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By Whitley D.

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3 it is apparent that the average value must be A/2. This process of detecting or rectifying sinusoids, then, has the characteristic of yielding only half the amplitude of the actual component. This presents no major problem though, as we can simply multiply all of the results by two, or use some other technique to correct for this phenomenon. 4 THE COSINE COMPONENT It is obvious that this scheme will work for any harmonic component; we need only change the frequency of the unit FFT/02 39 amplitude sine wave to match the frequency of the harmonic component being detected.

May be obtained by the Taylor series (as we explained previously); but, there is a problem in applying these series directly—they are too slow! They take too long to converge to the accuracy required for most practical work. Use of the Taylor series would be severely limited had not our friends, the mathematicians, figured out the following way to make it run faster: 24 Understanding the FFT We observe, as a practical matter, that all of the different series required are of the polynomial form: F(x) - A0 + A1x + A2x2 + A3x3 + A4x4 + ...

As the angle Ø between the two vectors approaches + 90 degrees, Cos Ø approaches zero, and the dot product approaches zero. It is apparent, then, that a zero dot product between any two finite vectors implies orthogonality. 4 - Dot Product vectors will always yield a zero dot product regardless of the angle (in fact, the notion of angle begs for definition here). 21) as the operative definition for orthogonality. DEFINITION 1: If A·B = 0 then A and B are orthogonal. Note that, by this definition, zero magnitude vectors are orthogonal to all other vectors, The definition of orthogonality between whole functions derives from an argument not completely dissimilar to the above.

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