Here is a
comparison to show the Multiresolution advantage of Wavelet Transform
over Fourier Transform & Windowed Fourier Transform.
Let us
consider a non-stationary signal shown below
On applying
Fourier transform to the above signal, we only get the frequency components of
the signal but no information about time at which these frequencies have
occurred.
On applying
Wavelet Transform that supports Multiresolution, we can see that the frequencies
of the signal have achieved time localization with Multiresolution.
Here
scale = 1/frequency and translation = time.
i.e. The
Multiresolution analysis has given good
time resolution and poor frequency resolution at high frequencies and good
frequency resolution and poor time resolution at low frequencies.
Thus the Wavelet Transform has
succeeded in overcoming the disadvantages of FT & WFT.
The above Wavelet Transform
output has been generated by us using a Digital Filter Bank designed by using
the Discrete Wavelet Transform Algorithm. We have successfully managed to generate our own code for the
digital filter bank .