Audio Noise Reduction Using High-Order Butterworth Filters: CTFT and FFT Frequency Analysis | Soumya Pandey, Praj Bhairamadgikar, Sardar Patel Institute of Technology

Soumya Pandey, Praj Bhairamadgikar · Department of Electronics and Telecommunication Engineering · Sardar Patel Institute of Technology (Bhavan's), Mumbai, India · Guided by Prof. Najib Ghatte and Dr. Payal Shah Speech recorded in real-world environments is corrupted by low-frequency hum and rumble and by high-frequency thermal hiss. This paper presents a theoretical and experimental study of audio noise reduction using Continuous-Time Fourier Transform (CTFT) analysis, Fast Fourier Transform (FFT) spectral decomposition, and cascaded IIR Butterworth filters. We derive the conditions for speech formant retention and noise suppression, analyze pole placement on the complex s-plane, and apply zero-phase forward-backward filtering to remove phase distortion. A Python DSP pipeline using SciPy at a 16 kHz sampling rate is implemented and benchmarked. A 4th-order high-pass (150 Hz) and low-pass (3000 Hz) cascade raises the signal-to-noise ratio from -4.21 dB to +18.92 dB while keeping the passband magnitude flat and speech power loss under 0.7%. We also compare filter orders (N = 2, 4, 6, 8) and discuss Butterworth against Chebyshev, Elliptic, and Bessel designs. The work was carried out at the Department of Electronics and Telecommunication Engineering, Sardar Patel Institute of Technology, Mumbai.