Math 5467, Spring 2000: HW 4: solutions of # 2 and # 4
2: Verify that the space V0 generated by the integer translates of the triangle scaling function T (t) shown
in gure 2.2(b) generates a multireso
Math 5467, Spring 2000
Homework 1, numbers 3(iii) and 4.
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3: For x R, dene H (x) := 1 if 0 < x < 1/2, H (x) := 1 if 1/2 < x < 1, and let H (x) := 0 for all other x.
(i) Find j, k so that Hjk = H
Math 5467, Spring 2000: Sample Questions: Test 2
What are the formulas for the Fourier transforms of f (t h) and f (t), > 0, in terms of f ( )?
What are the formulas for the Fourier transforms of f (t
Math 5467
Spring 00
Fourier Transform Facts
3/2/00
p1
A list of Fourier Transform formulas and properties
The list that follows is derived or obtained from references (in the same order) following the
Math 5467, Spring 2000
Homework 2, numbers 2(b) and 3.
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2(b): Suppose (for this part) f (t) dt = 0. Explain why it is impossible for cjk = 0 to be true for all j suciently
negative. The question
Math 5467, Spring 2000
Homework 3, numbers 1 and 2.
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1:
Find the element of V0 that is closest to H00 + H11 . Is there a simple recipe for solving this sort of
minimization problem? If so, what
Math 5467, Spring 2000: Assignments
Assignments are due at the start of class on the due date.
Give credit for help received, including books and hints from me and others; mention discussions.
If a pr
Math 5467
Spring 98
Checking a dierentiability hypothesis
We have
i 2
F (, x) = e(x+ 2 ) = ex eix e
2
2
4
and we want to show that, for each , there is an integrable function g (x) such that, for all
Math 5467, Spring 2000
Homework 5, number3. Remarks on 1, 2, 4.
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3: The Shannon scaling function is (t) = sinc(t) = sin t . Find ( ) and the coecients h(n) for its dilation
t
equation. Find the
Math 5467
Spring 00
Lebesgue theory - an overview
Page 1
Introduction
The theory of the Lebesgue integral is more complicated to learn that is the theory of the Riemann integral. But it
has distinct a