Additive Gaussian Noise Removal from Signals Using Bispectral and Wavelet Transform Methods

This article presents five computational programs designed to eliminate additive Gaussian noise from signals using bispectral analysis and wavelet transform techniques. The implementations include:

1. A bispectral analysis program for single variables that computes higher-order spectral characteristics through third-order cumulant estimation and two-dimensional Fourier transformation, enabling non-Gaussian signal analysis beyond conventional power spectrum.

2. An autocorrelation function calculation program utilizing inverse Fourier transform, which implements the Wiener-Khinchin theorem by transforming power spectral density back to time domain with proper normalization and lag handling.

3. A comprehensive spectral analysis suite employing FFT algorithms to compute preference spectra (user-defined frequency bands), power spectra (periodogram-based), root mean square spectra (amplitude characterization), and logarithmic spectra (decibel-scale representations) with windowing functions and spectral averaging.

4. A wavelet-based denoising pipeline for .wav audio files that implements multi-resolution analysis using wavelet decomposition trees, followed by thresholding operations on detail coefficients to remove additive white noise while preserving signal features.

5. A comparative evaluation framework that applies multiple wavelet families (Daubechies, Symlets, Coiflets) and thresholding strategies (soft, hard, universal) to identical noisy signals, quantifying performance metrics like SNR improvement and mean squared error for optimal parameter selection.

These programs provide robust methodologies for processing signals contaminated with additive Gaussian noise. The implementations incorporate proper error handling, parameter validation, and visualization capabilities to facilitate practical applications in signal processing research and development.