Comparison of FFT Algorithms and Low-Pass Filters in Noise Removal Applications

This article presents a comparative study of FFT algorithms and low-pass filters for noise removal applications. We begin by examining the fundamental principles underlying both methodologies.

The Fast Fourier Transform (FFT) algorithm serves as a cornerstone technique in digital signal processing, enabling efficient conversion of signals from the time domain to the frequency domain. By analyzing frequency components through spectrum analysis, engineers can implement frequency-domain filtering by identifying and eliminating noise-dominated frequency bands. A typical implementation involves applying FFT to decompose the signal, zeroing out high-frequency coefficients exceeding a threshold, and performing inverse FFT for reconstruction. This approach significantly enhances signal quality by attenuating noise interference.

Alternatively, low-pass filters operate directly in the time domain using convolution-based filtering. These filters employ difference equations or impulse responses to attenuate high-frequency components while preserving low-frequency signal characteristics. The filter design process involves critical parameter selection including cutoff frequency, filter order, and roll-off rate. Finite Impulse Response (FIR) filters, for instance, can be implemented using windowing methods with precise frequency response control, while Infinite Impulse Response (IIR) filters provide steeper attenuation with lower computational requirements.

Our comparison reveals distinct advantages and limitations for each approach. FFT-based processing excels in precise frequency manipulation and non-stationary signal analysis but demands substantial computational resources for real-time applications. Low-pass filters offer simpler implementation through direct convolution operations (e.g., using MATLAB's filter() function) and better suitability for hardware deployment, though they may exhibit reduced performance with complex noise patterns.

In conclusion, method selection should be driven by specific application requirements including computational constraints, noise characteristics, and real-time processing needs. Through systematic experimentation and parameter optimization, both FFT algorithms and low-pass filters can be effectively leveraged to enhance signal processing accuracy and reliability in various engineering scenarios.