FIR library

This library implements the Finite Impulse Response (FIR) filters for Q15 data type. Fast versions of Q15 is provided on Cortex-M4.
The functions operate on blocks of input and output data and each call to the function processes blockSize samples through the filter. Pointers pSrc and pDst point to input and output arrays containing blockSize values.

Algorithm

The FIR filter algorithm is based upon a sequence of multiply-accumulate (MAC) operations. Each filter coefficient b[n] is multiplied by a state variable which equals a previous input sample x[n] :

y[n] = b[0]*x[n] + b[1]*x[n-1] + b[2]*x[n-2] + ...+ b[numTaps-1]*x[n-numTaps+1]

pCoeffs points to a coefficient array of size numTaps. Coefficients are stored in time reversed order :

{b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}

pState points to a state array of size numTaps + blockSize - 1. Samples in the state buffer are stored in the following order :

x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]

Note that the length of the state buffer exceeds the length of the coefficient array by blockSize-1. The increased state buffer length allows circular addressing, which is traditionally used in the FIR filters,
to be avoided and yields a significant speed improvement. The state variables are updated after each block of data is processed; the coefficients are untouched.

Instance Structure

The coefficients and state variables for a filter are stored together in an instance data structure. A separate instance structure must be defined for each filter.
Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.

Initialization Function

There is also an associated initialization function for Q15 data type. The initialization function performs the following operations :

Use of the initialization function is optional. However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
To place an instance structure into a const data section, the instance structure must be manually initialized. Set the values in the state buffer to zeros before static initialization.

The code below statically initializes Q15 data type filter instance structure :

TFIR_Instance firInstance = {numTaps, pState, pCoeffs};

where :

Fixed-Point Behavior

Care must be taken when using Q15 fixed-point FIR filter functions. In particular, the overflow and saturation behavior of the accumulator must be considered. Refer to the function descriptions below for usage guidelines.

Scaling and Overflow Behavior

This fast Q15 library uses a 32-bit accumulator with 2.30 format. The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.
Thus, if the accumulator result overflows it wraps around and distorts the result. In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits.
The 2.30 accumulator is then truncated to 2.15 format and saturated to yield the 1.15 result.

Library Routines

FIR_Init

Prototype

function FIR_Init(firInstance : ^TFIR_Instance; numTaps : uint16_t; pCoeffs : ^q15_t; pState : ^q15_t; blockSize : uint32_t) : byte;
Description

This function initializes FIR filter.
Parameters
  • firInstance: points to an instance of the the Q15 FIR filter structure.
  • numTaps: Number of filter coefficients in the filter.
  • pCoeffs: points to the filter coefficients buffer.
  • pState points to the state buffer.
  • blockSize: the number of samples that are processed per call.

pCoeffs points to the array of filter coefficients stored in time reversed order :

{b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}

Note that numTaps must be even and greater than or equal to 4. To implement an odd length filter simply increase numTaps by 1 and set the last coefficient to zero. For example, to implement a filter with numTaps=3 and coefficients :

{0.3, -0.8, 0.3}

set numTaps=4 and use the coefficients :

{0.3, -0.8, 0.3, 0}.

Similarly, to implement a two point filter :

{0.3, -0.3}

set numTaps=4 and use the coefficients :

{0.3, -0.3, 0, 0}.

pState points to the array of state variables. pState is of length numTaps+blockSize-1, where blockSize is the number of input samples processed by each call of arm_fir_fast_q15.
Returns
  • 0 - if initialization is successful.
  • 1 - if numTaps is not even or if is less than 4.
Requires

Nothing.
Example 
const NUM_TAPS            as word = 30
const TEST_LENGTH_SAMPLES as word = 320
const BLOCK_SIZE          as word = 32

const firCoeffsQ15 as integer[NUM_TAPS] = (
  integer(0xFFC4), integer(0xFFCC), 0x0000, 0x0079, 0x0109, 0x0118, 0x0000, integer(0xFDC6),
  integer(0xFBA1), integer(0xFBBB), 0x0000, 0x08A8, 0x137B, 0x1C89, 0x2010, 0x1C89,
  0x137B, 0x08A8, 0x0000, integer(0xFBBB), integer(0xFBA1), integer(0xFDC6), 0x0000, 0x0118,
  0x0109, 0x0079, 0x0000, integer(0xFFCC), integer(0xFFC4), 0x0000
)

dim S as TFIR_Instance
    numTaps   as word
    firStateQ15 as integer[BLOCK_SIZE + NUM_TAPS - 1]
    blockSize as longword

numTaps = NUM_TAPS
blockSize = BLOCK_SIZE

' Call FIR init function to initialize the instance structure
FIR_Init(@S, numTaps, @firCoeffsQ15, @firStateQ15, blockSize)
Notes

None.

FIR_Fast

Prototype

procedure FIR_Fast(const firInstance : ^TFIR_Instance; pSrc : ^q15_t; pDst : ^q15_t; blockSize : uint32_t);
Description

This function applies FIR filter.
Parameters
  • firInstance: points to an instance of the Q15 FIR filter structure.
  • pSrc: points to the block of input data.
  • pDst: points to the block of output data.
  • blockSize: number of samples to process per call.
Returns

Nothing.
Requires

Nothing.
Example 
const NUM_TAPS            as word = 30
const TEST_LENGTH_SAMPLES as word = 320
const BLOCK_SIZE          as word = 32

const firCoeffsQ15 as integer[NUM_TAPS] = (
  integer(0xFFC4), integer(0xFFCC), 0x0000, 0x0079, 0x0109, 0x0118, 0x0000, integer(0xFDC6),
  integer(0xFBA1), integer(0xFBBB), 0x0000, 0x08A8, 0x137B, 0x1C89, 0x2010, 0x1C89,
  0x137B, 0x08A8, 0x0000, integer(0xFBBB), integer(0xFBA1), integer(0xFDC6), 0x0000, 0x0118,
  0x0109, 0x0079, 0x0000, integer(0xFFCC), integer(0xFFC4), 0x0000
)

dim cnt as word 
    numBlocks as longword
    S as TFIR_Instance
    inputQ15  as integer[TEST_LENGTH_SAMPLES]
    outputQ15 as integer[TEST_LENGTH_SAMPLES]  
    blockSize as longword
    numTaps   as word
    firStateQ15 as integer[BLOCK_SIZE + NUM_TAPS - 1]

numBlocks = TEST_LENGTH_SAMPLES/BLOCK_SIZE
numTaps = NUM_TAPS
blockSize = BLOCK_SIZE

' Call the FIR process function for every blockSize samples
for cnt = 0 to (numBlocks - 1)
  FIR_Fast(@S, @inputQ15 + (cnt * blockSize), @outputQ15 + (cnt * blockSize), blockSize)
next cnt
Notes

None.