[Lightning55]

I don't understand any of it at all. I really need something to stick me in the right direction. This stuff is far beyond me, but somehow, I got these problems to do.



Recall that a function H : Z -> R defined on integers needs to satisfy

1) Σkεz H(k) = 2
2) Σkεz H(k-2l)H(k) = 2γl,0
3) Σkεz H(k)(-1)^(k)*k = 0
in order for it to be used for constructing wavelets via multi-resolution analysis (MRA).


(a) Let φ  : R -> IR be the function dened by
φ (t) := { 1; if 0 < t < 1,

0; otherwise. }

Find a function Hφ : Z -> R such that
φ(t) = Σkεz H(k)φ(2t-k)


(b) Show that H found in part (a) satises the above three conditions.


(c) Let φ  : R -> IR be the function dened by

φ (t) := { t 1; if -1 < t < 0

1 - t; if 0 < t < 1



0; if |t| > 0 }



Find a function Hφ : Z -> R such that
φ(t) = Σkεz H(k)φ(2t-k)


(d) Determine whether H' found in part (c) satises the above three conditions or not.

[Unknown008]

Sorry, but there are many strange symbols appearing in your post :(

[Lightning55]

The weird Ek(micro)z are supposed to be sums. I haven't been here in a while so I forget the math type. I'm uploading my work. I don't get anything at all, as I said before. I just need a push in the right direction for a and b. If I understand that, I think I can get c and d.

[Unknown008]

Oh my I pass :p That's out of my league.