Part A: Periodic Signals Revisited

By sampling a CT periodic signal at different frequencies, one can produce both a periodic and non-periodic DT signal. I chose to use the tangent signal from Homework 1.


$ \tan\theta = \frac{\sin\theta}{\cos\theta}\, $



Tangent ECE301Fall2008mboutin.jpg


By sampling the signal with x[n]=tan[k+n] and k=1.5, it is possible to produce a non-periodic DT signal.

Tan nonperiodic ECE301Fall2008mboutin.jpg


By sampling the signal with x[n]=tan[k+n] and $ k = {\pi\over 8} $


Tan periodic ECE301Fall2008mboutin.jpg


One can also create a periodic signal by adding together an infinite number of shifted copies of a non-periodic signal periodically, either in CT or DT. I will use the natural logarithm function in CT to show this property. y=ln(x)


Ln periodic ECE301Fall2008mboutin.jpg

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett