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IIR.asm      Infinite impulse response filter (IIR)

Analog Devices, Inc.
DSP Division
Three Technology Way
P.O. Box 9106
Norwood, MA 02062

23-JUNE-2001 BJM

This directory contains an example ADSP-2191, single-core Infinite 
Impulse Response (IIR) filter.  
The IIR code uses coefficients, in an ordered array and applies them to
the filter. A detailed discussion of the IIR algorithm can be found 
in the source header comments of "IIR.ASM".

Files contained in this directory:

iir.asm      		ADSP-2191 source for an example IIR filter
iir_test.asm      	ADSP-2191 source to call iir.asm
adsp-2191.ldf     	Linker description file for the IIR example
iir.dpj          	The VDSP project file for the IIR example.
inreal_256.dat         	Input data for IIR example in 1.15 format.
coefs_hex.dat    	Coefficients for IIR example in 1.15 format.
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CONTENTS

I.    FUNCTION/ALGORITHM DESCRIPTION
II.   IMPLEMENTATION DESCRIPTION
III.  DESCRIPTION OF INPUT DATA         

I. FUNCTION/ALGORITHM DESCRIPTION

The IIR filter code executes a canonical form (also called direct form II)
realization structure.  The equation of the canonical form is
    
    w(n)=x(n) + b1*w(n-1) + b2*w(n-2)
    y(n)=w(n) + a1*w(n-1) + a2*w(n-2)

The input sample is x(n) and the output is y(n).  The term w(n) is the
intermediate value; w(n-1) is the previous value and w(n-2) the one before
that.  The variables a and b are the coefficients for the filter.

This example of canonical equation uses a variant that limits the summation
in the canonical form to two.  This type of IIR is called a biquad and is a 
second order filter.  Higher order filters can be achieved by cascading several
sections of biquads together.


II.   IMPLEMENTATION DESCRIPTION

The assembly language module IIR_TEST.ASM initializes the input and 
coefficient buffers and then calls IIR.ASM.   
     
The first buffer declared, INBUF, is N_samp sample locations long.

The next buffer declared, OUTBUF, is also N_samp samples long, and stores the 
output of the filter.

DLINE is the third buffer declared.  This buffer holds the delay line for each
biquad.  That is w(n-1) and w(n-2) for each biquad section of the filter.  Since
there are two past intermediate vales for each stage of the biquad, the length of
this buffer is twice as long as the stages.

The coefficient buffer, COEFS, contains the IIR filter coefficients.  The 
coefficients are typically generated by a filter 
design software package.

The linker descriptive file is ADSP-2191.LDF, which describes the hardware in 
terms of memory spaces and peripherals.

Because there is no data dependency between DSP cores, it is possible 
to do perform an IIR in DSP core 1, while also performing an IIR in DSP core 2 
on separate input data, using different coefficients.


III.  DESCRIPTION OF INPUT DATA

1. INPUT SAMPLES:
-----------------
This IIR routine expects input data which conforms to the following criteria:

Generate input data such that an array of input fixed point values are 
in 1.15 format, with the data being arranged in the following order:

INPUT DATA

indata(0)      
indata(1)      
indata(2)      
indata(3)      
etc...         


2. COEFFICIENT DATA:
-----------------------
This IIR routine expects [Biquad_secs*4] fixed point values to be used as coefficients.


COEFFICIENT DATA

A2(0)
A1(0)
B2(0)
B1(0)
... 
... 
...