Normalized LMS Filters

Collaboration diagram for Normalized LMS Filters:

Functions
void	tpt_lms_norm_f32 (f32_t *aOutData, f32_t *aErrData, tpt_lms_norm_f32_t *aFilter, const f32_t *aInData, const f32_t *aRefData, uint32_t aCount)
	Processing function for floating-point normalized LMS filter. More...
void	tpt_lms_norm_init_f32 (tpt_lms_norm_f32_t *aFilter, uint16_t aTaps, f32_t *aCoeffs, f32_t *aState, f32_t aMu, uint32_t aCount)
	Initialization function for floating-point normalized LMS filter. More...
void	tpt_lms_norm_init_q15 (tpt_lms_norm_q15_t *aFilter, uint16_t aTaps, q15_t *aCoeffs, q15_t *aState, q15_t aMu, uint32_t aCount, uint8_t aShift)
	Initialization function for Q15 normalized LMS filter. More...
void	tpt_lms_norm_init_q31 (tpt_lms_norm_q31_t *aFilter, uint16_t aTaps, q31_t *aCoeffs, q31_t *aState, q31_t aMu, uint32_t aCount, uint8_t aShift)
	Initialization function for Q31 normalized LMS filter. More...
void	tpt_lms_norm_q15 (q15_t *aOutData, q15_t *aErrData, tpt_lms_norm_q15_t *aFilter, const q15_t *aInData, const q15_t *aRefData, uint32_t aCount)
	Initialization function for Q15 normalized LMS filter. More...
void	tpt_lms_norm_q31 (q31_t *aOutData, q31_t *aErrData, tpt_lms_norm_q31_t *aFilter, const q31_t *aInData, const q31_t *aRefData, uint32_t aCount)
	Initialization function for Q31 normalized LMS filter. More...

Detailed Description

This set of functions implements a commonly used adaptive filter. It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization factor which increases the adaptation rate of the filter. The DSP Library only contains normalized LMS filter functions that operate on floating-point data types.

A normalized least mean square (NLMS) filter consists of two components as shown below. The first component is a standard transversal or FIR filter. The second component is a coefficient update mechanism. The NLMS filter has two input signals. The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter. That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input. The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input. This "error signal" tends towards zero as the filter adapts. The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.

Internal structure of the NLMS adaptive filter

The functions operate on blocks of data and each call to the function processes aCount samples through the filter. aInData points to input signal, aRefData points to reference signal, aOutData points to output signal and aErrData points to error signal. All arrays contain aCount values.

The functions operate on a block-by-block basis. Internally, the filter coefficients b[n] are updated on a sample-by-sample basis. The convergence of the LMS filter is slower compared to the normalized LMS algorithm.

Algorithm

The output signal y[n] is computed by a standard FIR filter:

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

The error signal equals the difference between the reference signal d[n] and the filter output:

    e[n] = d[n] - y[n].
  

After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:

    E = x[n] ^ 2 + x[n - 1] ^ 2 + ... + x[n - uTaps + 1] ^ 2.
  

The filter coefficients b[k] are then updated on a sample-by-sample basis:

    b[k] = b[k] + e[n] * (fMu / E) * x[n - k],  for k = 0, 1, ..., uTaps - 1
  

where fMu is the step size and controls the rate of coefficient convergence.

In the APIs, pCoeffs points to a coefficient array of size uTaps. Coefficients are stored in time reversed order.

    { b[uTaps - 1], b[uTaps - 2], ..., b[1], b[0] }
  

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

    { x[n - uTaps + 1], x[n - uTaps], x[n - uTaps - 1], ..., x[0],
      x[1], x[2], ..., x[aCount - 1] }
  

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

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 and coefficient and state arrays cannot be shared among instances.

Initialization Functions

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

• Sets the values of the internal structure fields.
• Zeros out the values in the state buffer. To do this manually without calling the init function, assign the follow subfields of the instance structure: uTaps, pCoeffs, fMu, fEnergy, fX0, pState. Also set all of the values in pState to zero.

Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.

Function Documentation

tpt_lms_norm_f32()

void tpt_lms_norm_f32	(	f32_t *	aOutData,
		f32_t *	aErrData,
		tpt_lms_norm_f32_t *	aFilter,
		const f32_t *	aInData,
		const f32_t *	aRefData,
		uint32_t	aCount
	)

Processing function for floating-point normalized LMS filter.

