Suppose that we have a periodic signal x(n) = x(n + N) with period N = 8
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Question:
Suppose that we have a periodic signal x(n) = x(n + N) with period N = 8 defined as follows :
This signal can be arranged into a vector X which is defined as :
X = [x(1) x(2) · · · x(8)]^T
In this problem, we would like to perform a decomposition of this periodic signal X using different set of bases q1, q2, · · · , q8 so that X can be written as :
X = a1q1 + a2q2 + · · · + a8q8
Let us consider 3 different set of bases q1, q2, · · · , q8 as described below.
- Determine the value of a1, a2, · · ·, a8 for each set of bases!
- Based on the result of Fourier decomposition, which frequency components are contained in signal x(n)?
- If we use these 3 sets of bases to construct a file compression algorithm, which set of bases will produce the smallest file size for this particular signal x(n)?
Related Book For
Introduction to Statistical Quality Control
ISBN: 978-1118146811
7th edition
Authors: Douglas C Montgomery
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