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Fourier Transformation Exam Questions and Answers

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Fourier Transformation Exam Questions and Answers Discrete Fourier Transform - Answer-All our data is digital and the FT works on analog. So we need a discrete formation of the FT Discrete Fourier Transform (DFT) - Answer-1)Assumes regularly spaced data values 2)Returns the value of the fouri...

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  • August 14, 2024
  • 2
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers

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  • fourier transformation
  • fourier transformation exam questions and answers
  • discrete fourier transform

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  • Fourier Transformation
  • Fourier Transformation

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Fourier Transformation Exam Questions
and Answers

Discrete Fourier Transform - Answer-All our data is digital and the FT works on analog.
So we need a discrete formation of the FT

Discrete Fourier Transform (DFT) - Answer-1)Assumes regularly spaced data values
2)Returns the value of the fourier transform for a set of values
in frequency space which are
equally spaced

Matlab Functions - Answer-fft(X)
fft2(X)
fftn(X)
Phase Spectrum = angle(fft(X,N))

Linear Operator - Answer-If f(X) and g(X) are two functions with Fourier transforms F(U)
and G(U) then the Fourier transform of af(X) + bg(X) where a and b are constants is
simply aF(U) + bG(U).

Shifting - Answer-Shifting the real space data through a fixed distance has the effect
that:
If f(X) is a function with the Fourier transform F(U) then the Fourier
transform of f(x =x0) is given by e^(-2pi i x0 u)F(U)

Scaling - Answer-If we scale the spacing of the real space data in distance, we have
that:

Scaling - Theorem - Answer-If f(X) is a function with the Fourier transform F(U) then the
Fourier
transform of f(AX) where a is a real constant is given by 1/mod(A) F(U/A)

Rotation - Answer-If we rotate the real space data, its fourier transform is rotated by the
same angle, or more exactly

So what is this all about ......Fourier Transform huh
Basic Principle - Answer-If you had a smoothie and wanted to figure out the ingredients
you could use the Fourier transform.
But instead of a smoothie you are given a wave and the ingredients are a couple of
particular sine waves added together.

Fourier Applications - Answer-1)Filtering

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