Filter Design for Noise Signal Removal

1. First, generate a continuous signal containing low, medium, and high frequency components. Implement this using a combination of sinusoidal signals with different frequencies (e.g., 10Hz, 50Hz, and 200Hz). Sample the signal at an appropriate sampling rate (typically >2× highest frequency) and perform spectral analysis using FFT. Design three types of digital filters: high-pass filter (using butter() or cheby1() functions with cutoff above medium frequencies), low-pass filter (cutoff below medium frequencies), and band-pass filter (passing only medium frequency range). Apply these filters using filter() or filtfilt() functions and observe the filtered spectra through frequency domain visualization to understand filter characteristics and performance.

2. For practical noise removal, acquire a speech signal contaminated with noise. This can be achieved by recording in noisy environments or programmatically adding noise (like white Gaussian noise using awgn() function) to clean recordings. Sample the signal following Nyquist criteria and perform spectral analysis to identify noise characteristics (typically visible as peaks in specific frequency bands). Design an appropriate filter (FIR or IIR) using filter design tools (fdatool or designfilt) based on the noise frequency profile. Implement filtering using convolution or filter functions, then evaluate the enhancement through spectral comparison and perceptual quality assessment to improve speech intelligibility.