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Understanding the Image output in Frequency Domain

  1. Sep 28, 2012 #1
    I need help understanding how frequencies are distributed when taking the FFT of an Image and how can i determine those frequencies, I really need a detailed and easy tutorial with practical example to understand it.

    When we take the FFT of a Sine/Cos wave we can easily see its frequencies in FFT, here is my example i added comments in detail to understand,

    Code (Text):
    %Matlab Code,
    f=1e3;   %Frequency of Wave -> 1KHz
    A=4;    %Amplitude
    Fs = 1e6;  %Sampling Frequency
    Ts = 1/Fs;   %Sampling Rate
    t = 10/f;       %Time period of 10 Oscillation
    n = 0:Ts:t;  %Generating Samples
    % (1/f)/T = 1000 %Length for 1 Oscillation after Sampling
    % So Length of the Signal for 10 Oscillations is 10,000
    subplot(2,1 ,1);
    % 100,000/10,000 = 100Hz <- First point = 100Hz
    % 2nd Point = 200Hz
    % 3rd Point = 300Hz
    % 4th Point = 400Hz
    % .
    % .
    % 10th Point = 1KHz <- Original Signal Frequency
    subplot(2,1 ,2);
    xlim ([0 100])    % 0 = 100 , 1 = 200......10=1000......100 = 10,000
    set(gca, 'XTickLabel', ((get(gca,'XTick')))*100)
    xlabel ('Frequency in Hz')
    and here is the output image,

    See how easily I can see the frequency of actual signal in Frequency domain, this is because i knew that the original frequency was 1KHz.

    but in case of Images, what are the frequencies ?

    here is the simple code,

    Code (Text):
    image = [0 0 0 0 1 1 1 1]
    The above discrete signal has 8 points so N = 8 How can i determine the frequencies and amplitude of this signal ? just like i did above for Sine wave

    If i take its FFT and display it ,

    Code (Text):
    f = fft2(image)
    imshow(fftshift(f)); % plotting

    it is nothing but 3-colors the middle one is white. (as expected)
    I've no idea what does that output mean , how could i understand what are the frequencies in the image from this output ?

    Can somebody explain me just one example of image FFT and how to determine the frequency etc like i did above in case of Sine wave?
    Last edited: Sep 28, 2012
  2. jcsd
  3. Sep 28, 2012 #2


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    Science Advisor
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    2017 Award

    your output image isnt showing

  4. Sep 28, 2012 #3
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