Generate a Sinusoidal Signal with White Noise and Low-Pass Filtering

This process involves generating a sinusoidal signal and adding white noise to obtain a mixed signal containing both components. The white noise is then processed using a low-pass filter. In implementation, parameters such as sinusoidal signal frequency and amplitude, along with white noise intensity and spectral characteristics, can be programmatically adjusted. For example, the sinusoidal signal can be generated using waveform synthesis functions (e.g., numpy.sin() in Python or sin() in MATLAB), while white noise can be added through random number generators with specified variance. By modifying these parameters, diverse mixed signal types and waveforms can be produced, facilitating deeper understanding of signal processing principles and technical applications. Additionally, alternative filter types such as high-pass or band-pass filters can be implemented (e.g., using scipy.signal or filter design tools) to explore different signal processing effects. Through advanced signal processing and analysis techniques, including frequency domain transformations and filter response evaluations, further investigation into signal processing domains and practical applications becomes possible.