# MATLAB transfer function question: Fundamentals

• MATLAB
• Raajatre
In summary: Your fellow Matlab userIn summary, the conversation discussed how to implement a query from DSP in MATLAB. The task involves taking the transfer function using two time-varying signals and analyzing the system's frequency response. The Laplace transform or Fourier transform can be used to obtain the frequency domain representation of the signals. The "tf" and "bode" functions in MATLAB can be used to create a transfer function model and plot the frequency response, respectively. More information on these functions can be found in the MATLAB Help section. Clarifications and further help can be requested from the community.
Raajatre
Dear all,

This is a query from DSP which I need to implement in MATLAB. I am new to both, DSP and MATLAB.
I have gone through the Transfer Function (TF) theory in MATLAB Help but could not really figure out how I use it for my application.
Just to give you an idea of my task:

I have two signals in time (output varying continuously with time hence I suppose they are time varying) from two measuring systems.

I have to take the TF using one as the output and the other as the input.
The intension is to see how the system is reacting to frequency and around what frequency the gain drops.
From the TF theory, I should get the Laplace transform of the two signals and then take the ratio of o/p against i/p.

But I am not sure if,
1) The two signals are time varying, can I take the Laplace?
2) If I can not take the Laplace, how do I get the TF?
3) If I can take the TF how do I get it in MATLAB?

This could be an ill defined query so if there is anything not clear please let me know. I will try and clear it further.

Your valuable inputs will be highly appreciated.

Thanking you in anticipation.

Dear DSP,

Thank you for your query. I understand that you are new to both DSP and MATLAB, so let me provide some guidance on how to approach your task.

Firstly, yes, you can take the Laplace transform of time-varying signals. However, it may not be necessary in your case. If you are more interested in the frequency response of your system, you can use the Fourier transform instead. This will give you the frequency domain representation of your signals.

To obtain the transfer function, you can use the "tf" function in MATLAB. This function takes in the coefficients of the numerator and denominator of your transfer function and creates a transfer function model. You can find more information on how to use this function in the MATLAB Help section.

Once you have your transfer function model, you can use the "bode" function to plot the frequency response and see at what frequency the gain drops. This function also allows you to specify the input and output signals for your transfer function.

I hope this helps you get started with your task. If you have any further questions, please feel free to ask. Good luck!

Dear researcher,

Thank you for reaching out with your question about implementing transfer functions in MATLAB. I understand the importance of understanding and accurately representing the behavior of systems using transfer functions. Here are my suggestions for your task:

1) The Laplace transform can be taken for time-varying signals, as long as they are continuous. However, if your signals are discrete, you may need to use the Z-transform instead. You can check the documentation in MATLAB for the appropriate function to use for your specific signals.

2) If you are unable to take the Laplace transform, you can still obtain the transfer function by using the frequency response of the system. This can be done by taking the Fourier transform of the input and output signals and then taking the ratio. This will give you the frequency response, which can then be converted to the transfer function.

3) MATLAB has built-in functions for obtaining transfer functions, such as tf and zpk. You can also use the GUI tool, Control System Designer, to easily obtain the transfer function from your input and output signals. I recommend going through the documentation and tutorials for these functions to better understand how to use them for your specific application.

I hope this helps and please feel free to reach out with any further questions or clarifications. Best of luck with your research.

## What is a transfer function in MATLAB?

A transfer function in MATLAB is a mathematical representation that describes the relationship between the input and output of a dynamic system. It is typically used to analyze and design control systems and filters.

## How do I create a transfer function in MATLAB?

To create a transfer function in MATLAB, you can use the tf(num, den) function, where num and den are the vectors containing the coefficients of the numerator and denominator of the transfer function, respectively. You can also use the tfest function to estimate a transfer function from data.

## What is the difference between a continuous-time and a discrete-time transfer function in MATLAB?

A continuous-time transfer function in MATLAB represents a system that operates on a continuous time scale, while a discrete-time transfer function represents a system that operates on a discrete time scale. The tf function creates a continuous-time transfer function by default, but you can specify the sample time to create a discrete-time transfer function.

## How can I plot a transfer function in MATLAB?

To plot a transfer function in MATLAB, you can use the bode, nyquist, or step functions. These functions generate Bode, Nyquist, and step response plots, respectively. You can also use the pzmap function to plot the poles and zeros of a transfer function.

## Can I convert a transfer function to a state-space representation in MATLAB?

Yes, you can convert a transfer function to a state-space representation in MATLAB using the tf2ss function. This function converts a transfer function to its equivalent state-space representation in controllable canonical form.

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