# Frequency response functions

• arpwpagr
In summary: So what you would do is thisIn summary, In this conversation, the expert explains that you should not use matrices to convert time domain data to frequency domain, but instead use a lookup table.
arpwpagr
Hi all,
I have input force data and output acceleration data to calculate frequency response functions. As these data are in time domain I converted it to frequency domain using fft function in MATLAB. This is the procedure I used.
As an example Let's think, Force matrix =a
Acceleration matrix= b
c=fft2(a)./fft(b);
d=real(c);
There are 24 sensors in the system and I used all data once by using a matrix. I am not sure whether this is correct or not. Should I use one data at once or matrix is correct. Can anyone help me? It is a great help for me.
Thank you!

Since you have the input and output relationship in the frequency domain, I think you would be better off leaving the matrices alone and leaving them a lookup table to interpolate with.

Or you could divide the two expressions given and pass your values through the resulting expression.

What you are doing is conceptually wrong.

I have input and output values in the time domain and I want to convert it to frequency domain to find frequency response functions. Then I used fft function in MATLAB to do that. I have 8192 data points from 24 locations which means dimension of acceleration matrix is 8192*24 and force matrix is 8192*1.
I used this formula
The basic formula for a frequency response function is
H(f)=Y(f)/X(f)

Where H(f) is the frequency response function.

And Y(f) is the output of the system in the frequency domain.

And where X(f) is the input to the system in the frequency domain.

Ok yes I take back what I said earlier, reviewing the equations that operation does give you the frequency response of your system. I was thinking you were doing matrix division not a scalar division (missed the dot next to the division sign " ./ " ).

Hi there,

Your approach to using FFT (Fast Fourier Transform) to convert your input and output data from time domain to frequency domain seems correct. This is a common method used in signal processing and analysis.

As for your question about using a matrix with all 24 sensors versus using one data at a time, it depends on your specific research or experiment. If all 24 sensors are measuring the same input and output data, then using a matrix would be appropriate. However, if each sensor is measuring different input and output data, then it would be more accurate to analyze one data at a time.

I would recommend consulting with your colleagues or supervisor to determine the best approach for your specific project. They may also have additional insight or resources to help you with your frequency response function calculations.

Best of luck with your research!

## What are frequency response functions?

Frequency response functions are mathematical representations of the relationship between input and output signals in a system, with respect to frequency. They show how a system responds to different frequencies of input signals, and can be used to analyze and predict the behavior of a system.

## Why are frequency response functions important?

Frequency response functions are important because they provide valuable information about the performance and stability of a system. They can help identify potential issues or weaknesses in a system, and can be used to optimize and improve system performance.

## How are frequency response functions measured?

Frequency response functions can be measured using various techniques, such as sine sweeps, impact testing, or random excitation. These methods involve applying a known input signal to the system and measuring the resulting output signal at different frequencies.

## What is the difference between magnitude and phase in a frequency response function?

Magnitude refers to the amplitude or strength of the output signal relative to the input signal, while phase refers to the delay or shift in the output signal compared to the input signal. Both magnitude and phase are important aspects of a frequency response function and can provide insight into the behavior of a system.

## How are frequency response functions used in real-world applications?

Frequency response functions are used in a variety of real-world applications, such as in designing and optimizing electronic circuits, analyzing the performance of mechanical systems, and testing and troubleshooting equipment. They are also used in fields such as acoustics, signal processing, and control systems engineering.

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