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Unformatted text preview: ECE 3250 HOMEWORK ASSIGNMENT VIII Fall 2009 1. Note that ψ N = e j 2 π N is already in polar form. (a) Show that { ψ k N : 0 ≤ k < N } is the set of socalled N th roots of unity. I.e., this is the complete set of solutions to the polynomial equation z N 1 = 0. (b) Indicate (a diagram is okay) where these numbers lie in the complex plane. 2. You want to send a bunch of telephone conversations simultaneously over the same pair of copper wires using timedivision multiplexing. Each conversation signal is bandlimited to within 3400 Hz. Your channel specifications are as follows: • The channel will pass without excessive distortion a pulse 1 microsecond long. • The switch that switches from conversation to conversation to set up the TDM takes .5 microseconds to travel from one conversation terminal to the next. How many conversations can you multiplex at once given these constraints and signal properties?...
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 '07
 DELCHAMPS
 Digital Signal Processing, Complex number, Circular convolution, 5point circular convolution

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