Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

A large family of signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation.

An example of this would be Franz Kafka's story The Metamorphosis, in which the salesman Gregor Samsa's plans for supporting his family and rising up in rank by hard work and determination are suddenly thrown topsy-turvy by his sudden and inexplicable transformation into a man-sized insect.

The most famous was The Merzbau, the transformation of six ( or possibly more ) rooms of the family house in Hannover, Waldhausenstrasse 5.

An infranatural transformation η from F to G is simply a family of morphisms.

Though he never married, he adopted a young orphan boy named Danny in the final season, completing his transformation from rebel to family man.

Bennett and some of the Coombe Springs residents had moved into a nearby house in Kingston upon Thames, where the family ( the Bennetts now had two sons and two young daughters ) would live quietly for four years before Bennett embarked on his last great project-an experimental school for passing on techniques for spiritual transformation.

At the beginning of the 18th century a radical transformation project involving both the exterior and the interior was undertaken at the request and expense of the Manin family.

" In Hiroshi Aro's Futaba-kun Change, the sex transformation is inherited and everyone in the main character's family changes sexes, either at will or when they're excited, after they become sexually mature.

There eventually came a point when the people of Magosung 마고성 ( 麻姑城 ) began blaming Jiso ( 지소 ) for the transformation, and he along with his family and all those who had eaten the grapes were forced to leave Magosung 마고성 ( 麻姑城 ).

In category theory, given any family P < sub > n </ sub > of invertible n-by-n matrices defining a similarity transformation for all rectangular matrices sending the m-by-n matrix A into P < sub > m </ sub >< sup >− 1 </ sup > AP < sub > n </ sub >, the family defines a functor that is an automorphism of the category of all matrices, having as objects the natural numbers and morphisms from n to m the m-by-n matrices composed via matrix multiplication.

The transformation was caused by two further waves of invasion: the first by speakers of the Scandinavian branch of the Germanic language family, who conquered and colonized parts of Britain in the 8th and 9th centuries ; the second by the Normans in the 11th century, who spoke Old Norman and ultimately developed an English variety of this called Anglo-Norman.

He approaches old family nemesis Dr Van Helsing ( Dennis Price ), who agrees to enable the Count's transformation, much to the dismay of the residents of the Underworld.

The mission of OSL is “ to seek the transformation of prisoners and their reconciliation to God, family and community through the power and truth of Jesus Christ.

The historic events of the time sparked his transformation from a privileged family member of Loyalists to a dedicated Patriot.

Nantasket Beach and the Nantasket Hotel, State Bath House and Paragon Park in the background, circa 1910. The catalyst for Polly Jacob Peabody's transformation was her introduction and eventual marriage to Harry Crosby, a wealthy scion of a socially prominent Boston family and another veteran and victim of the recent war.

With Gospel values we dialogue with peoples of different cultures, faiths, and religions, in the search for an integral transformation of society ; we work with others to safeguard human dignity, nurture family, foster harmony, promote a culture of peace, and respond to the calls of justice and integrity of creation ”

Another part of the transformation was the addition of Battersea Fun Fair: rollercoasters, swings, roundabouts and general fun for all the family.

Mispronunciation of the name led to its transformation as the family moved to the non-Arabic speaking Turkey in the 16th century.

Surely he is meeting just punishment – somewhere .” After her tribulations, Jane also loses her vanity ; in the beginning, she “ cared most for the dream and the assurance and the allurement of her beauty … Hordes of Mormon and Gentile suitors had fanned the flame of natural vanity in her .” This transformation eventually allows her to abandon her townsmen and many Mormon customs, and in the end, she is left only with the two Gentiles – Lassiter and Fay Larkin – that constitute her new family ....

Elizabeth admits the complete transformation of her feelings and agrees to an engagement, which takes her family by surprise.

When trying to prevent Mona's family from discovering her transformation, Lestat falls in love with Rowan Mayfair.

A defining feature of Barnabas ' character development is his gradual but persistent transformation from a frightening creature of the night into the show's protagonist, who selflessly, heroically and repeatedly risks his life to save the Collins family from catastrophe.

Those fit for transformation were converted into Tekkamen in the same way as D-Boy ( and his family and friends ) had been on the Argos.

In recent years, recreational interests, shopping and tourism have emerged as a strong economic transformation with Rock Hall serving as one of the larger charter boat fishing and sailing centers on the Eastern Shore.

Some strip malls are undergoing a transformation into Lifestyle centres ; entailing investments in common areas and facilities ( plazas, cafes ) and shifting tenancy from daily goods to recreational shopping.

The centre was built and owned by the Myer Emporium, and marked the transformation of shopping in Australia from the traditional central city and strip-shopping precincts to the now familiar mall-type shopping centre.

The transformation that turned Newbury Street into a trendy shopping district for young people probably began in the 1970s with the opening of the original Newbury Comics.

A shot of RIR in 1989 during the transformation from racetrack to shopping mall, note the new section of pavement for racing to continue

A fourth view is the transformation of emotion, as in Housman's fine phrase on the arts: they `` transform and beautify our inner nature ''.

Clearly, the transformation is involutorial.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Now consider the transformation of the lines of a bundle with vertex, P, on **zg which is effected by the involution as a whole.

the way in which the transformation of state depends on the operating variables for the main types of reactors is discussed in the next chapter.

He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.

This transformation is uniquely determined by Af and we therefore speak of the process as deterministic.

The whole role, by the way, is a considerable transformation for anyone who has seen Seigner in his other parts.

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation.

Bruce Hindmarsh suggests that the secular popularity of " Amazing Grace " is due to the absence of any mention of God in the lyrics until the fourth verse ( by Excell's version, the fourth verse begins " When we've been there ten thousand years "), and that the song represents the ability of humanity to transform itself instead of a transformation taking place at the hands of God.

James Basker also acknowledged this force when he explained why he chose " Amazing Grace " to represent a collection of anti-slavery poetry: " there is a transformative power that is applicable ...: the transformation of sin and sorrow into grace, of suffering into beauty, of alienation into empathy and connection, of the unspeakable into imaginative literature.

A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside.

At the opposite extreme, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside.

The shift in Aalto's design approach from classicism to modernism is epitomised by the Viipuri Library ( 1927 – 35 ), which went through a transformation from an originally classical competition entry proposal to the completed high-modernist building.

Some theories connect these flows directly, implying that there is significant upwelling of dense deep waters within the Southern Ocean, transformation of these waters into light surface waters, and a transformation of waters in the opposite direction to the north.

This is because such flows can produce a net southward flow in the troughs and a net northward flow over the ridges without requiring any transformation of density.

Skewing is an example of a transformation not usually considered.

This gradual transformation is an important consideration when studying the properties of elemental berkelium and its chemical compounds, since the formation of californium brings not only chemical contamination, but also self-radiation damage, and self-heating from the emitted alpha particles.

In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f < sup > x </ sup > and f < sub > y </ sub > are all linear transformations.

The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above.