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Cross correlation, as the name and it's definition suggests, is the represents the similarity between two different signal. If two signals are overlapped by sliding one of them in the time domain, the area under the overlapped region is the measure of thecross-correlation. Larger the value, more similar are the two functions.
The same thing for the same signal is the autocorrelation. The function is overlapped onto itself and overlapped area is measured. This is useful is measuring randomness of a signal. Suppose you have a random signal. Then it's autocorrelation should be zero at all values except t = 0. And the value should be large for t = 0. This relative measure of the autocorrelation values at t = 0 and t ≠0 gives the measure of randomness of the signal.
You can do one simple experiment. Use a scrambler circuit of your own choise and feed clock to it to generate a pseudo random signal. The signal will be pseudorandom in the sense that it will have some low frequency periodicity but over a large time it loks random. Then use shift register to generate different delay in the signal. Now and them bit by bit and at the output connect a LPF and measure the average outut voltage using a multimeter. You can find that the value of the average output is very small at all dela values except at delay = 0, ±((2^n)-1) where n is the no.f scrambling stages how many shift stages you have used for generating the PRN signal in the scrambler circuit.
Here again, incontinuation to subharpe, I would like to give you example of a practical project that I worked with, for Auto-correlation".
An-board (missile) subsystem which is responsible to trigger off warhead when in proximity to the taget uses "auto-correlation", for certain information. Here a PN-code encripted signal is transmitted, which "hits" the target, and is again received by this on-board system. Obviously the incoming signal will have delay+doppler. Now when this received signal is "correlated" with the reference signal, delay being calculated, tells "how-far" is the target present and "how-fast" is it approaching/receeding.
Thank you for reference of the wonderful experiment. I have a query. When the object is stationary the received signal will be delayed with resoect to the transmitted signal and the inyut output relatin is of the form
o/p(t) = K i/p(t - T)
where T is 2*distance /speed of the signal. So the output is a delayed replica of the input PRS. From proper mapping of the autocorrelation with the delay the delay can be found. But how does this technique help in cae of moving object when Doppler effect comes into picture? Canyou be a little detailed?
IT is not easy to explain u these concepts, u sshould have fundamentals of RANDOM VARIABLES and SPECTRRAL ANALYSIS. better u should refer to books like TAUB SCHILLING,and SIMON HAYKIN
Iam sorry, I did not mention that the Rx signal is actually "Bifercated" into two circuits. One circuit extracts doppler information and the other does what I previously mentioned.
The Tx signal is PN encryped. The number of bits to be used for the "full-length" sequence is predetermined. During Tx the entire length is being repeated cyclically. So that is how it's possible to cross-correlate.
There are a lot of applications for these tools. The most important application of the Autocorrelation is in obtaining the power spectrum density. Indeed the fourier transform of the autocorrelation is the power spectrum density.
cross correlation shows the correlation between two different signal. In some designs it is required to use signals with low cross correlation such as Cdma signals.
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