Design of IIR Digital Notch Filter with Spectral Analysis

We need to design an IIR digital notch filter with a sampling rate of 6.4kHz, targeting specific notch frequencies at 50Hz, 150Hz, and 250Hz. For spectral analysis comparison before and after filtering, we will utilize the input data file c1.mat containing the raw signal data. The design process requires careful consideration of key parameters including filter order, cutoff frequencies, passband and stopband characteristics. In MATLAB implementation, this typically involves using functions like iirnotch for single frequency notch filters or designing a higher-order filter using butter/cheby1 functions with appropriate frequency specifications. The filter design process should systematically document each step - from frequency response specification to coefficient calculation and stability verification - to enable future adjustments and optimization. The final validation will be performed through spectral analysis using FFT-based techniques (via fft function in MATLAB) to compare power spectral density before and after filtering. This analysis will demonstrate the filter's effectiveness in attenuating the target frequencies while minimizing impact on other frequency components, ensuring the notch filter meets its design specifications.