# Why shift, take absolute value and perform log transform to the frequency spectrum of an image obtained by fft2?

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ForcedByMathWorks on 6 Nov 2021
Edited: Chris on 21 Apr 2022
I have to obtain the frequency spectrum of a grayscale image using FFT in MATLAB and plot the spectrum. I used fft2() and plotted the output.
I watched a tutorial on plotting frequency spectrum and in that, they perform fftshit(), take the absolute value, apply a log transformation, scale pixels using mat2gray() and then convert into uint8 before plotting the spectrum.
im2uint8(mat2gray(log(abs(fft_shifted)+1)))
My question is, is that necessary to perform all those steps before plotting the frequency spectrum?
I know fftshift() is used to center the spectrum around 0th frequency coefficient. But what is the use of performing other functions?
I plotted the frequency spectrum without shifting, after shifting, and after applying the above-mentioned steps.
After this, I have to apply a low pass filter to the grayscale image and compare frequency spectrums. (This is a homework question)
Any advice is much appreciated. Thank you!

yanqi liu on 8 Nov 2021
im2uint8(mat2gray(log(abs(fft_shifted)+1)))
sir，i think
abs(fft_shifted)+1 to avoid log(0) or log(neg)
log to display result in log space，to avoid some data too big with some data too small

Chris on 8 Nov 2021
take the absolute value
The log of a negative number is undefined, which would make for a boring image.
apply a log transformation
It's likely some intensities will be orders of magnitude higher than some others. Applying a log scale allows you to see the smaller values as well. Otherwise, the image will be boring.
scale pixels using mat2gray() and then convert into uint8
I don't know what function you're using to display the image, but functions like imshow() expect integers on a 0 to 255 scale (an 8-bit pixel map). im2uint8(mat2gray()) accomplishes that scaling.
##### 2 CommentsShowHide 1 older comment
Chris on 21 Apr 2022
If it's in matrix form, like an image, abs() will make all points positive.

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