Correlation
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
user.
The user can also introduce a lag L [samples] between signals. The
cross correlation of the signal and the delayed signal is computed.
Aims
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
random signals
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
signals.
Initially, choose
- non-normalized correlation
- zero lag between the signals (time
series)
- 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 R_{x}(0)? Could you have calculated R_{x}(0)
in advance?
- Can you from the shown R_{x}(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 R_{x}(L)
indicate that the signal is ransom (with zero bias)?
- Use a normalized correlation function R_{x}. Describe
the difference between this R_{x} and the non-normalized
correlation?
- Does R_{x} 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.)
[SimView] [TechTeach]
Updated 21. January 2008.
Developed by
Finn Haugen.
E-mail: finn@techteach.no. |