This project explores the application of wavelet transforms in bio-signal processing. It covers the study of wavelet properties, time-frequency analysis using continuous and discrete wavelet transforms, and signal denoising and compression through discrete wavelet transforms. The performance of various wavelets, including the Mexican Hat, Haar, and Daubechies 9-tap (Db9), is evaluated and compared.
- Derived the Mexican Hat wavelet mathematically, demonstrating zero mean, unity energy, compact support and analyzed the daughter wavelets and and their spectras.
- Applied CWT to signals with distinct frequency components, analyzing temporal and spectral characteristics.
- Signal:
- Spectogram:
- Decomposed various signals(signals with various shapes and noise levels) into approximation and detail coefficients using Haar and Db9 wavelets.
- Reconstructed the signal and analysed the effectiveness of Haar and Db9 wavelet for reconstructing the each signal.
- Ex: -
- Noisy(corrupted) signal(named y2 in the project) along with the noise free signal(x2).
- A10, D10, D9, …., D2, D1 for signal y2 with haar wavelet.
- FInal reconstructed signal(y2).
- Used a Thresholding approach; suppressed coefficients below a threshold and reconstructed; (used hard thresholding).
- Ex:-
- Denoising y2 signal with db9 wavelet and Haar wavelet.
- Using db9:
- Using Haar:
- Here we analyzed the importance of selecting the correct wavelet for signal denoising.
- Retained 99% of the signal energy by keeping the most significant coefficients during the compression.
- Calculated the Compression ratio based on the number of retained coefficients and total coefficients.
- Ex:- (Original and reconstructed signals using compressed data; compression ratio - 16.08).
This project was completed as part of the BM4152 Bio-Signal Processing course.