Frequency Domain Filtering in Digital Image Processing
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Questions and Answers

What did Jean Baptiste Joseph Fourier's contribution state?

  • Any function can be expressed as the integral of sines and/or cosines multiplied by a weighting function.
  • Any periodic function can be expressed as the sum of sines and/or cosines of different frequencies, each multiplied by a different coefficient. (correct)
  • Any periodic function can be expressed as a sum of squares and/or cubes of different frequencies, each multiplied by a different coefficient.
  • Any function can be expressed as a sum of squares and/or cubes of different frequencies, each multiplied by a different coefficient.

What is the formulation in the case of functions that are not periodic?

  • The Fourier series.
  • The sum of squares and/or cubes of different frequencies, each multiplied by a different coefficient.
  • The integral of sines and/or cosines multiplied by a weighting function.
  • The Fourier transform. (correct)

How did Jean Baptiste Joseph Fourier express non-periodic functions?

  • As the integral of sines and/or cosines multiplied by a weighting function. (correct)
  • As the sum of sines and/or cosines of different frequencies, each multiplied by a different coefficient.
  • He did not express non-periodic functions mathematically.
  • As the sum of squares and/or cubes of different frequencies, each multiplied by a different coefficient.

What is the 1-D Discrete Fourier Transform?

<p>It is a method for transforming a one-dimensional signal into the frequency domain (A)</p> Signup and view all the answers

What does the Fourier transform involve for functions that are not periodic?

<p>Expressing them as the integral of sines and/or cosines multiplied by a weighting function (B)</p> Signup and view all the answers

What type of filtering is used for image sharpening in the Frequency Domain?

<p>Highpass Filters (D)</p> Signup and view all the answers

What can be expressed as the sum of sines and/or cosines of different frequencies, each multiplied by a different coefficient?

<p>Periodic functions (A)</p> Signup and view all the answers

What is the key concept presented by Jean Baptiste Joseph Fourier in his contribution?

<p>The representation of periodic functions using sines and cosines (A)</p> Signup and view all the answers

What is the main application of the 1-D Discrete Fourier Transform in digital image processing?

<p>Frequency domain filtering (A)</p> Signup and view all the answers

How are non-periodic functions expressed in the Fourier transform?

<p>As the integral of sines and/or cosines multiplied by a weighting function (D)</p> Signup and view all the answers

What is the primary purpose of using lowpass frequency domain filters in digital image processing?

<p>To reduce noise and blur images (A)</p> Signup and view all the answers

In digital image processing, what does the 2-D Discrete Fourier Transform allow for?

<p>Analysis of frequency components in both horizontal and vertical directions (B)</p> Signup and view all the answers

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