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Estimate empirical transfer functions and periodograms

estimates a
transfer function of the form:`g`

= etfe(`data`

)

$$y(t)=G(q)u(t)+v(t)$$

`data`

contains time- or frequency-domain input-output
data or time-series data:

If

`data`

is time-domain input-output signals,`g`

is the ratio of the output Fourier transform to the input Fourier transform for the data.For nonperiodic data, the transfer function is estimated at 128 equally-spaced frequencies

`[1:128]/128*pi/Ts`

.For periodic data that contains a whole number of periods (

`data.Period = integer`

), the response is computed at the frequencies`k*2*pi/period`

for`k = 0`

up to the Nyquist frequency.If

`data`

is frequency-domain input-output signals,`g`

is the ratio of output to input at all frequencies, where the input is nonzero.If

`data`

is time-series data (no input channels),`g`

is the periodogram, that is the normed absolute square of the Fourier transform, of the data. The corresponding spectral estimate is normalized, as described in Spectrum Normalization and differs from the`spectrum`

normalization in the Signal Processing Toolbox™ product.

applies
a smoothing operation on the raw spectral estimates using a Hamming
Window that yields a frequency resolution of about `g`

= etfe(`data`

,`M`

)`pi/M`

.
The effect of `M`

is similar to the effect of `M`

in `spa`

. `M`

is ignored for
periodic data. Use this syntax as an alternative to `spa`

for
narrowband spectra and systems that require large values of `M`

.

specifies
the frequency spacing for nonperiodic data.`g`

= etfe(`data`

,`M`

,`N`

)

For nonperiodic time-domain data,

`N`

specifies the frequency grid`[1:N]/N*pi/Ts`

rad/TimeUnit. When not specified,`N`

is 128.For periodic time-domain data,

`N`

is ignored.For frequency-domain data, the

`N`

is`fmin:delta_f:fmax`

, where`[fmin fmax]`

is the range of frequencies in`data`

, and`delta_f`

is`(fmax-fmin)/(N-1)`

rad/TimeUnit. When not specified, the response is computed at the frequencies contained in data where input is nonzero.