Howtosignalprocessing
- Is discrete-time sequence sampled from continuous time periodic signal also periodic?
- Is the output always periodic when sampling a continuous time signal if not why?
- Why sampling is required for continuous time signals?
- What is the relationship between continuous time signals and discrete-time signals?
Is discrete-time sequence sampled from continuous time periodic signal also periodic?
A periodic discrete-time signal satisfies x[n]=x[n+N] for all integers n. The period N is an integer. If you sample a periodic continuous-time signal, you don't necessarily get a periodic sequence.
Is the output always periodic when sampling a continuous time signal if not why?
You will have approximately 4.2 samples per period. However you will not be able to sample the sine wave exactly at the same place. Hence your digital signal will not be periodic. However, if you sampled the same 1-kHz signal at 4 kHz, you would get a periodic discrete signal.
Why sampling is required for continuous time signals?
If samples of a bandlimited continuous-time signal are taken frequently enough, then they are sufficient to represent the signal exactly. The continuous-time signal can then be recovered from the samples. This task is ideally performed by a discrete-to-continuous-time (D/C) converter.
What is the relationship between continuous time signals and discrete-time signals?
A continuous-time signal has values for all points in time in some (possibly infinite) interval. A discrete time signal has values for only discrete points in time. Signals can also be a function of space (images) or of space and time (video), and may be continuous or discrete in each dimension.