Parameters

[out]	aOutData	points to the block of output data.
[out]	aErrData	points to the block of error data.
[in]	aFilter	points to an instance of the floating-point normalized LMS filter structure.
[in]	aInData	points to the block of input data.
[in]	aRefData	points to the block of reference data.
[in]	aCount	number of samples to process

Returns

none

tpt_lms_norm_init_f32()

void tpt_lms_norm_init_f32	(	tpt_lms_norm_f32_t *	aFilter,
		uint16_t	aTaps,
		f32_t *	aCoeffs,
		f32_t *	aState,
		f32_t	aMu,
		uint32_t	aCount
	)

Initialization function for floating-point normalized LMS filter.

Parameters

[in]	aFilter	points to an instance of the floating-point LMS filter structure.
[in]	aTaps	number of filter coefficients
[in]	aCoeffs	points to coefficient buffer.
[in]	aState	points to state buffer.
[in]	aMu	step size that controls filter coefficient updates
[in]	aCount	number of samples to process

Returns

none

Details

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

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

The initial filter coefficients serve as a starting point for the adaptive filter. aState points to an array of length aTaps + aCount - 1 samples, where aCount is the number of input samples processed by each call to tpt_lms_norm_f32().

tpt_lms_norm_init_q15()

void tpt_lms_norm_init_q15	(	tpt_lms_norm_q15_t *	aFilter,
		uint16_t	aTaps,
		q15_t *	aCoeffs,
		q15_t *	aState,
		q15_t	aMu,
		uint32_t	aCount,
		uint8_t	aShift
	)

Initialization function for Q15 normalized LMS filter.

Parameters

[in]	aFilter	points to an instance of the Q15 LMS filter structure.
[in]	aTaps	number of filter coefficients
[in]	aCoeffs	points to coefficient buffer.
[in]	aState	points to state buffer.
[in]	aMu	step size that controls filter coefficient updates
[in]	aCount	number of samples to process
[in]	aShift	bit shift applied to coefficients

Returns

none

Details

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

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

The initial filter coefficients serve as a starting point for the adaptive filter. aState points to an array of length aTaps + aCount - 1 samples, where aCount is the number of input samples processed by each call to tpt_lms_norm_f32().

tpt_lms_norm_init_q31()

void tpt_lms_norm_init_q31	(	tpt_lms_norm_q31_t *	aFilter,
		uint16_t	aTaps,
		q31_t *	aCoeffs,
		q31_t *	aState,
		q31_t	aMu,
		uint32_t	aCount,
		uint8_t	aShift
	)

Initialization function for Q31 normalized LMS filter.

Parameters

[in]	aFilter	points to an instance of the Q31 LMS filter structure.
[in]	aTaps	number of filter coefficients
[in]	aCoeffs	points to coefficient buffer.
[in]	aState	points to state buffer.
[in]	aMu	step size that controls filter coefficient updates
[in]	aCount	number of samples to process
[in]	aShift	bit shift applied to coefficients

Returns

none

Details

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

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

The initial filter coefficients serve as a starting point for the adaptive filter. aState points to an array of length aTaps + aCount - 1 samples, where aCount is the number of input samples processed by each call to tpt_lms_norm_f32().

tpt_lms_norm_q15()

void tpt_lms_norm_q15	(	q15_t *	aOutData,
		q15_t *	aErrData,
		tpt_lms_norm_q15_t *	aFilter,
		const q15_t *	aInData,
		const q15_t *	aRefData,
		uint32_t	aCount
	)

Initialization function for Q15 normalized LMS filter.

Processing function for Q15 normalized LMS filter.

Parameters

[in]	aFilter	points to an instance of the Q15 LMS filter structure.
[in]	aTaps	number of filter coefficients
[in]	aCoeffs	points to coefficient buffer.
[in]	aState	points to state buffer.
[in]	aMu	step size that controls filter coefficient updates
[in]	aCount	number of samples to process
[in]	aShift	bit shift applied to coefficients

Returns

none

tpt_lms_norm_q31()

void tpt_lms_norm_q31	(	q31_t *	aOutData,
		q31_t *	aErrData,
		tpt_lms_norm_q31_t *	aFilter,
		const q31_t *	aInData,
		const q31_t *	aRefData,
		uint32_t	aCount
	)

Initialization function for Q31 normalized LMS filter.

Processing function for Q31 normalized LMS filter.

Parameters

[in]	aFilter	points to an instance of the Q31 LMS filter structure.
[in]	aTaps	number of filter coefficients
[in]	aCoeffs	points to coefficient buffer.
[in]	aState	points to state buffer.
[in]	aMu	step size that controls filter coefficient updates
[in]	aCount	number of samples to process
[in]	aShift	bit shift applied to coefficients

Returns

none