When x ( t ) {\displaystyle x(t)} is a function with a Fourier transform X ( f ) {\displaystyle X(f)} : 1. X ( f ) ≜ ∫ − ∞ ∞ x ( t ) e − i 2 π f t d t , {\displaystyle X(f)\ \triangleq \ \int _{-\infty }^{\infty }x(t… See more

When there is no overlap of the copies (also known as "images") of X ( f ) {\displaystyle X(f)} , the k … See more

Poisson shows that the Fourier series in Eq.1 produces the periodic summation of X ( f ) {\displaystyle X(f)} , regardless of f s {\displaystyle f_{s}} and B {\displaystyle B} . Shannon, h… See more

The sampling theorem is usually formulated for functions of a single variable. Consequently, the theorem is directly applicable to time-dependent signals and is normally for… See more