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# Inverse DFT PowerPoint PPT Presentation

Inverse DFT. Frequency to time domain. Sometimes calculations are easier in the frequency domain then later convert the results back to the time domain Convert Time -> Frequency with DFT Convert Frequency -> Time with the Inverse Discrete Fourier Transform. From Last week, the DFT is:.

Inverse DFT

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## Inverse DFT

### Frequency to time domain

• Sometimes calculations are easier in the frequency domain then later convert the results back to the time domain

• Convert Time -> Frequency with DFT

• Convert Frequency -> Time with the Inverse Discrete Fourier Transform

• From Last week, the DFT is:

• The IDFT is:

Where x is effectively a row matrix of size N

h is the required harmonic

N is number of Fourier coefficients

F(h) is the complex DFT value

• To speed up the manual analysis, remember:

• Relate this to the argand diagram…

• Similarly

• So the vector rotates clockwise

### Example

• Consider the 4 DFT values generated from last week’s example: {2,1+j,0,1-j}

### DFT processing cost

• DFT processing cost is expensive

• Each term is a product of a complex number

• Each term is added so for an 8 point DFT need 8 multiplies and 7 adds (N and N-1)

• There are 8 harmonic components to be evaluated (h=0 to 7)

• So an 8 point DFT requires 8x8 complex multiplications and 8x7 complex additions

• An N point transform needs N2 Complex multiplications and N(N-1) complex adds

### Fast Fourier Transform

• Processing cost for DFT is:

• Processing cost for FFT is:

• 1024 point:

DFT: 1048576x and 1047552+

FFT: 5120x and 10240+