Property

DFT symmetry vs DFT duality in Richard Lyons' Understanding DSP

DFT symmetry vs DFT duality in Richard Lyons' Understanding DSP
  1. What is symmetry property of DFT?
  2. What is duality property in DFT?
  3. Is DFT symmetrical?
  4. What is the difference between DFS and DFT give example for your comparison?

What is symmetry property of DFT?

DFT conjugate symmetry says that there is redundancy in the spectral content of a real-valued signal. But what exactly is the minimal set of frequencies that we must compute to fully represent the signal? We can think of this by working through each. N − 1 and seeing which other components can be inferred once we have ...

What is duality property in DFT?

The Duality Property tells us that if x(t) has a Fourier Transform X(ω), then if we form a new function of time that has the functional form of the transform, X(t), it will have a Fourier Transform x(ω) that has the functional form of the original time function (but is a function of frequency).

Is DFT symmetrical?

And without going into mathematical details, DFT of real valued function is symmetric, i.e. resultant Fourier function has both real and imaginary parts which are mirror images with respect to 0 frequency component.

What is the difference between DFS and DFT give example for your comparison?

Basically, DFS is used for periodic and infinite sequence. Whereas, DFT is used for non-periodic and finite sequence. Although, They are same Mathematically.

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