Design of FIR Low-pass, Band-pass, and High-pass Filters for Speech Frequency Bands

This document presents the design of Finite Impulse Response (FIR) low-pass, band-pass, and high-pass filters specifically tailored for speech frequency bands. These filters serve as fundamental tools for voice signal processing, implemented using windowing methods or Parks-McClellan algorithm for optimal frequency response. Through MATLAB or Python implementations using functions like fir1() or scipy.signal.firwin(), these filters enable precise processing and analysis of speech signals to meet diverse application requirements. The low-pass filter attenuates high-frequency components above the cutoff frequency (typically 4 kHz for speech), smoothing and softening the signal using convolution operations with symmetric coefficients. Band-pass filters employ dual cutoff frequencies to selectively pass specific frequency ranges (e.g., 300 Hz-3.4 kHz for telephone bandwidth) through difference-of-low-pass techniques, facilitating targeted spectral analysis. High-pass filters remove low-frequency components below the cutoff (commonly 100-300 Hz) using frequency inversion methods, enhancing articulation and prominence. These filter designs incorporate linear phase characteristics and stability guarantees inherent to FIR structures, significantly improving speech signal quality and reliability while expanding possibilities in voice processing applications such as noise reduction and feature extraction.