Fourier s theorem

Now let us eonsider a funetion that is periodie in time with period T. Fourier s theorem states that any periodie funetion ean be expressed in a Fourier series as a linear eombination (infinite series) of Sines and Cosines whose frequeneies are multiples of a... 

Fourier s theorem determines the law for the expansion of any arbitrary function in terms of sines or cosines of multiples of the independent variable, x. If f(x) is a periodic function with respect to time, space, temperature, or potential, Fourier s theorem states that... 

Since the eigenfunctions are unit vectors, an arbitrary function is representable as an eigenfunction expansion. This is because, based on Fourier s theorem that an arbitrary function can be expanded by the series expansion of trigonometrical functions, a function is always expanded by the eigenfunctions of the translational motions, which are trigonometrical functions. 

According to Fourier s theorem, all small-amplitude techniques must yield identical results (i.e. the same interfacial impedance), regardless of the form of the excitation. This is clearly the case for the system discussed above, as shown in Figure 4.4.4. In this figure, polarization resistance data, obtained using the impedance... 

If the object has an exactly sinusoidal variation of absorption, thickness or refractive index in one dimension, diffracted beams appear only when d sin (/) = A (i.e. m = 1). This is important because of Fourier s Theorem, which states that any (single valued) function of a variable x can be expanded as a sum of sines and cosines of multiples of x. Thus any phase or intensity variation in the sample can be considered as a sum of sinusoidal variations of different wavelength, each giving a certain intensity at a single characteristic angle 0. The intensity at a point in the diffraction pattern corresponds to the strength of a variation of some sample property... 

Fibonacci Leonardo of Pisa (-1170-1230) It. math., best known for his book of Abacus, putting thus end to old Roman system of numerical notations, his series are now called Fibonacci s Pick Adolf Eugen (1829—1901) Ger. physiol, who made important discoveries in every branch of psychology, well-knownfor the Law of difftision (Ann. Phys. 94(1855)59) named after him Flynn Joseph Henry (1922-) US phys., known for Flynn kinetic evaluation method Fourier Jean Baptiste Joseph (1768—1830) Fr. math., evolved mathematical series knovm by his name and important in harmonic analysis, providing source of all modem methods in mathematical physics, originated Fourier s theorem on vibratory motions... 

Even without detailed modeling, it can be said that the attractive and repulsive interactions change the motion of the cantilever away from the simple sinusoidal motion of free resonance. By Fourier s theorem, any such altered motion can be broken down into the basic fundamental... 

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