Design and Application of Digital Filters

This project implements simulation of three core processes from the "Digital Signal Processing" course - spectral analysis, digital filter design, and signal filtering - using MATLAB software, with composite signal separation as a practical example. The complete workflow and results are presented below. Specific implementation steps: (1) Construct the original composite signal s(t) by combining multiple frequency components using MATLAB's signal generation functions like sin() or chirp() (2) Plot the frequency spectrum of s(t) using FFT (Fast Fourier Transform) analysis with functions such as fft() and fftshift() for proper frequency domain representation (3) Design elliptic digital filters (IIR type), including low-pass and band-pass configurations, using MATLAB's ellip() function with specified parameters like passband ripple and stopband attenuation. Display the magnitude-frequency characteristics using freqz() for visualization (4) Apply the designed filters to separate the composite signal into three component signals (s1, s2, s3). Observe both time-domain waveforms using plot() function and frequency characteristics through spectral analysis to verify proper separation (5) Attempt to reconstruct the original signal by recombining the three separated signals s1, s2, and s3 using simple summation or weighted combination methods Key question: Why doesn't the reconstructed signal exactly match the original signal? Potential factors include phase distortions introduced by IIR filters, non-ideal filter characteristics causing amplitude alterations, or accumulation of numerical errors during processing. Could anyone provide a detailed technical explanation? Thank you! Contact: QQ:664519036