Is this statement contradicting with the band-limiting theorem?

1. How do you know if a signal is band-limited?
2. Why is it necessary to limit the band of a signal?
3. What is band limiting process?
4. What is a band-limited function?

How do you know if a signal is band-limited?

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 is it necessary to limit the band of a signal?

Band limiting ensures that the original input signal can be reconstructed exactly from the ADC's output samples when a sampling frequency ( Undesirable signals, above f_s/2, of a sufficient level can create spectrum overlap and add distortion to the desired baseband signal.

What is band limiting process?

Bandlimiting is the limiting of a signal's frequency domain representation or spectral density to zero above a certain finite frequency.

What is a band-limited function?

1. n. [Geophysics] A function or time series whose Fourier transform is restricted to a finite range of frequencies or wavelengths.