Compute estimate of frequencydomain transfer function of system
Estimation / Power Spectrum Estimation
dspspect3
The Discrete Transfer Function Estimator block estimates the frequencydomain transfer function of a system using the Welch’s method of averaged modified periodograms.
The block takes two inputs, x and y. x is the system input signal and y is the system output signal. x and y must have the same dimensions. For 2D inputs, the block treats each column as an independent channel. The first dimension is the length of the channel. The second dimension is the number of channels. The block treats 1D inputs as one channel. The sample rate of the block is equal to 1/T. T is the sample time of the inputs to the block.
The block buffers the input data into overlapping segments. You can set the length of the data segment and the amount of data overlap through the parameters set in the block dialog box.
The block first applies a window function to the two inputs, x and y, and then scales them by the window power. It takes the FFT of each signal, calling them X and Y. The block calculates P_{xx} which is the square magnitude of the FFT, X. The block then calculates P_{yx} which is X multiplied by the conjugate of Y. The output transfer function estimate, H, is calculated by dividing P_{yx} by P_{xx}.
Source of the window length value. You can set this parameter to:
Same as input frame length
(default)
— Window length is set to the frame size of the input.
Specify on dialog
—
Window length is the value specified in Window length.
This parameter is nontunable.
Length of the window, in samples, used to compute the spectrum
estimate, specified as a positive integer scalar greater than 2
.
This parameter applies when you set Window length source to Specify
on dialog
. The default is 1024
. This
parameter is nontunable.
Percentage of overlap between successive data windows, specified
as a scalar in the range [0,100
). The default is 0
.
This parameter is nontunable.
Specify the number of spectral averages. The Transfer Function
Estimator block computes the current estimate by averaging the last N estimates. N is
the number of spectral averages. It can be any positive integer scalar,
and the default is 1
.
Specify the source of the FFT length value. It can be one of Auto
(default)
or Property
. When the source of the FFT length
is set to Auto
, the Transfer Function Estimator
block sets the FFT length to the input frame size. When the source
of the FFT length is set to Property
, you
specify the FFT length in the FFT length parameter.
Specify the length of the FFT that the Transfer Function Estimator block uses to compute spectral estimates. It can be any positive integer scalar, and the default is 128.
Specify a window function for the Transfer Function Estimator block. Possible values are:
Hann
(default)
Rectangular
Chebyshev
Flat Top
Hamming
Kaiser
Specify the sidelobe attenuation of the window. It can be any
real positive scalar value in decibels (dB). The default is 60
.
This parameter is visible only when Window function is
set to Kaiser
or Chebyshev
.
Specify the frequency range of the transfer function estimate.
centered
(default)
When you set the frequency range to centered
,
the Transfer Function Estimator block computes the centered twosided
transfer function of the real or complex input signals, x and y.
onesided
When you set the frequency range to onesided
,
the Transfer Function Estimator block computes the onesided transfer
function of real input signals, x and y.
twosided
When you set the frequency range to twosided
,
the Transfer Function Estimator block computes the twosided transfer
function of the real or complex input signals, x and y.
Select this check box to compute and output the magnitude squared coherence estimate using Welch’s averaged, modified periodogram method. The magnitude squared coherence estimate indicates how well two inputs correspond to each other at each frequency.
Type of simulation to run. You can set this parameter to:
Code generation
(default)
Simulate model using generated C code. The first time you run
a simulation, Simulink^{®} generates C code for the block. The C
code is reused for subsequent simulations, as long as the model does
not change. This option requires additional startup time but provides
faster simulation speed than Interpreted execution
.
Interpreted execution
Simulate model using the MATLAB^{®} interpreter. This
option shortens startup time but has slower simulation speed than Code
generation
.
The Discrete Transfer Function Estimator block supports real and complex inputs.
Port  Supported Data Type 

x 

y 

Output, H 

This example shows how to use the Discrete Transfer Function Estimator block to estimate the frequencydomain transfer function of a system.
The Random Source block represents the system input signal. The sample rate of the system input is 44.1 KHz. The Random Source input passes through a lowpass filter with a normalized cutoff frequency of 0.3. The filtered signal represents the system output signal. Because the Discrete Transfer Function Estimator block outputs complex values, take the magnitude of the output to see a plot of the transfer function estimate.
To view this example, execute ex_discrete_transfer_function_estimator
in MATLAB Command
prompt.
The transfer function plot displays the system transfer function, a lowpass filter that matches the frequency response of the Discrete FIR Filter block.