Convolution

Collaboration diagram for Convolution:

Functions
void	tpt_conv_f32 (f32_t *aOutData, const f32_t *aInDataA, uint32_t aLenA, const f32_t *aInDataB, uint32_t aLenB)
	Convolution of floating-point sequences. More...
tpt_status	tpt_conv_fast_f32 (f32_t *aOutData, const f32_t *aInDataA, uint32_t aLenA, const f32_t *aInDataB, uint32_t aLenB)
	Convolution of floating-point sequences (fast version). More...
void	tpt_conv_q15 (q15_t *aOutData, const q15_t *aInDataA, uint32_t aLenA, const q15_t *aInDataB, uint32_t aLenB)
	Convolution of Q15 sequences. More...
void	tpt_conv_q31 (q31_t *aOutData, const q31_t *aInDataA, uint32_t aLenA, const q31_t *aInDataB, uint32_t aLenB)
	Convolution of Q31 sequences. More...
void	tpt_conv_q7 (q7_t *aOutData, const q7_t *aInDataA, uint32_t aLenA, const q7_t *aInDataB, uint32_t aLenB)
	Convolution of Q7 sequences. More...

Detailed Description

Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector. Convolution is similar to correlation and is frequently used in filtering and data analysis. The DSP library contains functions for convolving Q15, Q31, and floating-point data types. The library also provides fast versions of the floating-point functions.

Algorithm

Let a[n] and b[n] be sequences of length aLenA and aLenB samples respectively. Then the convolution

    c[n] = a[n] * b[n]
  

is defined as

Note that c[n] is of length aLenA + aLenB - 1 and is defined over the interval n=0, 1, 2, ..., aLenA + aLenB - 2. aInDataA points to the first input vector of length aLenA and aInDataB points to the second input vector of length aLenB. The output result is written to aOutData and the calling function must allocate aLenA+aLenB-1 words for the result.

Conceptually, when two signals a[n] and b[n] are convolved, the signal b[n] slides over a[n]. For each offset n, the overlapping portions of a[n] and b[n] are multiplied and summed together.

Note that convolution is a commutative operation:

    a[n] * b[n] = b[n] * a[n].
  

This means that switching the A and B arguments to the convolution functions has no effect.

Fixed-Point Behavior

Convolution requires summing up a large number of intermediate products. As such, the 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.

Fast Versions

Fast versions are supported for floating-point. Time complexity for Fast versions are less compared to floating-point of conv and the design consumes more memory.

Function Documentation

tpt_conv_f32()

void tpt_conv_f32	(	f32_t *	aOutData,
		const f32_t *	aInDataA,
		uint32_t	aLenA,
		const f32_t *	aInDataB,
		uint32_t	aLenB
	)

Convolution of floating-point sequences.

Parameters

[out]	aOutData	points to the location where the output result is written. Length aLenA + aLenB - 1.
[in]	aInDataA	points to the first input sequence.
[in]	aLenA	length of the first input sequence
[in]	aInDataB	points to the second input sequence.
[in]	aLenB	length of the second input sequence

Returns

none

Remarks

Refer to tpt_conv_fast_f32() for a faster but consumes more memory of this function.

tpt_conv_fast_f32()

tpt_status tpt_conv_fast_f32	(	f32_t *	aOutData,
		const f32_t *	aInDataA,
		uint32_t	aLenA,
		const f32_t *	aInDataB,
		uint32_t	aLenB
	)

Convolution of floating-point sequences (fast version).

Parameters

[out]	aOutData	points to the location where the output result is written. Length aLenA + aLenB - 1.
[in]	aInDataA	points to the first input sequence
[in]	aLenA	length of the first input sequence
[in]	aInDataB	points to the second input sequence
[in]	aLenB	length of the second input sequence

Returns

execution status

• TPT_MATH_SUCCESS : Operation is successful.
• TPT_MATH_ARGUMENT_ERROR : length is not supported.

tpt_conv_q15()

void tpt_conv_q15	(	q15_t *	aOutData,
		const q15_t *	aInDataA,
		uint32_t	aLenA,
		const q15_t *	aInDataB,
		uint32_t	aLenB
	)

Convolution of Q15 sequences.

Parameters

[out]	aOutData	points to the location where the output result is written. Length aLenA + aLenB - 1.
[in]	aInDataA	points to the first input sequence.
[in]	aLenA	length of the first input sequence
[in]	aInDataB	points to the second input sequence.
[in]	aLenB	length of the second input sequence

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.

tpt_conv_q31()

void tpt_conv_q31	(	q31_t *	aOutData,
		const q31_t *	aInDataA,
		uint32_t	aLenA,
		const q31_t *	aInDataB,
		uint32_t	aLenB
	)

Convolution of Q31 sequences.

Parameters

[out]	aOutData	points to the location where the output result is written. Length aLenA + aLenB - 1.
[in]	aInDataA	points to the first input sequence
[in]	aLenA	length of the first input sequence
[in]	aInDataB	points to the second input sequence
[in]	aLenB	length of the second input sequence

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 the inputs by log2(min(aLenA, aLenB)) (log2 is read as log to the base 2) times to avoid overflows, as maximum of min(aLenA, aLenB) number of additions are carried internally. The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.

tpt_conv_q7()

void tpt_conv_q7	(	q7_t *	aOutData,
		const q7_t *	aInDataA,
		uint32_t	aLenA,
		const q7_t *	aInDataB,
		uint32_t	aLenB
	)

Convolution of Q7 sequences.

Parameters

[out]	aOutData	points to the location where the output result is written. Length aLenA + aLenB - 1.
[in]	aInDataA	points to the first input sequence.
[in]	aLenA	length of the first input sequence
[in]	aInDataB	points to the second input sequence.
[in]	aLenB	length of the second input sequence

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 then saturated to 1.7 format.