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Signal Processing & Wavelength. Problems # 6-7. See attached file for full problem description.

6. For each of the signals given, determine mathematically if the signal is even, odd, or neither. Sketch the waveforms to verify your results. For signals that are neither, find the even or odd parts of the signal.
a) x(t) = 5u(t)
b) x(t) = 5 + e^(-t) + e^t
c) x(t) = sin(3t - pi/2)
d) x(t) = 5 + e^(-t)

7. Write mathematical functions for the waveforms given below. You can use the singularity functions disscussed in class.

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The solutions shows how to determine mathematically if the signal is even, odd, or neither. It also shows how to write the signal function mathematically according to the waveforms. The solution is detailed and has a '5/5' rating.

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Please see the attached file.

a)

And
So x(t) is neither an even function nor odd function.

Now we define , and
Then
Then f(t) is the even part of x(t), g(t) is the odd part of x(t).

(b)
So . Therefore, x(t) is an even function.

As shown from the above figure, x(t) is symmetric about the line t = 0, so it is an even function.

(c) Using trigonometry relationship, we have

Then
Therefore,
Then x(t) is an even function.

It is symmetric about t = 0, so it is an even function.

(d)
...

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