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DFT of x[n] is defined as Select one:

Question

DFT of x[n] is defined as Select one:

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Solution

I'm sorry, but you didn't provide a question or a list of options to choose from. The Discrete Fourier Transform (DFT) of a sequence x[n] is typically defined as:

X[k] = Σ (from n=0 to N-1) x[n] * e^(-j2pikn/N)

Where:

  • X[k] is the kth DFT coefficient
  • x[n] is the nth sample of the sequence
  • N is the total number of samples
  • j is the imaginary unit
  • e is the base of the natural logarithm
  • pi is a mathematical constant whose value is the ratio of any circle's circumference to its diameter
  • The sum is over n, which goes from 0 to N-1

This formula essentially transforms the sequence from the time domain to the frequency domain.

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