Band-limited and time limited signals

1. What is band-limited and time limited signals?
2. What is band-limited signal?
3. Can a signal be both time limited and band-limited?
4. What is a time limited signal?

What is band-limited and time limited signals?

In signal processing, there is a time-frequency duality. Band-limited signals have infinite time duration and time-limited signals have infinite bandwidth.

What is 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.

Can a signal be both time limited and band-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.

What is a time limited signal?

A time limited signal is one that is nonzero only for a finite length time interval. A signal is said to be a band limited signal if all of it's frequency components are zero above a certain finite frequency. i.e it's power spectral density should be zero above the finite frequency.