)/2; a0 = 1 + Alpha; a2 = 1-alpha; calculation of second-order IIR low-pass filter coefficients: b0 = (1-Cos)/2; b1 = 1-Cos; b2 = (1-Cos)/2; a0 = 1 + Alpha; a1 =-2 * Cos; a2 = 1-alpha; coefficient calculation of second-order IIR band-pass filter: b0 = sin/2 = Q * alhpa; b1 = 0; b2 =-Sin/2 =-Q * Alpha; a0 = 1 + Alpha; a1 =-2 * Cos;

A2 = 1-alpha;