Controlling Frequency Resolution of Spectral Models
This section supports the estimation procedures Estimate Frequency-Response Models in the App and Estimate Frequency-Response Models at the Command Line.
What Is Frequency Resolution?
Frequency resolution is the size of the smallest frequency for which details in the frequency response and the spectrum can be resolved by the estimate. A resolution of 0.1 rad/s means that the frequency response variations at frequency intervals at or below 0.1 rad/s are not resolved.
Finer resolution results in greater uncertainty in the model estimate.
Frequency Resolution for etfe and spa
spa, the frequency
resolution is approximately equal to the following value:
M is a scalar integer that sets the size of the lag window.
The value of
M controls the trade-off between bias and variance
in the spectral estimate.
The default value of M for
spa is good
for systems without sharp resonances. For
etfe, the default
value of M gives the maximum resolution.
A large value of M gives good resolution, but results in more
uncertain estimates. If a true frequency function has sharp peak, you should specify
Frequency Resolution for spafdr
In case of
spa, the frequency
response is defined over a uniform frequency range,
0-Fs/2 radians per second, where
Fs is the sampling
frequency—equal to twice the Nyquist frequency. In contrast,
spafdr lets you increase the resolution in a specific
frequency range, such as near a resonance frequency. Conversely, you can make the
frequency grid coarser in the region where the noise dominates—at higher
frequencies, for example. Such customizing of the frequency grid assists in the
estimation process by achieving high fidelity in the frequency range of
spafdr, the frequency resolution around the frequency
k is the value R(k). You can enter
R(k) in any one of the following
Scalar value of the constant frequency resolution value in radians per second.
The scalar R is inversely related to the M value used for
Vector of frequency values the same size as the frequency vector.
Expression using MATLAB® workspace variables and evaluates to a resolution vector that is the same size as the frequency vector.
The default value of the resolution for
spafdr is twice the
difference between neighboring frequencies in the frequency vector.
etfe Frequency Resolution for Periodic Input
If the input data is marked as periodic and contains an integer number of periods
data.Period is an integer),
computes the frequency response at frequencies .
For periodic data, the frequency resolution is ignored.