DFT Noise Filtering

In this UW AMATH582 assignment we are provided with noisy acoustic submarine positioning data. The data comprises discrete time measurements made at half hour increments organized into a 4D array. Each time frame is a 3D array of cartesian coordinates containing the acoustically detected intensity volume. The data is transformed into reciprocal space by 3D FFT. Averaging the transformed signal increases the signal to noise ratio and allows discovery of the frequency "signature". In reciprocal space, the frequency volume containing the signal remains centered at the same position regardless of time index while the signal position in lab space follows a trajectory. The fixed location of the center frequency in reciprocal space allows placement of a Gaussian filter centered at the central frequency component. Each time frame is FFT 3D transformed, filtered in k space and subsequently transformed back. The resulting denoised echo is now positioned by a simple maximum allowing the recovery of the de-noised trajectory.

Read a detailed explanation of the discrete Fourier transform and DFT noise filtering here.

The Github project is availabe here: https://github.com/aruymgaart/AMATH/tree/master/dft_noise_filter_582HW1.

Example source code:

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