Gaussian White Noise Generation Function with Zero Mean and Specified Variance

This document discusses the generation of Gaussian white noise with zero mean and specified variance, as well as complex Gaussian white noise. Gaussian white noise is a random signal characterized by a Gaussian distribution, typically with zero mean and unit variance. It serves as a fundamental tool in numerous signal processing and communication applications. Through Gaussian white noise generation functions, we can produce noise signals with desired statistical properties. In MATLAB implementations, this is commonly achieved using the randn() function for real-valued noise, where scaling by the standard deviation (square root of variance) adjusts the noise power accordingly.

In certain applications, complex Gaussian white noise must be considered, which consists of noise signals where both real and imaginary components follow Gaussian distributions. Complex Gaussian white noise finds extensive applications in digital communications and image processing systems. Therefore, understanding how to generate these signals is crucial. For complex noise generation, we typically combine two independent randn() outputs for real and imaginary parts, ensuring proper scaling based on the target variance. The implementation typically involves creating two independent Gaussian random variables and combining them as real and imaginary components of a complex signal.

Key implementation considerations include: ensuring statistical independence between real and imaginary parts, proper variance scaling for both components, and maintaining the circular symmetry property of complex Gaussian noise. The generated noise should exhibit flat power spectral density (white characteristic) and proper correlation properties for both real and complex cases.