FRF magnitude calculation

Hello all!

I have a question regading the caluculation of FRF magnitude spectra that I would really appreciate some help with.

I have a number of files, each containing single sided FRFs with the real part in the first column and the imaginary part in the second. The question is how to obtain the magnitude spectra. Does this work in the same way as for a FFT, i.e. i take abs(re+im), to get the magnitude, or do I simply extract the real part (first column) from the file?

This might seem as a trivial question, but I'm having real trouble finding a good answer.

Regards, Felix

[Hector Aguila]

La magnitud de la transformada se calcula sacando el valor absoluto del complejo que la representa, y la potencia espectral se calcula como el cuadrado de la magnitud de la transformada.

Answer 1

[Wayne King]

Hi Felix, you should form complex numbers in MATLAB from the first and second columns and take the magnitude squared (if it is a power calculation) of those complex numbers.

[Felix Torner]

Thank you for your answer.

This is sort of what I figured. What I do now is that I take abs(column1 + i*column2) wich I guess gives me the magnitude. If I understand your answer correctly I should calculate (abs(column1 + i*column2))^2. This would be the FRF power spectra then?

Is there an intuitive way of understanding what this represents? I get how a power spectrum for a normal FFT works, but since the FRF represents the transfer function I have a bit of a problem getting to grips with things.

Answer 2

[Dr. Seis]

Or... if you want the magnitude and the input data is really just two columns of numbers(second column not specifically formatted as imaginary), then

data = % Read in data

data_mag = hypot(data(:,1),data(:,2));

[Felix Torner]

That is exactly the case. Thank you very much!

Still having trouble understanding why it is not simply enough to use the real part of it though, or more specifically what the different values represent. I always thought that the real part was the magnitude and the imaginary represented phase. Seems as if that is not the case.

[Dr. Seis]

The magnitude is the length of the vector and the phase is the angle of the vector when complex value is plotted on a grid where the x-axis is the real part and the y-axis is the imaginary part. So... if

data_complex = complex(data(:,1),data(:,2));

Then,

data_mag = abs(data_complex);

data_phase = angle(data_complex);

[Felix Torner]

That makes perfect sense. I haven't dealt with any of this since I graduated but it's slowly coming back now. Thank you very much!