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 averaging method as Running
or
Exponential
. In the running averaging method,
the block computes an equally weighted average of specified number of
spectrum estimates defined by Number of spectral
averages parameter. In the exponential method, the block
computes the average over samples weighted by an exponentially decaying
forgetting factor.
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
.
This parameter applies when Averaging method is set
to Running
.
Select this check box to specify the forgetting factor from an input port. When you do not select this check box, the forgetting factor is specified through the Forgetting factor parameter.
This parameter applies when Averaging method is set
to Exponential
.
Specify the exponential weighting forgetting factor as a scalar value
greater than zero and smaller than or equal to one. The default is
0.9
.
This parameter applies when you set Averaging method
to Exponential
and clear the Specify
forgetting factor from input port parameter.
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.