What does $[-\pi \; \pi]$ band-limited signal mean?

1. What is a band-limited signal?
2. Why are signal bands limited?
3. What is band-limited channels?
4. Can a band-limited signal be time limited?

What is a band-limited signal?

A signal is said to be band-limited if the amplitude of its spectrum goes to zero for all frequencies beyond some threshold called the cutoff frequency.

Why are signal bands limited?

A signal is called bandwidth – limited or simply band-limited when the amplitude of the spectrum goes to zero whenever its frequency crosses the allowable limits. Thus, its Fourier transform is non-zero only for a finite frequency interval. A band-limited signal is represented by a finite number of harmonics.

What is band-limited channels?

band-limited channel A transmission channel with defined finite bandwidth. All physically realizable channels are band-limited by the constraints of the transmission medium and the drivers and receivers. The bandwidth may be deliberately constrained by filtering to limit the emission of or susceptibility to EMI.

Can a band-limited signal be time limited?

A bandlimited signal cannot be also timelimited. More precisely, a function and its Fourier transform cannot both have finite support unless it is identically zero. This fact can be proved using complex analysis and properties of the Fourier transform.