Snapshot of the front panel of the simulator:
The user can generate a signal x(n) as sum of a constant (or bias)
and a random signal. The auto correlation of x(n) is calculated in real
time based on a number of samples (of historical data) defined by the
The user can also introduce a lag L [samples] between signals. The
cross correlation of the signal and the delayed signal is computed.
The aims of this simulator is as follows:
- How the correlation function works
- How the correlation function represents random signals
- How the cross correlation function represents a time delay between
The autocorrelation of a signal can be used to express the random
character of a signal.
The cross correlation can be used to detect a time delay between two
- non-normalized correlation
- zero lag between the signals (time
- Auto correlation of a constant signal:
Let x(n) be a constant.
- Use a non-normalized correlation function. What is the value of
the correlation Rx(0)? Could you have calculated Rx(0)
- Can you from the shown Rx(L) in the
simulator determine which kind of correlation the correlation
function implemented in LabVIEW implements? (Is there avaraging,
i.e. division by number of samples N? Is there a compensation in the
correlation function for large L-values?)
- Auto correlation of a random signal:
Let x(n) be a pure random signal with zero mean.
- Does the form of the correlation function Rx(L)
indicate that the signal is ransom (with zero bias)?
- Use a normalized correlation function Rx. Describe
the difference between this Rx and the non-normalized
- Does Rx clearly express the dandomness of
a signal if the number of samples of the signal of which the
correlation function is calculated, is small?
- Select non-normalized
correlation. Read off the energy of x from the correlation function.
- Correlation of lagged random signals:
Let x(n) be a random signal with zero mean. Introduce some lag in the
signal. Use non-normalized correlation. The correlation is now being
calculated between x(n) and x(n-L).
- In which way is the lag expressed by the correlation function?
(You may try with different lags.)
Updated 21. January 2008.