# 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

## 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 Cancellation**

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.