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Previous: Prerequisites
You can either write your answers to theoretical questions on paper or
edit them in the file hw3/paper.tex. Please show all the
mathematical derivations that you perform.
- The Taylor series expansion of the inverse sine function around zero is
|
(1) |
- Show how one can use expansion (1) to design a
digital filter that approximates the derivative
operator.
Hint: Use the identity
.
- In particular, find a seven-point derivative filter of the form
|
(2) |
- The parabolic B-spline is a function defined as
|
(3) |
where
|
(4) |
and
|
(5) |
- Find an explicit expression for .
- Show that decomposing a continuous data function into the convolution basis
with parabolic B-spines
|
(6) |
leads to an interpolation filter of the form
|
(7) |
Define , , , , , and .
Next: Interpolation after coordinate transformation
Up: Homework 3
Previous: Prerequisites
2022-10-05