Given x(n) = 2n+ (a-b) ; for n from 0 to 15; where a and b are 8 and 5 respectively

Math Apr 27, 2021

Given x(n) = 2n+ (a-b) ; for n from 0 to 15; where a and b are 8 and 5 respectively. Calculate the DFT coefficients using DIF FFT method.include full numerical calculations.

Expert Solution

Answer:

The real parts of the co-efficients are in the cells colored blue, while the imaginary parts of the co-efficients are in the cells colored orange.

X0 = 288 + i.0
X1 = -16 + i*80.44
X2 = -16 + i*38.63 and so on...

The general formula for the co-efficients is as follows:

X(k) = ∑ x(n) e ^{-j2πnk / N}

an image of how the DFT co-efficients are actually calculated. It involves the application of a single formula multiple times until we get all the co-efficient values.

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