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You can either write your answers to theoretical questions on paper or
edit them in the file hw2/paper.tex. Please show all the
mathematical derivations that you perform.
- The varimax attribute is defined as
![\begin{displaymath}
\phi[\mathbf{a}] = \frac{\displaystyle N\,\sum\limits_{n=1...
...n^4}{\displaystyle \left(\sum\limits_{n=1}^{N} a_n^2\right)^2}
\end{displaymath}](img1.png) |
(1) |
Suppose that the data vector
contains random noise:
the data values
are independent and identically distributed with
a zero-mean Gaussian distribution:
,
,
. Find the mathematical expectation of
.
- Consider the parabolic filter
defines as
![\begin{displaymath}
F(Z) = 1 + 4 Z + 9 Z^2 + \ldots + N^2 Z^{N-1}\;.
\end{displaymath}](img9.png) |
(2) |
- Show that this filter can be implemented using recursive filtering (polynomial division).
- What is the advantage of recursive filtering? Does it depend on
?
- Show that, using the helix transform and imposing helical boundary conditions, it is possible to compute a 2-D digital Fourier transform using 1-D FFT program. Assuming the input data is of size
, would this approach have any computational advantages?
Next: Running median and running
Up: Homework 2
Previous: Prerequisites
2022-09-20