# Complex-by-Complex MultiplicationComplex Math Functions

## Functions

void arm_cmplx_mult_cmplx_f32 (float32_t *pSrcA, float32_t *pSrcB, float32_t *pDst, uint32_t numSamples)
Floating-point complex-by-complex multiplication.

void arm_cmplx_mult_cmplx_q15 (q15_t *pSrcA, q15_t *pSrcB, q15_t *pDst, uint32_t numSamples)
Q15 complex-by-complex multiplication.

void arm_cmplx_mult_cmplx_q31 (q31_t *pSrcA, q31_t *pSrcB, q31_t *pDst, uint32_t numSamples)
Q31 complex-by-complex multiplication.

## Description

Multiplies a complex vector by another complex vector and generates a complex result. The data in the complex arrays is stored in an interleaved fashion (real, imag, real, imag, ...). The parameter `numSamples` represents the number of complex samples processed. The complex arrays have a total of `2*numSamples` real values.

The underlying algorithm is used:

```for(n=0; n<numSamples; n++) {
pDst[(2*n)+0] = pSrcA[(2*n)+0] * pSrcB[(2*n)+0] - pSrcA[(2*n)+1] * pSrcB[(2*n)+1];
pDst[(2*n)+1] = pSrcA[(2*n)+0] * pSrcB[(2*n)+1] + pSrcA[(2*n)+1] * pSrcB[(2*n)+0];
}
```

There are separate functions for floating-point, Q15, and Q31 data types.

## Function Documentation

 void arm_cmplx_mult_cmplx_f32 ( float32_t * `pSrcA, ` float32_t * `pSrcB, ` float32_t * `pDst, ` uint32_t `numSamples ` )
Parameters
 [in] `*pSrcA` points to the first input vector [in] `*pSrcB` points to the second input vector [out] `*pDst` points to the output vector [in] `numSamples` number of complex samples in each vector
Returns
none.

Referenced by main().

 void arm_cmplx_mult_cmplx_q15 ( q15_t * `pSrcA, ` q15_t * `pSrcB, ` q15_t * `pDst, ` uint32_t `numSamples ` )
Parameters
 [in] `*pSrcA` points to the first input vector [in] `*pSrcB` points to the second input vector [out] `*pDst` points to the output vector [in] `numSamples` number of complex samples in each vector
Returns
none.

Scaling and Overflow Behavior:

The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.
 void arm_cmplx_mult_cmplx_q31 ( q31_t * `pSrcA, ` q31_t * `pSrcB, ` q31_t * `pDst, ` uint32_t `numSamples ` )
Parameters
 [in] `*pSrcA` points to the first input vector [in] `*pSrcB` points to the second input vector [out] `*pDst` points to the output vector [in] `numSamples` number of complex samples in each vector
Returns
none.

Scaling and Overflow Behavior:

The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format. Input down scaling is not required.

Referenced by arm_dct4_q31().