# How to find the system FRF with available input and output FRF?

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Hello,
I did a frequency sweep from 10hz-15kHz through a lock in amplifier (LIA) with two inputs to the LIA. The LIA gives me the demodulated magnitude R, phase (theta), in-phase component X and quadrature component Y for both the input signal.
Now i would like to calculate the total FRF which is the output of the system divided by the input. In this case, demodulated values of signal input 1 is the output and demodulated values of signal input 2 is the input of the system. I would also like to visualise the plot in inertance (acceleration) and receptance (displacement) format.
Can anyone guide me on how to compute the total FRF? Because I was expecting the peak resonance to occur at -90 degree phase and the real part has to be zeo at that frequency. I attached a matlab file, where you can find the r,phase,x and y values. Here the demod 1 is the demodulated values of signal input 1 & demod 4 is the demodulated values of signal input 2.
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### Antworten (1)

Gokul Nath S J am 25 Mai 2023
Hi Yaser,
To compute the total FRF and visualize the plot in inertance (acceleration) and receptance (displacement) format, you can follow the steps below:
1. Load the data into MATLAB: You can load the demodulated magnitude R, phase (theta), in-phase component X, and quadrature component Y values for both input signals into MATLAB. You can load the data using the load function or read it from a file using the appropriate file I/O functions.
2. Calculate the FRF: To calculate the FRF, you need to divide the demodulated values of signal input 1 by the demodulated values of signal input 2.
3. Convert the FRF to inertance and receptance: To visualize the plot in the inertance (acceleration) and receptance (displacement) format, you need to convert the FRF from complex to polar coordinates (magnitude and phase). Then you can use the following equations to convert the FRF to inertance and receptance: Plot the FRF in the inertance and receptance format: Finally, you can plot the FRF in the inertance and receptance format using the semilogx function to plot the magnitude and semilogy function to plot the phase:
FRF = demod1 ./ demod4;
Inertance = -imag(FRF) / (2*pi*f)^2
Receptance = real(FRF) / (2*pi*f)
figure;
semilogx(freq, abs(Inertance));
xlabel('Frequency (Hz)');
ylabel('Inertance (m/s^2)');
figure;
semilogx(freq, abs(Receptance));
xlabel('Frequency (Hz)');
ylabel('Receptance (m/N)');
with regards,
Gokul Nath S J
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Hi, thnaks for the reply. However I do't understand why you are dividing imaginary part by the negative denominator for inertance (accelerance) plot. Signal input 1 is from the accelerometer which gives the acceleration when we multiply it with the sensitivty value right? So when we divide the acceleration with the input load, we should get the inertance FRF? The problem is the load cell is having some resoance at certain frequencies and hence the load is not constant over the entire frequency (refer to the blue plot from the attached figure-This is obtained after multiplying signal input 2 with load cell sensitivity).
Only to convert inertance to receptance format we have to divide the inertance FRF by "-(2*pi*f)^2" correct?

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