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.
||Data matrix for autocorrelation matrix estimation|
||Modulo-N circular convolution|
||Convolution and polynomial multiplication|
||Deconvolution and polynomial division|
Determine if a signal matches a segment of a noisy longer stream of data.
Learn to align signals of different lengths using cross-correlation.
Synchronize data collected by different sensors at different instants.
Use cross-correlation to fuse asynchronous data.
Verify the presence of cycles in a noisy signal, and determine their durations.
Create confidence intervals for the autocorrelation sequence of a white noise process.
Use autocorrelation with a confidence interval to analyze the residuals of a least-squares fit to noisy data.
Use filtering to introduce autocorrelation into a white noise process.
Find and plot the cross-correlation sequence between two moving average processes.
Use the cross-correlation sequence to detect the time delay in a noise-corrupted sequence.
Use the cross-correlation sequence to estimate the phase lag between two sine waves.
Establish an equivalence between linear and circular convolution.