ELEM018Advanced Transform Methods
Lab 2:The Wavelet Transform (2weeks)
Exercises 3.1Discrete Wavelet Transform Filter Bank
Explain how this Matlab function works and check that it implements the recursion formulas similar −=−i i
m n m c n i h c ,0,1]2[2to −=−i
j m n m c n i h d ,1,1]2[2and (Are the filters h0and h1in the Matlab code exactly the same filters as h 0and h 1in these formulas?Explain any difference(s)you discover).
The function is iteration function.At first the function will check validation of the input.Then the function will generate two sequences lowpass_c=conv(h 0,c)and hipass_c=conv(h1,c),they are convolution of the input sequence c with high -pass filter h1and low-pass filter h0.Then it will subsample the sequences with factor of 2with a coefficient 2as the formula d1=sqrt(2)*hipass_c(2:2:end)and c1=sqrt(2)*lowpass_c(2:2:end).The result d1is high frequency part,it will be put back in the output sequence .The result c1is low frequency part,it will be took as input sequence of the nest iteration.For the formular h0=[1/21/2]and h1=[1/2-1/2].In the code h0is the same,h1is inversed.Science the function needs to do the convolution in each iteration,it will get the same result as the formulas do .
3.2Inverse DWT Filter Bank
Explain how this Matlab function works,and check that it implements a recursion formula
⎞⎜⎝⎛−+−∑∑−−=i i i m i m n m d i n h c i n h c ,11,10,]22[2Answer: