IIR Filtering: Exercise on TI TMS320C54x (ECE 320 specific) 2.4 2003/01/21 2003/07/31 10:32:29.013 GMT-5 Mark D. Butala butala@uiuc.edu Mark D. Butala butala@uiuc.edu Robert L. Morrison rlmorris@uiuc.edu infinite impulse response IIR LTI linear time-invariant direct fortm II difference equation zeros poles gain factor freqz impulse response notch filter butter quantize conv elinfinite impulse response IIR LTI linear time-invariant direct fortm II difference equation zeros poles gain factor freqz impulse response notch filter butter quantize conv elliptic low-pass filter ellip block repeat counter DSP You will implement a fourth-order, elliptical, low-pass infinite impulse-response (IIR) filter as a cascade of two second-order sections.

Implementation On the DSP, you will implement the elliptic low-pass filter designed using the ellip command from IIR Filters: Filter-Design Exercise in MATLAB. You should not try to implement the notch filter designed in IIR Filtering: Filter-Coefficient Quantization Exercise in MATLAB, because it will not work correctly when implemented using Direct Form II. (Why not?) To implement the fourth-order filter, start with a single set of second-order coefficients and implement a single second-order section. Make sure you write and review pseudo-code before you begin programming. Once your single second-order IIR is working properly you can then proceed to code the entire fourth-order filter.

Large coefficients You may have noticed that some of the coefficients you have computed for the second-order sections are larger than 1.0 in magnitude. For any stable second-order IIR section, the magnitude of the "0" and "2" coefficients ( a 0 and a 2 , for example) will always be less than or equal to 1.0. However, the magnitude of the "1" coefficient can be as large as 2.0. To overcome this problem, you will have to divide the a 1 and b 1 coefficients by two prior to saving them for your DSP code. Then, in your implementation, you will have to compensate somehow for using half the coefficient value.

Repeating code Rather than write separate code for each second-order section, you are encouraged first to write one section, then write code that cycles through the second-order section code twice using the repeat structure below. Because the IIR code will have to run inside the block I/O loop and this loop uses the block repeat counter (BRC), you must use another looping structure to avoid corrupting the BRC. You will have to make sure that your code uses different coefficients and states during the second cycle of the repeat loop.

Gain It may be necessary to add gain to the output of the system. To do this, simply shift the output left (which can be done using the ld opcode with its optional shift parameter) before saving the output to memory.

Grading Your grade on this lab will be split into three parts: 1 point: Prelab 4 points: Code. Your DSP code implementing the fourth-order IIR filter is worth 3 points and the MATLAB exercise is worth 1 point. 5 points: Oral quiz. The quiz may cover differences between FIR and IIR filters, the prelab material, and the MATLAB exercise.