50Hz Notch Filter Design Code for FFR Notch Filter Implementation

The 50Hz notch filter is a specialized digital filter designed to eliminate 50Hz power-line interference, widely used in bioelectric signal acquisition (such as ECG and EEG) and industrial sensor signal processing. The FFR (Fixed-Frequency Rejection) notch filter achieves deep attenuation at specific frequencies through strategic pole-zero placement, with its core mechanism involving the construction of a transfer function that creates sharp attenuation precisely at the 50Hz frequency point. In code implementation, this typically involves calculating filter coefficients using frequency transformation methods and designing the digital filter structure accordingly.

Standard design procedures begin with determining the sampling frequency and notch center frequency (50Hz), implemented using a second-order IIR structure. The transfer function's zeros are positioned on the unit circle corresponding to 50Hz, while poles are placed at the same angle but slightly contracted toward the origin, creating sharp notch characteristics while maintaining system stability. The quality factor (Q value) selection directly affects the notch bandwidth, where higher Q values produce narrower stopbands. Algorithm implementation requires careful calculation of pole/zero positions using trigonometric functions and frequency normalization relative to the sampling rate.

In practical implementation, special attention must be paid to coefficient quantization effects to prevent poles from moving outside the unit circle, which would cause system instability. For embedded systems, floating-point coefficients typically need conversion to fixed-point numbers while maintaining sufficient precision. This notch filter effectively suppresses power-line interference while preserving useful signals, serving as a critical component in signal preprocessing chains. Code implementation often includes stability checks, coefficient scaling routines, and proper handling of numerical precision issues.