spa
Estimate frequency response with fixed frequency resolution using spectral analysis
Description
estimates the frequency response, along with
uncertainty,
and the noise spectrum from time- or frequency-domain data
G
= spa(data
)data
. If data
is a time series,
spa
(data)
returns the output power
spectrum along with uncertainty. spa
computes the spectra at
128 equally spaced frequency values between 0 (excluded) and π, using a Hann
window.
Examples
Input Arguments
Output Arguments
More About
Algorithms
spa
applies the Blackman-Tukey spectral analysis method by
following these steps:
Compute the covariances and cross-covariance from u(t) and y(t):
Compute the Fourier transforms of the covariances and the cross-covariance:
where is the Hann window with a width (lag size) of M. You can specify M to control the frequency resolution of the estimate, which is approximately equal to 2π/M rad/sample time.
By default, this operation uses 128 equally spaced frequency values between 0 (excluded) and π, where
w
=[1:128]/128*pi/Ts
andTs
is the sample time of that data set. The default lag size of the Hann window isM = min(length(data)/10,30)
. For default frequencies, the operation uses fast Fourier transforms (FFT), which are more efficient than for user-defined frequencies.Compute the frequency-response function and the output noise spectrum .
spectrum
is the spectrum matrix for both the output and the input
channels. That is, if z = [data.OutputData
,
data.InputData]
, spectrum
contains as spectrum
data the matrix-valued power spectrum of z
.
Here, '
is a complex-conjugate transpose.
References
[1] Ljung, Lennart. System Identification: Theory for the User. 2nd ed. Prentice Hall Information and System Sciences Series. Upper Saddle River, NJ: Prentice Hall PTR, 1999.
Version History
Introduced before R2006a