# Thread: Making a Fourier Transformation by hand for Infrared Spectroscopy

1. ## Making a Fourier Transformation by hand for Infrared Spectroscopy

Hello

I want to make a Fourier Transformation by Hand for Infrared Spectroscopy. I decided to use the method of real DTF because it is a good starting point. My Problem:

How I understand it so far:
To record FT-IR spectra a time dependent signal is recorded. I ignore the time at all, and take the magnitudes. In that way I have a 1 x N Matrix, which is my "Time Domain"

Now I make real DFT with it and obtain two 1 x (N/2+1) matrices the Real and the Imaginary.

My Problem is: real DFT is over now, but I haven't got a new spectrum now, with the time Domain converted to frequency Domain.

My Idea is to convert the rectangular notation into polar notation. This will make two 1 x (N/2+1) matrices Magnitude and Phase. After that I want to draw the Magnitude in function of the Wave number (which is calculated from the Phase)

My question: Is this the right way? Is it possible to calculate the wave number out of the phase without knowing the place, time and Angular frequency? What I have to do with my two spectrums to obtain an IR-Spectrum?

2. Ok now I have the solution. I have to draw the absolute value to the power of 2 (X^2)

But my new problem: Does anybody know how to make out of Re(X) and Im(X) the Normal X matrix?

Edit:
I am sorry I missed to use the edit button. I won't do it again

3. Originally Posted by Boojakascha
Hello

I want to make a Fourier Transformation by Hand for Infrared Spectroscopy. I decided to use the method of real DTF because it is a good starting point. My Problem:

How I understand it so far:
To record FT-IR spectra a time dependent signal is recorded. I ignore the time at all, and take the magnitudes. In that way I have a 1 x N Matrix, which is my "Time Domain"

Now I make real DFT with it and obtain two 1 x (N/2+1) matrices the Real and the Imaginary.

My Problem is: real DFT is over now, but I haven't got a new spectrum now, with the time Domain converted to frequency Domain.

My Idea is to convert the rectangular notation into polar notation. This will make two 1 x (N/2+1) matrices Magnitude and Phase. After that I want to draw the Magnitude in function of the Wave number (which is calculated from the Phase)

My question: Is this the right way? Is it possible to calculate the wave number out of the phase without knowing the place, time and Angular frequency? What I have to do with my two spectrums to obtain an IR-Spectrum?
What is the signal that the instrument is recording?

CB

4. @ CaptainBlack

Thank you for your interest in helping me.

I switched the technique to complex DFT through correlation and was successful.
And this gave me power to try it again with real DFT. Yesterday I was successful with real DFT too.

My Signal is time dependent
I have to delete the time data, and make Fourier Transformation with the Amplitudes.
After that I calculate the power (Absolute value in the power of 2) and make up a new x Axis only using the number of Data.
( On real DFT you make X^2 = Re(X)^2 + Im(X)^2 as in complex numbers, even if the values here are just sine and cosinus amplitudes)

In this way the obtained spectra are great, but I still have some minor problems with the intensity which varies depending which DFT method I chose. But today I will look it up in a book.

5. Originally Posted by Boojakascha
@ CaptainBlack

Thank you for your interest in helping me.

I switched the technique to complex DFT through correlation and was successful.
And this gave me power to try it again with real DFT. Yesterday I was successful with real DFT too.

My Signal is time dependent
I have to delete the time data, and make Fourier Transformation with the Amplitudes.
After that I calculate the power (Absolute value in the power of 2) and make up a new x Axis only using the number of Data.
( On real DFT you make X^2 = Re(X)^2 + Im(X)^2 as in complex numbers, even if the values here are just sine and cosinus amplitudes)

In this way the obtained spectra are great, but I still have some minor problems with the intensity which varies depending which DFT method I chose. But today I will look it up in a book.
You might want to consider the Lomb-Scargle periodogram as an alternative to the FFT

CB