Generation of Complex Noise Signals

Generation of complex noise signals, including Gaussian white noise and colored noise (with definable filters). Noise signals refer to undesired random interference signals introduced during signal transmission or processing. Gaussian white noise is a random signal with uniform power spectral density and equal energy at all frequencies, commonly used for modeling signal processing and communication systems. In code implementation, Gaussian white noise can be generated using functions like randn() in MATLAB or numpy.random.randn() in Python to create independent real and imaginary components with zero mean and unit variance. Colored noise refers to random signals with varying power spectral density, where energy is unevenly distributed across different frequencies. By defining appropriate filters, the spectral characteristics of colored noise can be adjusted to meet specific application requirements. Implementation typically involves generating white noise first, then applying digital filters (such as FIR or IIR filters) to shape the frequency response. For example, one can use filter design functions like fir1() in MATLAB or scipy.signal.lfilter() in Python to create custom frequency-domain characteristics. Therefore, when generating complex noise signals, one can choose between Gaussian white noise or colored noise, and define their spectral characteristics through appropriate filtering operations. The complex noise generation process generally involves creating independent noise components for real and imaginary parts, followed by potential filtering stages for spectral shaping.