Inverse DFT

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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:.

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## PowerPoint Slideshow about 'Inverse DFT' - nova

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Presentation Transcript

### 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+