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Figuring Out Sampling Theory by Playing Around with Complex SinusoidsConsider , with . Then we can write in polar form as

where , , and are real numbers.Forming a geometric sequence based on yields the sequence

where . Thus, successive integer powers of produce asampled complex sinusoidwith unit amplitude, and zero phase. Defining thesampling intervalas in seconds provides that is theradian frequencyin radians per second.

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