Generating Colored Noise Using Butterworth Filters

This program provides a comprehensive toolset for generating colored noise and processing it through Butterworth filters to obtain both waveform visualizations and power spectrum analyses. The implementation features several key components: 1. Butterworth Filter Implementation: The program incorporates a digital Butterworth filter designed using standard signal processing algorithms (typically employing MATLAB's butter() function for filter coefficient calculation). The filter parameters (order and cutoff frequency) can be configured to achieve specific frequency response characteristics, ensuring smooth and clear noise filtering. 2. Colored Noise Generation: The code generates various types of colored noise (white, pink, brown noise) through different algorithmic approaches. For white noise, it uses random number generation with uniform distribution; for pink/brown noise, it implements frequency-domain shaping or autoregressive models. Parameters controlling frequency distribution and amplitude can be adjusted through configurable variables in the noise generation functions. 3. Waveform Visualization: The program includes plotting functionality (using MATLAB's plot() or similar functions) to display generated noise waveforms graphically. This allows users to observe time-domain characteristics and analyze noise patterns through interactive visualization tools. 4. Power Spectrum Analysis: Beyond waveform display, the code performs spectral analysis using FFT-based algorithms (typically pwelch() or periodogram functions) to compute power spectral density. This helps users understand frequency distribution patterns and energy concentration across different frequency bands. Overall, this program offers an integrated environment for generating, processing, and analyzing colored noise, providing practical insights into noise characteristics and their applications in signal processing. The modular code structure allows easy customization of filter parameters and noise properties for different experimental requirements.