Howtosignalprocessing
- How do you prove the sampling theorem?
- What is the sampling state and proof of the sampling theorem for low pass signals?
- What does the sampling theorem tell us?
- What does Shannon's sampling theorem state?
How do you prove the sampling theorem?
Proof of Sampling Theorem. To prove the sampling theorem, we need to show that a signal whose spectrum is band-limited to fm Hz, can be reconstructed exactly without any error from its samples taken uniformly at a rate fs > 2 fm Hz. Let us consider a continuous time signal x(t) whose spectrum is band-limited to fm Hz.
What is the sampling state and proof of the sampling theorem for low pass signals?
SAMPLING THEOREM FOR LOW-PASS SIGNALS:-
Statement: - “If a band –limited signal g(t) contains no frequency components for ׀f׀ > W, then it is completely described by instantaneous values g(kTs) uniformly spaced in time with period Ts ≤ 1/2W.
What does the sampling theorem tell us?
The Sampling Theorem states that a signal can be exactly reproduced if it is sampled at a frequency F, where F is greater than twice the maximum frequency in the signal.
What does Shannon's sampling theorem state?
Shannon's Sampling theorem states that a digital waveform must be updated at least twice as fast as the bandwidth of the signal to be accurately generated. The same image that was used for the Nyquist example can be used to demonstrate Shannon's Sampling theorem.
