Discrete Transfer Function Estimator

Compute estimate of frequency-domain transfer function of system

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Libraries:
DSP System Toolbox / Estimation / Power Spectrum Estimation

Description

The Discrete Transfer Function Estimator block estimates the frequency-domain transfer function of a system using the Welch’s method of averaged modified periodograms.

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 sample rate of the block is equal to 1/T. T is the sample time of the inputs to the block.

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.

Examples

Estimate Frequency-Domain Transfer Function of System Using Random Excitation Input

This example shows how to use the Discrete Transfer Function Estimator block to estimate the frequency-domain transfer function of a system.

Open the ex_discretetransferfunctionestimator.slx model. The Random Source block generates the system input signal that you pass through the x port of the Discrete Transfer Function Estimator block. The sample rate of the input signal is 44.1 KHz. This input signal passes through a lowpass filter with a normalized cutoff frequency of 0.3. The filtered signal represents the system output signal that you input through the port y of the Discrete Transfer Function Estimator block. Because the Discrete Transfer Function Estimator block outputs complex values, compute the magnitude of the output signal to generate a plot of the transfer function estimate.

Run the model. The array plot shows the system transfer function, a lowpass filter that matches the frequency response of the Discrete FIR Filter block.

Ports

Input

x — System input signal

vector | matrix

Specify the system input signal as a vector or a matrix.

The inputs x and y must have the same size and data type.

Data Types: double | single

y — System output signal

vector | matrix

Specify the system output signal as a vector or a matrix.

The inputs x and y must have the same size and data type.

Data Types: double | single

Output

Output — Transfer function estimate

vector | matrix

Transfer function estimate, returned as a vector or a matrix. For more details on how the block computes the transfer function estimate, see Algorithms.

Data Types: double | single

Parameters

Window length source — Window length source

Same as input frame length (default) | Specify on dialog

Specify the source of the window length value. You can set this parameter to:

• Same as input frame length — Window length is set to the frame size of the input.

• Specify on dialog — Window length is the value you specify in Window length.

Window length — Window length

1024 (default) | positive integer ≥ 2

Specify the length of the window, in samples, used to compute the spectrum estimate as a positive integer greater than or equal to 2.

Dependencies

To enable this parameter, set Window length source to Specify on dialog.

Window overlap (%) — Percentage of overlap between windows

0 (default) | nonnegative scalar

Specify the percentage of overlap between successive data windows as a nonnegative scalar in the range [0,100).

Averaging method — Averaging method

Running (default) | Exponential

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 forgetting factor from input port — Specify forgetting factor from input port

off (default) | on

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.

Dependencies

To enable this parameter, set Averaging method to Exponential.

Forgetting factor — Forgetting factor

0.9 (default) | positive scalar ≤ 1

Specify the exponential weighting forgetting factor as a positive scalar ≤ 1.

Dependencies

To enable this parameter, set Averaging method to Exponential and clear the Specify forgetting factor from input port parameter.

Number of spectral averages — Number of spectral averages

1 (default) | positive integer

Specify the number of spectral averages as a positive integer. The Transfer Function Estimator block computes the current estimate by averaging the last N estimates. N is the number of spectral averages.

Dependencies

To enable this parameter, set Averaging method to Running.

FFT length source — Source of FFT length value

Auto (default) | Property

Specify the source of the FFT length value as Auto or Property.

When the source of the FFT length is set to Auto, the 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.

FFT length — FFT length

128 (default) | positive integer

Specify the length of the FFT that the Discrete Transfer Function Estimator block uses to compute spectral estimates as a positive integer.

Window function — Window function

Hann (default) | Chebyshev | Flat Top | Hamming | Kaiser | Rectangular

Specify a window function for the Discrete Transfer Function Estimator block. Possible values are:

• Hann

• Chebyshev

• Flat Top

• Hamming

• Kaiser

• Rectangular

Sidelobe attenuation of window (dB) — Sidelobe attenuation of window

60 (default) | positive scalar

Specify the sidelobe attenuation of the window as a positive scalar in dB.

Dependencies

To enable this parameter, set Window function to Kaiser or Chebyshev.

Frequency range — Frequency range of the transfer function estimate

Centered (default) | One-sided | Two-sided

Specify the frequency range of the transfer function estimate.

• Centered –– The block computes the centered two-sided transfer function of the real or complex input signals, x and y.

• onesided –– The block computes the one-sided transfer function of real input signals, x and y.

• twosided –– The block computes the two-sided transfer function of the real or complex input signals, x and y.

Output magnitude squared coherence estimate — Magnitude squared coherence estimate

off (default) | on

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.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Specify the type of simulation to run. You can set this parameter to:

• Interpreted execution –– Simulate model using the MATLAB^® interpreter. This option shortens startup time.

• Code generation –– 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 subsequent simulations.

Block Characteristics

Data Types	double | single
Multidimensional Signals	No
Variable-Size Signals	No

Algorithms

Welch's Method of Averaged Modified Periodograms

Give two signal inputs, x and y:

1. Multiply the inputs by the window and scale the result by the window power.

2. Take FFT of the signals, X and Y.

3. Compute the current power spectral density estimates, Pxx, Pyy, and the current cross power spectral density estimate, Pyx, by taking the moving average of last N number of Z₁, Z₂, and Z₃ vectors, respectively:

   • Z₁ = X.*conj(X)

   • Z₂ = Y.*conj(Y)

   • Z₃ = Y.*conj(X)

   For details on the moving average methods, see Averaging Method.

The transfer function estimate is calculated by dividing Pyx by Pxx.

The magnitude squared coherence, Cxy, is defined by the following equation:

$$C_{xy}=\frac{\left(\text{abs}\left(P_{xy}\right).^2\right)}{\left(P{}_{xx}.*P_{yy}\right)}$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2014a

R2024a: Change in the default value of Simulate using parameter

The default value of the Simulate using parameter is now Interpreted execution. With this change, the block uses the MATLAB interpreter for simulation by default.