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The Collaborative International Dictionary

Wavelet \Wave"let\, n. A little wave; a ripple.

Douglas Harper's Etymology Dictionary

1808, mainly in poetry, from wave (n.) + diminutive suffix -let.


n. 1 A small wave; a ripple. 2 (context mathematics English) A fast-decaying oscillation.


n. a small wave on the surface of a liquid [syn: ripple, rippling, riffle]


A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful for signal processing. Wavelets can be combined, using a "reverse, shift, multiply and integrate" technique called convolution, with portions of a known signal to extract information from the unknown signal. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly a 32nd note. If this wavelet was to be convolved with a signal created from the recording of a song, then the resulting signal would be useful for determining when the Middle C note was being played in the song. Mathematically, the wavelet will correlate with the signal if the unknown signal contains information of similar frequency. This concept of correlation is at the core of many practical applications of wavelet theory.

As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including – but certainly not limited to – audio signals and images. Sets of wavelets are generally needed to analyze data fully. A set of "complementary" wavelets will decompose data without gaps or overlap so that the decomposition process is mathematically reversible. Thus, sets of complementary wavelets are useful in wavelet based compression/decompression algorithms where it is desirable to recover the original information with minimal loss.

In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set or frame of a vector space, for the Hilbert space of square integrable functions.

Usage examples of "wavelet".

Day, and the shine of the tardy sun reaches the fronts of the beetling castles, but scarcely descends far enough to touch the wavelets of the river winding leftwards across the many-leagued picture from Schaffhausen to Coblenz.

The boat would lie moveless, rocking ever so little to unseen wavelets, and the only sounds were their muffled slap and the fog dripping from ice-sheathed tackle.

The dense forest of West Country Marre pine cut the wind into innocuous puffs that soughed through the needle-laden branches, causing them to dip and sway like the wavelets of a becalmed sea.

But Naomi listened to every sound with eager intentness--the light plash of the blue wavelets that washed to her feet, the ripple of their crests when the Levanter chased them and caught them, the dip of the oars of the boatman, the rattle of the anchor-chains of ships in the bay, and the fierce vociferations of the negroes who waded up to their waists to unload the cargoes.

Apart from a brazen sky and silphium scrub, their constant companion was the sea, a huge expanse of polished aquamarine, fluffed with white where rocks lurked, breaking in gentle wavelets upon beach after beach after beach.

The old fountain brimmed with water, slopping in ebony wavelets over its leeward edge.

It fills them with little wavelets of shimmering light and makes you drowsy, so drowsy that even the sparklets begin to dim away because you are so terribly sleepy .

And down thro' all the shadows The star-gleams softly crept, And kissed, with lips all shining, The wavelets ere they slept.

Greece, so on the twelfth day he anchored his fleet in unsheltered but placid conditions off Cretan Gaudos Isle, and there made sure that every barrel and amphora he owned was filled to the brim from a spring that gushed out of a cliff into the wavelets.

The first ripples appear at two knots, at five knots wavelets form and at nine knots the crests start to break.

Bright wavelets wove the scarf of blue That well became the valley fair, And grassy fringe of greenest hue Hung round its borders everywhere.

Nearer and nearer it came, bobbing to the rise and fall of each wavelet with the last icy sunlight touching it up with reds and golds, nearer and nearer in the deadly hush of that forsaken region, and then at last so near it showed quite plainly on the purple water, a raft with some one sitting under a canopy.

Behind, the ungainly scapha floundered amid lapping wavelets, a floating marker to the graves of three men, and the monsters of Treachery Bay.

Not a wavelet stirred, And yet we heard The loneliest music of the weariest waves That ever roll.

Moonlight edged the wavelets with silver, and among those gleams it seemed he could see reflected the broken curve of his life: a kid living for Christmas, drawing pictures, receiving praise, growing up mindless to high school, sex, and drugs, growing beyond that, beginning to draw pictures again, and then, right where you might expect the curve to assume a more meaningful shape, it was sheared off, left hanging, its process demystified and explicable.