# 3.3 Lab 2: lab

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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. (Whynot?)

To implement the fourth-order filter, start with a single set of second-order coefficients and implement a singlesecond-order section. Make sure you write and review pseudo-code before you begin programming. Once your single second-order IIR is working properly you canthen 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 1.0in 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 beas 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 tocompensate 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, thenwrite code that cycles through the second-order section code twice using the repeat structure below. Because the IIRcode 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 ofthe repeat loop.

stm (num_stages-1),AR1 start_stage ; IIR code goes here banz start_stage,*AR1-

## 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 doneusing the ld opcode with its optional shift parameter) before saving the output to memory.

• 1 point: Prelab
• 4 points: Code. Your DSP code implementing the fourth-order IIR filter is worth 3 points and the MATLABexercise is worth 1 point.
• 5 points: Oral quiz. The quiz may cover differences between FIR and IIR filters, the prelab material, and theMATLAB exercise.

explain and give four Example hyperbolic function
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