AutoCorrelation Matrix VI
- Updated2025-07-30
- 3 minute(s) read
Computes the autocorrelation matrix of the input sequence X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance.
This VI uses the following equation to calculate the autocorrelation matrix.
where M is AutoCorrelation Matrix, R is data matrix, s is normalization factor. RH is the conjugate transpose of matrix R.
If method is AutoCorrelation, R is a matrix of size (N+k)-by-(k+1) defined as follows.
where xi is the i-th element in X, N is the length of X , and k is the order. The normalization factor, s, is equal to N.
If method is Pre-Windowed, R is a matrix of size N-by-(k+1) defined as follows.
The normalization factor, s, is equal to N.
If method is Post-Windowed, R is a matrix of size N-by-(k+1) defined as follows.
The normalization factor, s, is equal to N.
If method is Covariance, R is a matrix of size (N-k)-by-(k+1) defined as follows.
The normalization factor, s, is equal to N-k.
If method is Modified Covariance, R is a matrix of size 2(N-k)-by-(k+1) defined as follows.
where xi* is the complex conjugate of xi. The normalization factor, s, is equal to 2*(N-k).
This VI supports both single shot and continuous mode. The following figure illustrates how to use the AutoCorrelation Matrix VI in single shot and continuous mode. The two outputs, AutoCorrelation Matrix 1 and AutoCorrelation Matrix 2, always produce the same results.
Autocorrelation matrix is widely used in the field of spectrum analysis to estimate the spectral components within the input signal. In general, Covariance and Modified Covariance methods give better results in spectral estimation processing than the AutoCorrelation, Pre-Windowed and Post-Windowed methods. National Instruments recommends that you use the Covariance or the Modified Covariance method to estimate the autocorrelation matrix when performing spectrum analysis.