Functions | |
| void | arm_lms_init_f32 (arm_lms_instance_f32 *S, uint16_t numTaps, float32_t *pCoeffs, float32_t *pState, float32_t mu, uint32_t blockSize) |
| void | arm_lms_f32 (const arm_lms_instance_f32 *S, float32_t *pSrc, float32_t *pRef, float32_t *pOut, float32_t *pErr, uint32_t blockSize) |
| void | arm_lms_init_q31 (arm_lms_instance_q31 *S, uint16_t numTaps, q31_t *pCoeffs, q31_t *pState, q31_t mu, uint32_t blockSize, uint32_t postShift) |
| void | arm_lms_q31 (const arm_lms_instance_q31 *S, q31_t *pSrc, q31_t *pRef, q31_t *pOut, q31_t *pErr, uint32_t blockSize) |
| void | arm_lms_init_q15 (arm_lms_instance_q15 *S, uint16_t numTaps, q15_t *pCoeffs, q15_t *pState, q15_t mu, uint32_t blockSize, uint32_t postShift) |
| void | arm_lms_q15 (const arm_lms_instance_q15 *S, q15_t *pSrc, q15_t *pRef, q15_t *pOut, q15_t *pErr, uint32_t blockSize) |
LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions. LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal. Adaptive filters are often used in communication systems, equalizers, and noise removal. The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types. The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
An LMS 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 LMS 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 LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
Internal structure of the Least Mean Square filter
The functions operate on blocks of data and each call to the function processes blockSize samples through the filter. pSrc points to input signal, pRef points to reference signal, pOut points to output signal and pErr points to error signal. All arrays contain blockSize 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.
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[numTaps-1] * x[n-numTaps+1]
d[n] and the filter output:
e[n] = d[n] - y[n].
b[k] are updated on a sample-by-sample basis:
b[k] = b[k] + e[n] * mu * x[n-k], for k=0, 1, ..., numTaps-1
where mu is the step size and controls the rate of coefficient convergence. 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 order:
{x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
blockSize-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.
arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
where numTaps is the number of filter coefficients in the filter; pState is the address of the state buffer; pCoeffs is the address of the coefficient buffer; mu is the step size parameter; and postShift is the shift applied to coefficients.[-1 +1). The fixed-point functions have an additional scaling parameter postShift. At the output of the filter's accumulator is a shift register which shifts the result by postShift bits. This essentially scales the filter coefficients by 2^postShift and allows the filter coefficients to exceed the range [+1 -1). The value of postShift is set by the user based on the expected gain through the system being modeled.| void arm_lms_init_f32 | ( | arm_lms_instance_f32 * | S, |
| uint16_t | numTaps, | ||
| float32_t * | pCoeffs, | ||
| float32_t * | pState, | ||
| float32_t | mu, | ||
| uint32_t | blockSize | ||
| ) |
Initialization function for floating-point LMS filter.
| [in] | *S | points to an instance of the floating-point LMS filter structure. |
| [in] | numTaps | number of filter coefficients. |
| [in] | *pCoeffs | points to the coefficient buffer. |
| [in] | *pState | points to state buffer. |
| [in] | mu | step size that controls filter coefficient updates. |
| [in] | blockSize | number of samples to process. |
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]}
The initial filter coefficients serve as a starting point for the adaptive filter. pState points to an array of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_lms_f32(). Definition at line 61 of file arm_lms_init_f32.c.
| void arm_lms_f32 | ( | const arm_lms_instance_f32 * | S, |
| float32_t * | pSrc, | ||
| float32_t * | pRef, | ||
| float32_t * | pOut, | ||
| float32_t * | pErr, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for floating-point LMS filter.
This function operates on floating-point data types.
| [in] | *S | points to an instance of the floating-point LMS filter structure. |
| [in] | *pSrc | points to the block of input data. |
| [in] | *pRef | points to the block of reference data. |
| [out] | *pOut | points to the block of output data. |
| [out] | *pErr | points to the block of error data. |
| [in] | blockSize | number of samples to process. |
Definition at line 170 of file arm_lms_f32.c.
| void arm_lms_init_q31 | ( | arm_lms_instance_q31 * | S, |
| uint16_t | numTaps, | ||
| q31_t * | pCoeffs, | ||
| q31_t * | pState, | ||
| q31_t | mu, | ||
| uint32_t | blockSize, | ||
| uint32_t | postShift | ||
| ) |
Initialization function for Q31 LMS filter.
| [in] | *S | points to an instance of the Q31 LMS filter structure. |
| [in] | numTaps | number of filter coefficients. |
| [in] | *pCoeffs | points to coefficient buffer. |
| [in] | *pState | points to state buffer. |
| [in] | mu | step size that controls filter coefficient updates. |
| [in] | blockSize | number of samples to process. |
| [in] | postShift | bit shift applied to coefficients. |
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]}
The initial filter coefficients serve as a starting point for the adaptive filter. pState points to an array of length numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_lms_q31(). Definition at line 66 of file arm_lms_init_q31.c.
| void arm_lms_q31 | ( | const arm_lms_instance_q31 * | S, |
| q31_t * | pSrc, | ||
| q31_t * | pRef, | ||
| q31_t * | pOut, | ||
| q31_t * | pErr, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for Q31 LMS filter.
| [in] | *S | points to an instance of the Q15 LMS filter structure. |
| [in] | *pSrc | points to the block of input data. |
| [in] | *pRef | points to the block of reference data. |
| [out] | *pOut | points to the block of output data. |
| [out] | *pErr | points to the block of error data. |
| [in] | blockSize | number of samples to process. |
Definition at line 69 of file arm_lms_q31.c.
| void arm_lms_init_q15 | ( | arm_lms_instance_q15 * | S, |
| uint16_t | numTaps, | ||
| q15_t * | pCoeffs, | ||
| q15_t * | pState, | ||
| q15_t | mu, | ||
| uint32_t | blockSize, | ||
| uint32_t | postShift | ||
| ) |
Initialization function for the Q15 LMS filter.
| [in] | *S | points to an instance of the Q15 LMS filter structure. |
| [in] | numTaps | number of filter coefficients. |
| [in] | *pCoeffs | points to the coefficient buffer. |
| [in] | *pState | points to the state buffer. |
| [in] | mu | step size that controls filter coefficient updates. |
| [in] | blockSize | number of samples to process. |
| [in] | postShift | bit shift applied to coefficients. |
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]}
The initial filter coefficients serve as a starting point for the adaptive filter. pState points to the array of state variables and size of array is numTaps+blockSize-1 samples, where blockSize is the number of input samples processed by each call to arm_lms_q15(). Definition at line 66 of file arm_lms_init_q15.c.
| void arm_lms_q15 | ( | const arm_lms_instance_q15 * | S, |
| q15_t * | pSrc, | ||
| q15_t * | pRef, | ||
| q15_t * | pOut, | ||
| q15_t * | pErr, | ||
| uint32_t | blockSize | ||
| ) |
Processing function for Q15 LMS filter.
| [in] | *S | points to an instance of the Q15 LMS filter structure. |
| [in] | *pSrc | points to the block of input data. |
| [in] | *pRef | points to the block of reference data. |
| [out] | *pOut | points to the block of output data. |
| [out] | *pErr | points to the block of error data. |
| [in] | blockSize | number of samples to process. |
Definition at line 66 of file arm_lms_q15.c.
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