## Momentary ARMA spectrum

Purpose
Description
Tips
Macro Synopsis
Modules
Related Functions
References

### Purpose

Momentary ARMA Spectrum

### Description

Momentary ARMA spectrum estimates the momentary spectrum of the given signal x by fitting it to an instationary ARMA model given by

with being a white noise sequence that need not be known. This function yields a 2D signal of the adaptive time-frequency spectrum displaying time (x-axis) versus frequency (y-axis) with the power or amplitude spectral values given on the z-axis.

The model estimation algorithm provides a high frequency resolution as well as an arbitrarily high time resolution.

The spectral density

is obtained from the model coefficients and .

Parameters are:

• Lower frequency f0 in reciprocal x-axis units
• Upper frequency f1 in reciprocal x-axis units
• Order P of the AR (AutoRegressive) process
• Order Q of the MA (Moving Average) process
• Adaptation time ta for the variance estimator (in x-axis units)
• Adaptation factor f for parameter estimation
• the number of points tres for the plot resolution along the time axis
• the number of points fres for the plot resolution along the frequency axis
• Spectrum type (spectype), which is either
• "Power" (0) or
• "Amplitude" (1)
• Type of normalization (normtype), which is one of
• "Spectral density" (0)
• "Maximum norm" (1).

### Tips

For the choice of the model orders it can be helpful to run the function ARMA model order on stationary parts of the input signal. Increasing the maximum order by 2 or 3 improves the stability of the estimation procedure. 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 = MomARMAspect(x,f0,f1,P,Q,ta,f,tres,fres,spectype,normtype);
signal x, y;
float f0, f1;
int P, Q,
float ta, f;
int tres, fres;
option spectype, normtype

Note that y is a 2D signal.

Spectral

### Related Functions

Momentary ARMA bandpower, Momentary ARMA coherence, ARMA dependence, Momentary bandpower, Momentary frequency, Momentary mean, Momentary power, Multiscale TFD, STFT.

### References

Haykin [41], Schack et al. [42]