Spectral Models

The Spectral Model dialog is opened by chosing the corresponding item in the pop-up menu Estimate in the ident window.

This function estimates the frequency response of the Working Data set using spectral analysis. Open the Frequency response model View to see the results.

The spectral model is also calculated if you press the hotkey s in the ident window.

Methods
Frequencies
Resolution
Help topics.

Methods

The dialog offers a choice of three methods:
SPA (Blackman-Tukey)
This is the classical spectral analysis method, where windowed versions of the covariance functions are Fourier transformed. It corresponds to the command line method SPA.
SPAFDR (SPectral Analysis with Frequency Dependent Resolution.)
Fourier transforms of the outputs and inputs are first formed. Products of the inputs and outputs with the conjugate input transform are smoothed over local frequency regions, whose width may depend on the frequency. It corresponds to the command line method SPAFDR.
ETFE (Emprical Transfer Function Estimate
This is the Empirical Transfer Function Estimate, which in the raw form is the ratio of the output Fourier transform to the input one. If corresponds to the command line method ETFE.

Frequencies

The estimate is computed at frequencies that are determined by the popup-menu 'Frequency Spacing' and the edit box 'Frequencies'. The frequencies are always in rad/s. Two ways are possible:
1. Direct
Enter the frequency vector in the box Frequencies. This could be any MATLAB expression that evaluates to a vector, like 'logspace(-1,2,500)', or the name of any Workspace variable that is a vector. In this case the 'Frequency Spacing' menu has no effect.
2. Indirect
Choose linear or logarithmic spacing by the popup-menu, and enter the disired number of frequency values in the box Frequencies. Then a frequency vector vector with this number of points and this spacing is formed. The frequency span, for a time domain data set is from 0 (excluded) to the Nyquist frequency. For frequency domain data it is between the smallest and largest frequencies in the data set.
Note for ETFE:
For the EFTE method only linearly spaced frequencies are possible. Only the number of frequency points can be specified, and they will then be linearly spaced up to the Nyquist frequency.

Resolution

By 'resolution' is meant the finest detail in the frequency response that can be detected. A resolution of 0.1 rad/s means that peaks and details that differ with less then 0.1 rad/s will not be seen.

There is a trade-off between frequency resolution and uncertainty of the estimate: The better the resolution, the more uncertain estimate. This trade-off is controlled by the frequency resolution parameter, entered in the Frequency Resolution box. The interpretation of this depends on the method used:

For SPA and ETFE
enter a scalar integer M. It gives a frequency resolution of about pi/M rad/(sampling interval). The default choice of M - obtained by leaving the box empty - gives a reasonable choice for not-so-resonant systems for SPA and maximum resolution for ETFE (no smoothing).

For SPAFDR
enter either a number R that is the desired frequency resolution in rad/s or a vector R of the same size as the frequency vector. Then R(k) is the resolution around frequency(k). You may enter the name of a workspace variable that evaluates to such a vector.

or leave empty for default. The default is to let the resolution be twice the difference between the neigbouring frequencies. The resultion is thus determined by the frequency vector. Note that a scalar R is inversely related to the M used for SPA and ETFE

Help topics.


(file spa.htm)