MATLAB Implementation of FIR Filter to Eliminate 50Hz Power Frequency Interference in Speech Signals

In speech signal processing, 50Hz power frequency interference is a common noise source typically introduced through power lines. Using FIR (Finite Impulse Response) filters can effectively eliminate such narrowband interference while maintaining speech signal clarity. The following outlines the core implementation approach and workflow:

### 1. FIR Filter Design FIR filters are ideal for speech processing due to their linear phase characteristics. Key design parameters include: Cutoff Frequency: Set stopband and passband around 50Hz (e.g., 45Hz-55Hz stopband). Filter Order: Higher orders improve filtering performance but increase computational load, requiring balance with real-time processing needs. Window Function Selection: Commonly use Hamming or Blackman windows to suppress spectral leakage.

### 2. Signal Preprocessing Sampling Rate Matching: Ensure speech signal sampling rate (e.g., 8kHz) aligns with filter design. Normalized Frequency: Convert 50Hz to normalized frequency using `50/(Fs/2)` in MATLAB.

### 3. Filter Implementation After designing the filter using MATLAB's `fir1` or `fdesign` tools, apply filtering with the `filter` function. Key considerations: Zero-Phase Filtering: Use `filtfilt` for bidirectional filtering to avoid phase distortion and enhance speech quality. Spectral Verification: Compare pre- and post-filtering spectra via FFT analysis to verify effective 50Hz suppression.

### 4. Performance Evaluation Time-Domain Waveform: Inspect whether filtered signals retain speech characteristics while removing power frequency ripple. Signal-to-Noise Ratio (SNR): Quantitatively calculate SNR improvement before and after filtering.

This methodology can be extended to eliminate other fixed-frequency interferences (e.g., 60Hz grid interference) by simply adjusting the filter's center frequency.