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How to Reconstruct a Signal Using the FFT Function

Reconstructing a graphic signal from a deconstructed image (a graphic image represented as frequency wave forms) to an image stored as a standard graphic .png file (a graphic image represented as pixels at specific coordinates on the screen) can be accomplished with a FFT (Fast Fourier Transform) function. Specifically, an IFFT (Inverse Fast Fourier Transfer) function is used to reconstruct a standard graphic file (.png, .gif or .jpg) from a frequency waveform file and an FFT function is used to deconstruct a graphic .png file (or .jpg or .gif file) to a frequency waveform file.

Instructions

- 1
  Download the FFT computer code (ImageMagick) at the ImageMagick website (see Resources).
- 2
  Obtain or generate the frequency and phase component files for the deconstructed signal. If you don't have deconstructed frequency and phase component files, use the imageMagick software to generate a deconstructed graphic file from one of your own .gif or .jpg files (see Tips).
- 3
  Type into the imageMagicK command line editor the "convert" command to perform the graphic signal reconstruction from the waveform file to the standard graphic file (referred to as the spatial domain file). Specify in this command the "-ift" (inverse Fourier Transform) option, the deconstructed magnitude and phase file names and the file name that you want the reconstructed file to be stored in. .
  
  $magick> convert deconstructed-0.png deconstructed-1.png -ift reconstructed.png
  
  This command reads in the frequency and phase domain files (generated on deconstruction), performs the Inverse Fourier Transform function on the data in these files and stores the result in a file named "reconstructed.png."

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