Simon Ford / dsp

CMSIS DSP Library from CMSIS 2.0. See http://www.onarm.com/cmsis/ for full details

Dependents:   K22F_DSP_Matrix_least_square BNO055-ELEC3810 1BNO055 ECE4180Project--Slave2 ... more

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Correlation
Functions

Correlation
[Filtering Functions]

Correlation is a mathematical operation that is similar to convolution. More...

Functions

void arm_correlate_f32 (float32_t *pSrcA, uint32_t srcALen, float32_t *pSrcB, uint32_t srcBLen, float32_t *pDst)
 Correlation of floating-point sequences.
void arm_correlate_fast_q15 (q15_t *pSrcA, uint32_t srcALen, q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)
 Correlation of Q15 sequences (fast version).
void arm_correlate_fast_q31 (q31_t *pSrcA, uint32_t srcALen, q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)
 Correlate Q31 sequences (fast version)
void arm_correlate_q15 (q15_t *pSrcA, uint32_t srcALen, q15_t *pSrcB, uint32_t srcBLen, q15_t *pDst)
 Correlation of Q15 sequences.
void arm_correlate_q31 (q31_t *pSrcA, uint32_t srcALen, q31_t *pSrcB, uint32_t srcBLen, q31_t *pDst)
 Correlate Q31 sequences.
void arm_correlate_q7 (q7_t *pSrcA, uint32_t srcALen, q7_t *pSrcB, uint32_t srcBLen, q7_t *pDst)
 Correlation of Q7 sequences.

Detailed Description

Correlation is a mathematical operation that is similar to convolution.

As with convolution, correlation uses two signals to produce a third signal. The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution. Correlation is commonly used to measure the similarity between two signals. It has applications in pattern recognition, cryptanalysis, and searching. The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types. Fast versions of the Q15 and Q31 functions are also provided.

Algorithm
Let a[n] and b[n] be sequences of length srcALen and srcBLen samples respectively. The convolution of the two signals is denoted by 
  
                   c[n] = a[n] * b[n]
In correlation, one of the signals is flipped in time 
  
                   c[n] = a[n] * b[-n]
and this is mathematically defined as
CorrelateEquation.gif
The pSrcA points to the first input vector of length srcALen and pSrcB points to the second input vector of length srcBLen. The result c[n] is of length 2 * max(srcALen, srcBLen) - 1 and is defined over the interval n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2). The output result is written to pDst and the calling function must allocate 2 * max(srcALen, srcBLen) - 1 words for the result.

Fixed-Point Behavior

Correlation requires summing up a large number of intermediate products. As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation. Refer to the function specific documentation below for further details of the particular algorithm used.

Function Documentation

void arm_correlate_f32 ( float32_t *  pSrcA,
uint32_t  srcALen,
float32_t *  pSrcB,
uint32_t  srcBLen,
float32_t *  pDst 
)

Correlation of floating-point sequences.

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Definition at line 88 of file arm_correlate_f32.c.

void arm_correlate_fast_q15 ( q15_t *  pSrcA,
uint32_t  srcALen,
q15_t *  pSrcB,
uint32_t  srcBLen,
q15_t *  pDst 
)

Correlation of Q15 sequences (fast version).

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Scaling and Overflow Behavior:

This fast version 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. There is no saturation on intermediate additions. Thus, if the accumulator overflows it wraps around and distorts the result. The input signals should be scaled down to avoid intermediate overflows. Scale down one of the inputs by 1/min(srcALen, srcBLen) to avoid overflow since a maximum of min(srcALen, srcBLen) number of additions is carried internally. The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.
See arm_correlate_q15() for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.

Definition at line 63 of file arm_correlate_fast_q15.c.

void arm_correlate_fast_q31 ( q31_t *  pSrcA,
uint32_t  srcALen,
q31_t *  pSrcB,
uint32_t  srcBLen,
q31_t *  pDst 
)

Correlate Q31 sequences (fast version)

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Scaling and Overflow Behavior:

This function is optimized for speed at the expense of fixed-point precision and overflow protection. The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format. These intermediate results are accumulated in a 32-bit register in 2.30 format. Finally, the accumulator is saturated and converted to a 1.31 result.
The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result. In order to avoid overflows completely the input signals must be scaled down. The input signals should be scaled down to avoid intermediate overflows. Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a maximum of min(srcALen, srcBLen) number of additions is carried internally.
See arm_correlate_q31() for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.

Definition at line 67 of file arm_correlate_fast_q31.c.

void arm_correlate_q15 ( q15_t *  pSrcA,
uint32_t  srcALen,
q15_t *  pSrcB,
uint32_t  srcBLen,
q15_t *  pDst 
)

Correlation of Q15 sequences.

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Scaling and Overflow Behavior:

The function is implemented using a 64-bit internal accumulator. Both inputs are in 1.15 format and multiplications yield a 2.30 result. The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. This approach provides 33 guard bits and there is no risk of overflow. The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.
Refer to arm_correlate_fast_q15() for a faster but less precise version of this function.

Definition at line 65 of file arm_correlate_q15.c.

void arm_correlate_q31 ( q31_t *  pSrcA,
uint32_t  srcALen,
q31_t *  pSrcB,
uint32_t  srcBLen,
q31_t *  pDst 
)

Correlate Q31 sequences.

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Scaling and Overflow Behavior:

The function is implemented using an internal 64-bit accumulator. The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. There is no saturation on intermediate additions. Thus, if the accumulator overflows it wraps around and distorts the result. The input signals should be scaled down to avoid intermediate overflows. Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a maximum of min(srcALen, srcBLen) number of additions is carried internally. The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
See arm_correlate_fast_q31() for a faster but less precise implementation of this function.

Definition at line 68 of file arm_correlate_q31.c.

void arm_correlate_q7 ( q7_t *  pSrcA,
uint32_t  srcALen,
q7_t *  pSrcB,
uint32_t  srcBLen,
q7_t *  pDst 
)

Correlation of Q7 sequences.

Parameters:
[in]*pSrcApoints to the first input sequence.
[in]srcALenlength of the first input sequence.
[in]*pSrcBpoints to the second input sequence.
[in]srcBLenlength of the second input sequence.
[out]*pDstpoints to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
Returns:
none.

Scaling and Overflow Behavior:

The function is implemented using a 32-bit internal accumulator. Both the inputs are represented in 1.7 format and multiplications yield a 2.14 result. The 2.14 intermediate results are accumulated in a 32-bit accumulator in 18.14 format. This approach provides 17 guard bits and there is no risk of overflow as long as max(srcALen, srcBLen)<131072. The 18.14 result is then truncated to 18.7 format by discarding the low 7 bits and saturated to 1.7 format.

Definition at line 62 of file arm_correlate_q7.c.

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