Chat with our AI personalities
Limited is an antonym of boundless and vice versa.
A band-limited signal is one in which the Fourier transform is zero above a certain frequency. In other words it's a signal that ahas a finite frequency content. The simplest case is a pure sinusoidal signal, whose Fourier transform consists of a delta function centred on the frequency of the signal. A band-limited signal can be reconstructed exactly if it is sampled at at more than twice the maximum frequency present in the signal. A time-limited signal is a signal that is zero above a finite. An example of this would be a short pulse. The reason a signal cannot be both band-limited or time-limited is due to their relationship via the Fourier transform. One can show it is impossible for the Fourier transform of a signal with compact support ie either time or band-limited, to also have compact support. A time-limited signal must have a continuous frequency spectrum existing over all possible frequencies and a band-limited signal can only arise from signal existing for all time. Note this indicates in reality it is impossible to have a truly band-limited signal as it would take infinite time to transmit, but it is nonetheless a useful concept and we can produce nearly band-limited signal to a high degree of accuracy.
A limited existence.
Restricted
Family Limited Partnership