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Homework 4, ECE438, Fall 2015, Prof. Boutin
Hard copy due in class, Wedday September 23, 2015.
The goal of this homework is to get an intuitive understanding on how processing CT signals can be accomplished in an equivalent fashion by processing a sampling of that signal.
Question
A continuous-time signal x(t) is such that its CTFT X(f) is zero when when |f|>1,400 Hz. You would like to low-pass-filter the signal x(t) with a cut off frequency of 800Hz and a gain of 7. Let's call this desired filtered signal y(t).
a) Assume that you are only given a sampling of x(t), specifically a sampling obtained by taking 6000 samples per second (samples equally spaced in time). Can one process this sampling in such a way that a band-limited interpolation of the processed (output) DT signal would be the same as y(t)? Answer yes/no. If you answered yes, explain how. If you answered no, explain why not.
b) Now assume that the sampling from Part a) is downsampled by a factor 2. Can one process this downsampled signal in such a way a band-limited interpolation of the processed (output) DT signal would be the same as y(t)? Answer yes/no. If you answered yes, explain how. If you answered no, explain why not.
Hand in a hard copy of your solutions. Pay attention to rigor!
Presentation Guidelines
- Write only on one side of the paper.
- Use a "clean" sheet of paper (e.g., not torn out of a spiral book).
- Staple the pages together.
- Include a cover page.
- Do not let your dog play with your homework.
Discussion
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