Figuring Out Sampling Theory by Playing Around with Complex Sinusoids
Consider , 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 a sampled complex sinusoid with unit amplitude, and zero phase. Defining the sampling interval as in seconds provides that is the radian frequency in radians per second.
- What frequencies are representable by a geometric sequence?
- Recovering a Continuous-Time Signal from its Samples