Designing a Low-Pass Filter with Signal Input-Output Comparison

In this task, we need to design a low-pass filter to compare the input and output signals. Before undertaking this design, it is essential to understand the definition of low-pass filters and their applications in signal processing. A low-pass filter is a signal processing tool that reduces or eliminates high-frequency noise by allowing low-frequency signals to pass through while blocking high-frequency components. This type of filter is particularly useful in audio and video processing applications, as it helps remove static or noise and enhances signal quality. To design an effective low-pass filter, we must consider several factors including the filter type (such as Butterworth, Chebyshev, or elliptic filters), frequency response characteristics, and appropriate parameter selection. In practical implementation using programming languages like Python or MATLAB, key functions include scipy.signal.butter() for filter design and scipy.signal.filtfilt() for zero-phase filtering. The critical parameters to configure are the cutoff frequency, filter order, and sampling rate, which directly affect the filter's performance. After successfully designing the low-pass filter, we can compare the input and output signals to verify whether the filter effectively reduces high-frequency noise and improves signal quality. This typically involves plotting both signals in the time domain and frequency domain using FFT analysis, and calculating metrics like signal-to-noise ratio (SNR) to quantitatively assess filter performance.