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.

Functions

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Correlation

`corrcoef`	Correlation coefficients
`corrmtx`	Data matrix for autocorrelation matrix estimation
`xcorr`	Cross-correlation
`xcorr2`	2-D cross-correlation
`xcov`	Cross-covariance

Convolution

`cconv`	Modulo-n circular convolution
`conv`	Convolution and polynomial multiplication
`conv2`	2-D convolution
`convmtx`	Convolution matrix
`cov`	Covariance
`deconv`	Deconvolution and polynomial division

Signal Alignment

`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

Topics

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.
Echo Cancelation
Use autocorrelation to filter out an echo from a speech recording.

Autocorrelation and Cross-Correlation

Cross-Correlation with Multichannel Input
Compute autocorrelations and cross-correlations of a multichannel signal.
Confidence Intervals for Sample Autocorrelation
Create confidence intervals for the autocorrelation sequence of a white noise process.
Autocorrelation Function of Exponential Sequence
Compute the autocorrelation of an exponential sequence and compare it to the analytic result.
Cross-Correlation of Two Exponential Sequences
Compute the cross-correlation of two exponential sequences and compare it to the analytic result.
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.

Featured Examples

Measuring Signal Similarities

Compare signals with different sample rates or frequency content; measure delays; determine if there is a signal in a measurement.

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Accelerating Correlation with GPUs

Use a graphics processing unit to accelerate cross-correlation in applications that involve large data sets.

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Residual Analysis with Autocorrelation

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

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