However, this visible difference is merely a consequence of a deeper distinction: a DCT implies different boundary conditions than the DFT or other related transforms.

) However, the implicit periodicity of the DFT means that discontinuities usually occur at the boundaries: any random segment of a signal is unlikely to have the same value at both the left and right boundaries.

However, this visible difference is merely a consequence of a deeper distinction: a DST implies different boundary conditions than the DFT or other related transforms.

However, for composite sizes such as prime powers, the Cooley – Tukey FFT algorithm is much simpler and more practical to implement, so Rader's algorithm is typically only used for large-prime base cases of Cooley – Tukey's recursive decomposition of the DFT ( Frigo and Johnson, 2005 ).

However, these smaller DFTs have a length of N / 2, so we need compute only N / 2 outputs: thanks to the periodicity properties of the DFT, the outputs for < math > N / 2

However, these test generators, combined with low-overhead DFT techniques such as partial scan, have shown a certain degree of success in testing large designs.

However, the choice here makes the resulting DFT matrix unitary, which is convenient in many circumstances.

However, it was not of innocence in general that I was speaking, but of perhaps the frailest and surely the least important side of it which is innocence in romantic love.

However, in this case as elsewhere it was necessary to arrive at a single standard to be applied to all situations, representing an averaging of conditions, and thus to fix particular points in time which would be considered the dividing points between daytime and nighttime conditions.

However, the nonspecific staining by the Af in tumor sections was considered bright enough to be confused with the staining of small amounts of WTV antigen.

However, all admitted that the `` hindsight '' was not altogether lost.

However, she was able to relax and yield to the moment.

However, in this case the district manager was led to see the errors of his ways.

However, there was no real question of the justice of creating a strong Poland, both industrially and agriculturally, and one unplagued by large minorities of Germans or Russians.

However, the sovereign was not Hobbes' absolute monarch but rather the parliamentary sovereign of Austin.

However, a similar privilege was not specifically provided in section 168 for a person acquiring emergency facilities.

However, the Attorney General of California, at the request of the Secretary of Labor, sought to have the jurisdiction over the issue removed to the Federal District Court, on grounds that it was predominantly a Federal issue since the validity of the Secretary's Regulation was being challenged.

However, the Federal Court held that since the State had accepted the provisions of the Wagner-Peyser Act into its own Code, and presumably therefore also the regulations, it was now a State matter.

However nothing on four legs was supposed to be faster than a lion over a short distance, unless it was a cheetah.

However, it was virtually impossible to screen the mob outside, even if Bonner had manpower available for the purpose.

However likely it was, Pauling said, he couldn't limit himself to it.

However, Haney knew it was not a dream.

However, the confession, which was the only evidence against him, was retracted before the trial.

However, compared with March 1960 new car sales of 4,441, this March was off 23 per cent.

( However, there is little evidence that the late Lumumba was a Communist.

However, lacking requested reinforcements from McClellan, now commanding the Army of the Potomac, Pope was soundly defeated at the Second Battle of Bull Run in the summer of 1862, forcing the Army of the Potomac to defend Washington for a second time.

However Copperhead rhetoric argued that emancipation was a stumbling block to peace and reunification.

However, Plato reports that syntax was devised before him, by Prodicus of Ceos, who was concerned by the correct use of words.

However, in Icelandic, the accented letters such as á, í, and ö are considered to be distinct letters of the alphabet.

However, since Anatolia is now often considered to be synonymous with Asian Turkey, its eastern and southeastern borders are widely taken to be the Turkish borders with the neighboring countries, which are Georgia, Armenia, Iran, Iraq and Syria, in clockwise direction.

" However, their doctrines cannot be considered representative of traditional Arian doctrines or vice-versa.

However, Margaret Sleeboom-Faulkner of the Department of Anthropology at the University of Sussex said Kanzō Umehara considered the Ainu and some Ryukyuans to have " preserved their proto-Mongoloid traits " According to anthropologist Elsie Clews Parsons physical features of the Proto-Mongoloid were characterized as, " a straight-haired type, medium in complexion, jaw protrusion, nose-breadth, and inclining probably to round-headedness ".

However, this division into two groups is considered by some modern scholars to be too simplistic and often it is practically impossible to know whether a lyric composition was sung or recited, or whether or not it was accompanied by musical instruments and dance.

However, Pyxis is not considered part of Argo Navis, and its Bayer designations are separate from those of Carina, Puppis and Vela.

However, in 2004, Maher concluded that " Physical treatments, such as acupuncture, backschool, hydrotherapy, lumbar supports, magnets, TENS, traction, ultrasound, Pilates therapy, Feldenkrais therapy, Alexander technique, and craniosacral therapy are either of unknown value or ineffective and so should not be considered " when treating lower back pain with an evidence-based approach.

However, until the Revolution, many considered whiskey to be a coarse alcohol unfit for human consumption, as many believed that it caused the poor to become raucous and unkempt drunkards.

However, command problems ensued, as the assault guns were considered to be artillery by the Wehrmacht and therefore the assault guns were not under the control of the Panzer unit's commanding officer, reducing unit effectiveness.

However, these beverages are based on traditional hopped beers and therefore not considered to be alcopops.

However, this was considered " unmanly " and was frequently disallowed by additional rules negotiated by the Seconds of the Boxers.

However, at the time, " race music " and its white cousin, " hillbilly music ", were not considered to be worthy of consideration as art, rather as a low-cost product to be sold and soon forgotten.

However, drowsiness and tolerance become problems with continued use and none are now considered first-line choices for long-term epilepsy therapy.

However, Canada has evolved variations: party discipline in Canada is stronger than in the United Kingdom and more parliamentary votes are considered motions of confidence, which tends to diminish the role of non-Cabinet Members of Parliament ( MPs ).

However, members of these professions typically possess other software engineering skills, beyond programming ; for this reason, the term programmer is sometimes considered an insulting or derogatory oversimplification of these other professions.

However, printers are generally slow devices ( 30 pages per minute is considered fast, and many inexpensive consumer printers are far slower than that ), and the cost per page is actually relatively high.

However, the term is applied to multidimensional data as well as to univariate data and in situations where a transformation of the data values for some or all dimensions would usually be considered necessary: in the latter cases, the notion of a " central location " is retained in converting an " average " computed for the transformed data back to the original units.

However, some biological substances commonly called " monosaccharides " do not conform to this formula ( e. g., uronic acids and deoxy-sugars such as fucose ), and there are many chemicals that do conform to this formula but are not considered to be monosaccharides ( e. g., formaldehyde CH < sub > 2 </ sub > O and inositol ( CH < sub > 2 </ sub > O )< sub > 6 </ sub >).

However, these have a " grabby " action generally considered unsuitable for passenger cars.

However, the official attendances can be considered somewhat dubious in this era as many fans would get in by climbing over the fence from Bishops Park into the Putney End.

However the Glorious Revolution ( 1688 ), which established constitutional government, led to a reformulation of Toryism which now considered sovereignty vested in the three estates of Crown, Lords, and Commons.

However, the best modern analysis of the sources of the creed ( by A. de Halleux, in Revue Theologique de Louvain 7, 1976 ) and a reading of the acts, or proceedings, of the council ( recently translated into English ) show that the bishops considered Cyril the great authority and that even the language of ' two natures ' derives from him.

However, Hayward believes East Cushitic may not be a valid node and that its constituents should be considered separately when attempting to work out the internal relationships of Cushitic.