## Momentary ARMA bandpower

Purpose

Description

Tips

Macro Synopsis

Modules

Related Functions

References

### Purpose

Momentary power estimation from ARMA model

### Description

"Momentary ARMA bandpower" is an adaptive estimator function calculating the
momentary power of the input signal x within a certain frequency
range where x is fit to an adaptive ARMA model given by

with being a white noise sequence that need not be given.
The recursive estimation of the model coefficients and
is done adaptively where the adaptation speed can be
adjusted by the choice of the parameters f and t (see below). By
increasing f and decreasing t, a quicker reaction of the estimation
procedure is possible after rapid structure changes, but this will
also lead to an estimation sequence that is less smooth and tends to
be less robust on the other hand.

Parameters of "Momentary ARMA bandpower" are

- the lower frequency bound f1
- the upper frequency bound f2
- the order P of the AutoRegressive (AR) process
- the order Q of the Moving Average (MA) process
- the adaptation time
`ta` for the variance estimator (in
x-axis units)
- the dimensionless adaptation factor f for the parameter estimation
- the number
`step` of samples between two successive estimations steps.

### Tips

The adaptation factor f usually is around 0.01. With the choice
of a relatively high f (say, 0.03), a quick parameter adaptation is
achieved enabling the model to react more quickly after rapid
structure changes in the input signals, but this will also lead to
an estimation sequence that is less smooth and tends to be less
robust on the other hand.

### Macro Synopsis

`y = MomARMApower(x,f1,f2,P,Q,ta,f,step);`

signal x,y;

float f1,f2;

int P,Q;

float ta,f;

int step;

### Modules

Filter

### Related Functions

Momentary ARMA coherence,
ARMA dependence, Momentary ARMA spectrum,
Momentary bandpower, Momentary frequency,
Momentary mean,
Momentary power.

### References

Schack et al. [40]