Contents
What is cross correlation in signal processing?
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. The cross-correlation is similar in nature to the convolution of two functions.
What is correlation of discrete time signal?
A signal operation similar to signal convolution, but with completely different physical meaning, is signal correlation. The signal correlation operation can be performed either with one signal (autocorrelation) or between two different signals (crosscorrelation).
How do you calculate the correlation of a signal?
If x(n), y(n) and z(n) are the samples of the signals, the correlation coefficient between x and y is given by Sigma x(n) * y(n) divided by the root of [Sigma x(n)^2 * y(n)^2], where ‘ * ‘ denotes simple multiplication and ^2 denotes squaring. The summation is taken over all the samples of the signals.
How is cross correlation used to estimate impulse response?
Cross correlation is normally used for pattern recognition, signal detection etc. We will demonstrate how the properties of cross correlation can be utilized to estimate the impulse response of an unknown LTI (linear time invariant) system. Consider an LTI system as shown below:
How to calculate impulse response of a system?
For this method , the input must be a white noise with zero mean and unit variance. This method can be applied to model communication systems that are linear time invariant. To model such systems, only the response of the system to white noise input is needed to compute the impulse response.
How to calculate the impulse response of a LTI system?
To model such systems, only the response of the system to white noise input is needed to compute the impulse response. This can be summed up as follows. when \\ (x (n)\\) is zero unit variance white Gaussian Noise. Consider a low pass filter with Sampling Frequency \\ (F_s=1000\\; Hz\\) , Cut-off Frequency \\ (F_c=400 \\; Hz\\).
How to calculate the impulse response of a low pass filter?
Consider a low pass filter with Sampling Frequency \\ (F_s=1000\\; Hz\\) , Cut-off Frequency \\ (F_c=400 \\; Hz\\). We will estimate the impulse response of the filter using the above method and compare it with the actual impulse response of the system.