Fast Fourier Transform

C# implementation of Cooley–Tukey's FFT algorithm.
Cooley–Tukey's fast Fourier transform (FFT) algorithm is a method for computing the finite Fourier transform of a series of N (complex) data points in approximately N log, N operations. FFT operates on inputs that contain an integer power of two number of samples, the input data length will be augmented by zero padding at the end.
A chart visualizer tool is developed to visualize the input and output data.

Example 1

Simple cosine function 10 hz

Example 2

Summation of cos and sin functions 10, 20 30 and 70 hz

Example 3

Sine sweep 10 to 40 Hz 1G at 0.5 octave

References

• https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm
• https://rosettacode.org/wiki/Fast_Fourier_transform#C.23
• https://github.com/tha7556/Signal-Processing/blob/master/Signal%20Processing/Project3/Fourier.cs
• http://paulbourke.net/miscellaneous/dft/
• https://dsp.stackexchange.com/questions/36955/considering-the-fft-of-real-complex-signals
• https://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf
• https://www.gaussianwaves.com/2015/11/interpreting-fft-results-obtaining-magnitude-and-phase-information/
• https://www.gaussianwaves.com/2015/11/interpreting-fft-results-complex-dft-frequency-bins-and-fftshift/

Below used for chart visualizer development
• https://peltiertech.com/calculate-nice-axis-scales-in-your-excel-worksheet/
• https://peltiertech.com/calculate-nice-axis-scales-in-excel-vba/