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Frequancy Domain Filtering (FDF)

This lab focuses on filtering images in the frequency domain using Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) algorithms in MATLAB. The process includes reading an image, computing its DFT, obtaining the Fourier spectrum, and visualizing results through magnitude transformation and centered shifts. The log transformation enhances visual details in the frequency domain. Through step-by-step code examples and explanations, users will learn how to apply FFT techniques to images for improved filtering and analysis.

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Frequancy Domain Filtering (FDF)

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  1. Frequancy Domain Filtering (FDF) Lab 5

  2. Using FFT (Fast Fourier Transform ) algorithm • DFT (Discrete Fourier Transform) & inverse DFT

  3. Image Operation in Frequency Domain

  4. Fourier Transform • MATLAB provides a collection of functions for computing and working with Fourier transforms.

  5. fft2 • Y=fft2(X); % X is the spatial image • It Computes and returns a Discrete Fourier transform(DFT) of an image X, computed with Fast Fourier Transform (FFT) algorithm. • Y is the same size of X • The origin of Y(DFT) is at top left, with four quarter meeting at the center of the frequency.

  6. abs • S = abs(Y); • Used to obtain the Fourier spectrum. • It computes the magnitude of each element in the DFT.

  7. fftshift • Yc = fftshift(Y); • Used to move the origin of the DFT to the center(used to compute the centered DFT).

  8. Computing and visualizing the 2D DFT in MATLAB >> X = imread(‘………’); % load in spatial image >> Y = fft2(X); % compute DFT >> S = abs(Y); % compute magnitude for display >> imshow(S,[]); % shows in four corners of display, you can write it as imshow( abs(Y), [] ); >> Yc = fftshift(Y); % shift DFT to center >> imshow(abs(Yc) , [] ); % show magnitude of DFT in center

  9. NOTE • imshow(I,[low high]) displays the grayscale image I • The value low (and any value less than low) displays as black. • the value high (and any value greater than high) displays as white. • Values in between are displayed as intermediate shades of gray. • If you use an empty matrix [] for [low high], imshow uses [min(I(:)) max(I(:))]; that is: • the minimum value in I is displayed as black. • the maximum value in I is displayed as white.

  10. DFT in center can be visually enhanced(increase visual details) by log transformationc*log(1+double(f)) >> Yc2 = log(1 + abs(Yc) ); >> imshow(Yc2, [] ); % or imshow(abs(Yc2), [] );

  11. ifftshift • Y=ifftshift(Yc) • It reverses the centering. • Used to move the origin of the DFT from the center to the top left.

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