# Root mean square (RMS)
[Statistics Functions]

## Functions

void | arm_rms_f32 (float32_t *pSrc, uint32_t blockSize, float32_t *pResult)
void | arm_rms_q31 (q31_t *pSrc, uint32_t blockSize, q31_t *pResult)
void | arm_rms_q15 (q15_t *pSrc, uint32_t blockSize, q15_t *pResult)

## Detailed Description

Calculates the Root Mean Sqaure of the elements in the input vector. The underlying algorithm is used:

     	Result = sqrt(((pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]) / blockSize));

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

## Function Documentation

void arm_rms_f32 | ( | float32_t * | pSrc,
|  | uint32_t | blockSize,
|  | float32_t * | pResult
| ) |  |

Root Mean Square of the elements of a floating-point vector.

Parameters:

  [in] | *pSrc | points to the input vector
  [in] | blockSize | length of the input vector
  [out] | *pResult | rms value returned here

Returns:
  none.

Definition at line 65 of file arm_rms_f32.c.

void arm_rms_q31 | ( | q31_t * | pSrc,
|  | uint32_t | blockSize,
|  | q31_t * | pResult
| ) |  |

Root Mean Square of the elements of a Q31 vector.

Parameters:

  [in] | *pSrc | points to the input vector
  [in] | blockSize | length of the input vector
  [out] | *pResult | rms value returned here

Returns:
  none.

Scaling and Overflow Behavior:

  The function is implemented using an internal 64-bit accumulator. The input is represented in 1.31 format, and intermediate multiplication yields a 2.62 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. If the accumulator overflows, it wraps around and distorts the result. In order to avoid overflows completely, the input signal must be scaled down by log2(blockSize) bits, as a total of blockSize additions are performed internally. Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.

Definition at line 62 of file arm_rms_q31.c.

void arm_rms_q15 | ( | q15_t * | pSrc,
|  | uint32_t | blockSize,
|  | q15_t * | pResult
| ) |  |

Root Mean Square of the elements of a Q15 vector.

Parameters:

  [in] | *pSrc | points to the input vector
  [in] | blockSize | length of the input vector
  [out] | *pResult | rms value returned here

Returns:
  none.

Scaling and Overflow Behavior:

  The function is implemented using a 64-bit internal accumulator. The input is represented in 1.15 format. Intermediate multiplication yields a 2.30 format, and this result is added without saturation to a 64-bit accumulator in 34.30 format. With 33 guard bits in the accumulator, there is no risk of overflow, and the full precision of the intermediate multiplication is preserved. Finally, the 34.30 result is truncated to 34.15 format by discarding the lower 15 bits, and then saturated to yield a result in 1.15 format.

Definition at line 59 of file arm_rms_q15.c.

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