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.
- 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.