Why transform is Wavelet ?

In Fourier Transform, signal is decomposed as the constituent of sine and cosine functions losing time information about the signal signal that is FT can not give the time of occurrence for the particular frequency sine or cosine signal.

Where as in Wavelet Transform, in Continuous Wavelet Transform analysis function is correlated to small segment of signal to be analysed translating wavelet function to calculated wavelet coefficient and again wavelet is dilated and then again correlated to segments of signal to be analysed translating the dilated wavelet along the time axis. This seems that small segment is formed which is wavelet of the signal to be analysed.

In Discrete Wavelet Transform, signal is passed through bank of analysis filters which separates the signal of particular frequency band signal that is signal of particular band of frequency is separated which is small wavelet of the signal to be analysed. Thus this kind of analysis is sub band coding or multi resolutional analysis.

De-Noising a Signal with WT

Wavelet Transform is also one of the most useful tool to remove noise from the communication signal. Significant de-noising can be obtained with higher level of approximation coefficients in wavelets.

Fig. 1

In the above fig first plot is original signal with noise when sample area is 3000 and the signal is decomposed with wavelet transform and then reconstructed. As we go downwards smoother signal is reconstructed. Second Last plot is reconstructed plot with approximation lavel-5.

In addition to that, wavelet transform can be used for compression techniques which can give good compression with lossy or lossless type compression.