## 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;

Filter

### Related Functions

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

### References

Schack et al. [40]