Howtosignalprocessing
- What is a band-limited function?
- Why a signal Cannot be time limited and band-limited at the same time?
- How do you know if a signal is band-limited?
- Why are signals band-limited?
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.
Why a signal Cannot be time limited and band-limited at the same time?
A law of Fourier transformations says that if a signal is finite in time, its spectrum extends to infinite frequency, and if its bandwidth is finite, its duration is infinite in time. Clearly we cannot have a time-domain signal of infinite duration, so we can never have a truly band-limited signal.
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 are signals band-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.
