Homework 1, ECE438, Fall 2016, Prof. Boutin

Hard copy due in class, Wednesday August 31, 2016.

The goal of this homework is to practice transforming a CTFT in terms of $ \omega $ into a CTFT in terms of $ f $. You should be able to do all the problems by following the method presented in class.

Begin by reviewing the following table of CT Fourier transform pairs and properties, which lists the CT Fourier transform in terms of $ \omega $ in radians. (You should have seen and used each of these in ECE301.)

Now use the table to find the Fourier transform in terms of f (in hertz) of the following signals:

1. $ x(t)=e^{-j (200 \pi t )}, $
2. $ x(t)=\cos \left( \pi t\right), $
3. $ x(t)=\sin \left( 2 \pi t\right), $
4. The periodic function defined by repeating the function $ x(t)=u(t+\frac{1}{2})-u(t-\frac{1}{2}) $ with a period T=4,
5. The impulse train $ p_5(t)=\sum_{k=-\infty}^\infty \delta(t-3k) $

Simplify your answers as much as possible. Hand in a hard copy of your solutions. Pay attention to rigor!

Note: You will get zero credit if you simply write down the answers without any justification.

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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