AN540 datasheet(2/17 Pages) MICROCHIP

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DS00540B-page 2

Implementing IIR Digital Filters

DSPLAY is a trademark of Burr-Brown

DFDP is a trademark of Atlanta Signal Processing Inc.

Windows is a trademark of Microsoft Corporation

MathCad is a registered trademark of MathSoft, Inc.

The structure as shown in Figure 1 may be cascaded to

attain a higher order filter. For example, if two stages are

cascaded together, a 4th Order IIR Filter is obtained.

This way, the output of the 1st stage becomes the input

to the second stage. Multiple order filters are thus

implemented by cascading a 2nd order filter structure as

shown in Figure 1.

IMPLEMENTATION

A 4th order IIR Filter is implemented by cascading two

structures shown in Figure 1. The output Y (output of

each filter stage) is computed by direct implementation

of Equations (1) & (2). Since each stage is similar

algorithmically, it is implemented as a Macro using

Microchip’s Assembler/Linker for PIC17C42. This Macro

(labelled “BIQUAD”) is called twice for implementing a

4th order filter. The output of the 1st stage is directly fed

to the input of the second stage without any scaling.

Scaling is required depending on the particular applica-

tion. The user can modify the code very easily without

any penalty on speed. Also, saturation arithmetic is not

used. Overflows can be avoided by limiting the input

sequence amplitude. All numbers are assumed to be 16

bits in Q15 format (15 decimal points, MSB is sign bit).

Thus the user must scale and sign extend the input

sequence accordingly. For example, if the input is from

a 12-bit A/D converter, the user must sign extend the

12-bit input if bit 11 is a one.

The BIQUAD macro is a generic macro and can be used

for all IIR filters whether it is Low Pass, High Pass, Band

Pass or Band Stop. A general purpose 16x16 multiplier

routine is also provided. This routine is implemented as

a straight line code for speed considerations.

The 4th order IIR filter implemented is a Low Pass Filter

with the specifications as shown in Table 1.

BAND1

BAND2

Lower Band Edge

0.0

600 Hz

Upper Band Edge

500 Hz

1 Khz

Nominal Gain

1.0

0.0

Nominal Ripple

0.01

0.05

Maximum Ripple

0.00906

0.04601

Ripple in dB

0.07830

-26.75

Sampling Frequency = 2 Khz

TABLE 1 - FILTER CONSTANTS

The Low Pass Filter is designed using a digital filter

design package (DFDP by Atlanta Signal Processors

Inc.). The filter package produces filter constants of the

structure shown in Table 1. Table 2 shows the filter co-

efficients that are obtained for the above Low Pass filter

specification.

Co-efficients

Stage 1

-0.133331 0.167145 0.285431 0.462921 0.285431

Stage 2

0.147827 0.765900 0.698273 0.499908 0.698273

TABLE 2 - FILTER COEFFICIENTS

The above filter co-efficients (5 per stage) are quantized

to Q15 format (i.e they are multiplied by 32768) and

saved in program memory (starting at label

“_coeff_lpass”). The constants for both the stages are

read into data memory using TLRD and TABLRD in-

structions in the Initialization Routine (labelled

“initFilter”). The user may read the coefficients of only

one stage at a time and save some RAM at the expense

of speed.

The sample 4th order Low Pass IIR Filter is tested by

analyzing the impulse response of the filter. An impulse

signal is fed as input to the filter. This is simulated by

forcing the input to the filter by a large quantity (say

7F00h) on the first input sample, and the all zeros from

the 2nd sample onwards. The output sequence is the

filter’s impulse response and is captured

into the

PICMASTER’s (Microchip’s Universal In-Circuit Emula-

tor) real time trace buffer. This captured data from

PICMASTER is saved to file and analyzed. Analysis was

done using MathCad for Windows and DSP Analysis

program from Burr-Brown (DSPLAY). The Fourier Trans-

form of this Impulse response of the filter should display

the Filter’s frequency response, in this case being a Low

Pass type. The plots of the impulse response and the

frequency response are shown in figures below.

FIGURE 2 - IMPULSE RESPONSE

CAPTURED FROM PIC-MASTER

-4000

-2000

2000

4000

6000

8000

Impulse Response

Time *0.5 (mSec)

4-130

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