## Discrete Fourier Transform of an Arbitrary (Finite) Energy Signal |
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## Features- Input data is supplied by the user using the copy/paste mechanism from a local text file
- DFT approximation for various definitions of the continuous Fourier transform
- Plot for real-valued time-domain signal
- Plots for complex-valued frequency-domain signal in either Real/Imaginary or Magnitude/Argument format
- Scale factors are reported so the coordinates are well quantified if the data have physical dimensions attached
## Rules and TheoriesThere are many variations of continuous Fourier transform definitions. But, they all fall into one of the two categories: Type 1:
where and typically . This applet utilizes a discrete Fourier transform (DFT) via the popular FFT algorithm to approximate the Fourier transform. For a given definition and choice of C
where N is a number that is power of 2. The inverse transform is carried out using the inverse FFT algorithm. ## The Applet and User's Guide
- Enter a sequence of time-domain sampled data arranged in one column into the input text area. Alternatively, user can open a local file containing appropriate data, first copy then paste (using Ctrl-V) into the text area
- Change the time-domain sampling rate (Delta t) and set the correct number of points
- Click the "Forward Transform" button to perform the forward transform. Results will be used to plot the signals in both time and frequency domains. The spectral sequence is automatically filled
- Click the "Inverse Transform" to perform an inverse transform
## References[1] Alexander D. Poularikas, "The Transform and Applications Handbook", CRC Press, Boca Raton, 1996. [2] George Arfken, "Mathematical Methods for Physicists", Academic Press, San Diego, 1985. [3] William H. Press, Saul A. Teukolsky, Willaim T. Vetterling and Brian P. Flannery, "Numerical Recipes in C", Cambridge University Press, Cambridge, 1995. |
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