Correlation and 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.
Featured Examples
Measure Signal Similarities
Compare signals with different sample rates or frequency content, measure delays, and determine if there is a signal in a measurement.
Accelerate Correlation with GPUs
Use a graphics processing unit to accelerate cross-correlation in applications that involve large data sets.
Residual Analysis with Autocorrelation
Use autocorrelation with a confidence interval to analyze the residuals of a least-squares fit to noisy data.
Teaching Resources
Convolution in Digital Signal Processing
Learn the concepts of convolution, linear time invariance, and building convolution filters.
