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If we view the DFT as just a coordinate transformation which simply specifies the components of a vector in a new coordinate system, then the above is just the statement that the dot product of two vectors is preserved under a unitary DFT transformation.
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If and we
If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;
If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.
If art is to release us from these postulated things ( things we must think symbolically about ) and bring us back to the ineffable beauty and richness of the aesthetic component of reality in its immediacy, it must sever its connection with these common sense entities ''.
If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.
If and view
If they feel that we are taking a long-term view of their problems and are prepared to enter into reasonably long-term association with them in their development activities, they will be much more likely to undertake the difficult tasks required.
If this attitude is seriously questioned in the Soviet Union, it does not necessarily follow that the majority of the society in which I live is too aware of the necessity for clarity on this ethical as well as aesthetic point of view.
If he dwelt on the indignities he suffered he would lose all respect for her, and without the respect he might lose his view of her, too.
If products designed for the new standard can receive, read, view or play older standards or formats, then the product is said to be backward-compatible ; examples of such a standard include data formats and communication protocols.
Thus the view from Whitehall early in 1916: If defeat was not imminent, neither was victory ; and the outcome of the war of attrition on the Western Front could not be predicted.
If he sometimes seems to approach the symbolic view, at other times he comes very close to a strong realistic doctrine.
If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “ same picture ” comparison above.
If we are to explain language's evolution, according to this view, we must tackle it as part of a wider one — the evolutionary emergence of symbolic culture as such.
If this view is correct, the epistle should be dated somewhere around 47, depending on other difficult to date events, such as Paul's conversion.
If someone sees something completely different than another, our language prevents us from acknowledging the other's point of view by limiting our perception to fixed states.
If it is assumed that social change is not only affected, but in some points of view, directed by the advancement of technology, is it ethical to hold these technologies from certain people?
In 1951, he summed up his vision as follows: " If the camera is to make a contribution at all to dance, this must be the focal point of its contribution ; the fluid background, giving each spectator an undistorted and altogether similar view of dancer and background.
If Matthew's prime concern was to preserve the Jewish character of the church, he failed: Christianity became a Gentile religion, and Christianity and Judaism came to view each other as opposites.
If heaven is a state of supernatural happiness and union with God, and hell is understood as a state of torture and separation from God then, in this view, the Limbo of Infants, although technically part of hell ( the outermost part, " limbo " meaning " outer edge " or " hem ") is seen as a sort of intermediate state.
If, for instance, the algorithmic view is taken, then the reals as constructed here are essentially what classically would be called the computable numbers.
If some other method was used, the triples were first constructed and then reordered by, presumably for actual use as a " table ", i. e., with a view to applications.
If God in some sense knows ahead of time what will happen, then events in the universe are effectively predetermined from God's point of view.
If I have seen that from an ethical point of view I am just one person among the many in my society, and my interests are no more important, from the point of view of the whole, than the similar interests of others within my society, I am ready to see that, from a still larger point of view, my society is just one among other societies, and the interests of members of my society are no more important, from that larger perspective, than the similar interests of members of other societies ...
If the ball is spinning counterclockwise, it will curve right from the hitter's point of view and curve left if spinning clockwise.
If and DFT
If the expression that defines the DFT is evaluated for all integers k instead of just for, then the resulting infinite sequence is a periodic extension of the DFT, periodic with period N.
If only a small number of ω are desired, or if the STFT is desired to be evaluated for every shift m of the window, then the STFT may be more efficiently evaluated using a sliding DFT algorithm.
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