The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.

Nyquist Sampling Theorem states that to reconstruct a continuous analog signal from its sampled version accurately, the sampling rate must be at least twice the highest frequency present in the signal.

The Nyquist-Shannon Sampling Theorem states that a signal bandlimited to \(\left(-\pi / T_{s}, \pi / T_{s}\right)\) can be reconstructed exactly from its samples with sampling period \(T_s\).

The Sampling Theorem If signal is bandlimited → sample without loosing information. If x (t) is bandlimited so that X (jω) = 0 for | ω | >ω m then x (t) is uniquely determined by its samples x (nT) if 2 π. ω. s = > 2. ω. m. T. The minimum sampling frequency, 2. ω. m, is called the “Nyquist rate.” !

Shannon Sampling Theorem • If periodic x(t) is bandlimited to bandwidth and samples x[n] are obtained from x(t) by sampling at greater than Nyquist rate then can exactly reconstruct x(t) from samples using sinc interpolation formula • This is also called the cardinal series for x(t) Alfred Hero University of Michigan 33 Q. Why does sinc ...