MATLAB Code Implementation for Generating White, Pink, and Brown Noise

The process of generating white noise, pink noise, and brown noise represents a fascinating and complex area in signal processing. Using MATLAB's robust programming environment, which excels at handling sophisticated mathematical computations, developers can implement various noise generation algorithms through code manipulation. For white noise generation, MATLAB implementations typically use the randn() function to create Gaussian white noise with a flat power spectral density across all frequencies. Pink noise (1/f noise) requires spectral shaping using FFT-based methods or filtering approaches to achieve its characteristic -3 dB/octave roll-off. Brown noise (Brownian motion/red noise) can be generated through cumulative summation of white noise samples, resulting in a -6 dB/octave frequency response. These noise signals serve distinct applications: white noise is essential for testing audio equipment frequency responses, pink noise finds use in acoustic measurements and sound system calibration due to its equal energy per octave, while brown noise's soothing properties make it valuable in relaxation therapies and sleep assistance applications. Understanding these generation techniques benefits multiple disciplines ranging from audio engineering to psychological research. Key MATLAB functions involved include fft(), ifft() for frequency domain manipulation, filter design functions for spectral shaping, and cumulative operations for brown noise synthesis. Proper implementation requires attention to sampling rates, frequency normalization, and amplitude scaling to ensure accurate noise characteristics.