5. 4. Write a short note on the following: (i) Frames (ii) Wavelet series (iii) Multiresolution Analysis OR Let e L(IR) be a function such that the set ((x-k): ke ZZ) is an orthonormal set i.e. Sk. = < (-k), (-l)>. Then prove that- =ex (x) dx, je Z 2 Here denotes the Fourier transform of the function . Let {V}, ez be the MRA and be the corresponding scaling function. Then prove that- L (IR) = W;, W; = V}, je Z JEZ Define the centre and radius of a window function. Find the centre and radius of the function ga(t) = e 4a ; a > 0.