CxAutoCorrelate

Advanced Analysis Library Only

AnalysisLibErrType CxAutoCorrelate (NIComplexNumber inputArray[], ssize_t sizeOfInputArray, int norm, NIComplexNumber outputArray[]);

Purpose

Finds the autocorrelation of the complex input array. The autocorrelation Rxx(t) of a function x(t) is defined as the following:

where the symbol denotes correlation.

For the discrete implementation of this function, let Y represent a sequence whose indexing can be negative, let N be the number of elements in the input sequence inputArray, and assume that the indexed elements of inputArray that lie outside its range are equal to zero, as shown in the following relationship:

x_j = 0 , j < 0 or j ≥ N

Then CxAutoCorrelate obtains the elements of Y using the following equation:

for j = -(N–1), -(N–2), ..., -1, 0, 1, ..., (N–2), (N–1)

The elements of the output sequence outputArray are related to the elements in the sequence Y by

Rxx_i = y_i-(N–1)

for i = 0, 1, 2, ..., 2N–2

Notice that the number of elements in the output sequence outputArray is 2N–1. Because you cannot use negative numbers to index LabWindows/CVI arrays, the corresponding correlation value at t = 0 is the Nth element of the output sequence outputArray. Therefore, outputArray represents the correlation values that CxAutoCorrelate shifts N times in indexing.

In order to make the autocorrelation calculation more accurate, normalization is required in some situations. This function provides biased and unbiased normalization.

• Biased normalization
  
  If norm is ALGORITHM_CONCOR_BIASED_NORMALIZATION, LabWindows/CVI applies biased normalization as follows:
  
  

  

  for j = -(N–1), -(N–2), ..., -1, 0, 1, ..., (N–2), (N–1), and
  
  R_xx(biased) = y_i-(N–1)
  
  for i = 0, 1, 2, ..., 2N–2
  
  

• Unbiased normalization
  
  If norm is ALGORITHM_CONCOR_UNBIASED_NORMALIZATION, LabWindows/CVI applies unbiased normalization as follows:

  

  for j = -(N–1), -(N–2), ..., -1, 0, 1, ..., (N–2), (N–1), and
  
  R_xx(unbiased) = y_i-(N–1)
  
  for i = 0, 1, 2, ..., 2N–2

Note  This function temporarily allocates memory for use as a work area. If CxAutoCorrelate cannot allocate memory, the function returns an error code.

Example Code

/* Generate one array with random numbers and find its autocorrelation. */
NIComplexNumber x[256];
NIComplexNumber rxx[512];
double input[256];
int i;
int n;
n = 256;
WhiteNoise (n, 1, 17, input);
for(i = 0; i < n; i++)
{

x[i].real = input[i];
x[i].imaginary = input[i];

}
CxAutoCorrelate (x, n, ALGORITHM_CORCOR_NO_NORMALIZATION, rxx);

Parameters

Return Value

Additional Information

Library: Advanced Analysis Library

Include file: analysis.h

LabWindows/CVI compatibility: LabWindows/CVI 2012 and later