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Correlation and Convolution

Cross-correlation, autocorrelation, cross-covariance, autocovariance, linear and circular convolution

Signal Processing Toolbox™ provides a family of correlation and convolution functions that let you detect signal similarities. Determine periodicity, find a signal of interest hidden in a long data record, and measure delays between signals to synchronize them. Compute the response of a linear time-invariant (LTI) system to an input signal, perform polynomial multiplication, and carry out circular convolution.


corrcoef Correlation coefficients
corrmtx Data matrix for autocorrelation matrix estimation
xcorr Cross-correlation
xcorr2 2-D cross-correlation
xcov Cross-covariance
cconv Modulo-N circular convolution
conv Convolution and polynomial multiplication
conv2 2-D convolution
convmtx Convolution matrix
cov Covariance
deconv Deconvolution and polynomial division
alignsignals Align two signals by delaying earliest signal
dtw Distance between signals using dynamic time warping
edr Edit distance on real signals
finddelay Estimate delay(s) between signals
findsignal Find signal location using similarity search


Common Applications

Find a Signal in a Measurement

Determine if a signal matches a segment of a noisy longer stream of data.

Align Two Simple Signals

Learn to align signals of different lengths using cross-correlation.

Align Signals with Different Start Times

Synchronize data collected by different sensors at different instants.

Align Signals Using Cross-Correlation

Use cross-correlation to fuse asynchronous data.

Find Periodicity Using Autocorrelation

Verify the presence of cycles in a noisy signal, and determine their durations.

Autocorrelation and Cross-Correlation

Confidence Intervals for Sample Autocorrelation

Create confidence intervals for the autocorrelation sequence of a white noise process.

Residual Analysis with Autocorrelation

Use autocorrelation with a confidence interval to analyze the residuals of a least-squares fit to noisy data.

Autocorrelation of Moving Average Process

Use filtering to introduce autocorrelation into a white noise process.

Cross-Correlation of Two Moving Average Processes

Find and plot the cross-correlation sequence between two moving average processes.

Cross-Correlation of Delayed Signal in Noise

Use the cross-correlation sequence to detect the time delay in a noise-corrupted sequence.

Cross-Correlation of Phase-Lagged Sine Wave

Use the cross-correlation sequence to estimate the phase lag between two sine waves.

Linear and Circular Convolution

Establish an equivalence between linear and circular convolution.

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