a wave that starts and ends at amplitude zero

Wavelets: A wavelet is a wave that starts and ends at amplitude zero.

mathematical functions that transform the input signal into different frequency components [46]

Wavelets are mathematical functions that transform the input signal into different frequency components [46].

mathematical functions that split data into different frequency components

Wavelets are mathematical functions that split data into different frequency components.

mathematical functions that divide the considered data into different frequency components and work on features with a resolution matched to their scales

Wavelets are mathematical functions that divide the considered data into different frequency components and work on features with a resolution matched to their scales.

functions well localized both in space and frequency

Wavelets are functions well localized both in space and frequency.

a waveform of limited duration that has an average value of zero

A wavelet is a waveform of limited duration that has an average value of zero.

functions that satisfy certain mathematical requirements and are used in representing data or other functions

Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions.

a smaller version of a wave

As the name suggests, a wavelet is a smaller version of a wave; a wave has finite magnitude over some defined finite interval; beyond this interval, the value of a wavelet is (very close to) zero.

powerful statistical tools that are used for a wide range of applications, including signal description and data compression

Wavelets [31] are powerful statistical tools that are used for a wide range of applications, including signal description and data compression.

a threaded conversation that is spawned from a wave (including the initial conversation)

A wavelet is a threaded conversation that is spawned from a wave (including the initial conversation).

a mathematical tool for hierarchically decomposing functions

Wavelets are a mathematical tool for hierarchically decomposing functions.

the foundation for representing images in various degrees of resolution

Explanation: Wavelets are the foundation for representing images in various degrees of resolution.

representations of short wavelike oscillations with different frequency ranges and shapes

Wavelets are representations of short wavelike oscillations with different frequency ranges and shapes.