Filter Designing with Multi Resolution Analysis and Synthesis in Time and Frequency Domain

In this paper the key idea underlying the construction of multi resolution analysis (MRA) with various wavelet basis sets is nmelaborated. The implementation of one dimensional wavelet transform and their usefulness in time signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter families such as haar, Daubechies (db4), coiflet, symlet and dmey. The signal is then decomposed to a set of scaled and translated versions of the mother wavelet also known as time and frequency parameters. Analysis of the time signal is performed around 1.5 sec to 9 seconds for 10 observation sequences. Similarly for synthesis,the time signal is performed around 0.5 to 3 seconds. This was conducted to determine the effect of the choice of mother wavelet on the time signals. The results show that wavelet filter with MRA are useful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of the signal to noise ratio (SNR) value around 5dB-25dB.