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Topic: Fourier series

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	Signals, Systems, and Control Demonstrations
		A Java applet that displays Fourier series approximations and corresponding magnitude and phase spectra of a periodic continuous-time signal.
		Or enter coefficients in the mathematical expression for the Fourier series.
		Discrete-Time Fourier Transform Properties A Java applet that displays the effect that various operations on a discrete-time signal have on the amplitude and phase spectra of the signal.
	www.jhu.edu /~signals (1298 words)

	PlanetMath: example of Fourier series
		We will compute the Fourier coefficients for this function.
		"example of Fourier series" is owned by alozano.
		This is version 7 of example of Fourier series, born on 2003-09-10, modified 2006-02-21.
	www.planetmath.org /encyclopedia/ExampleOfFourierSeries.html (105 words)

	PlanetMath: Fourier sine and cosine series
		Thus the Fourier series of an even function contains mere cosine terms and of an odd function mere sine terms.
		Fourier sine series, Fourier cosine series, sine series, cosine series, half-interval, Fourier double sine series, Fourier double cosine series
		This is version 17 of Fourier sine and cosine series, born on 2006-02-23, modified 2007-01-13.
	planetmath.org /encyclopedia/FourierSineAndCosineSeries.html (256 words)

	Fourier series - Wikipedia, the free encyclopedia
		The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short.
		Fourier series serve many useful purposes, as manipulation and conceptualization of the modal coefficients are often easier than with the original function.
		Fourier series are named in honor of Joseph Fourier (1768-1830), who made important contributions to the study of trigonometric series, after preliminary investigations by Madhava, Nilakantha Somayaji, Jyesthadeva, Leonhard Euler, Jean le Rond d'Alembert, and Daniel Bernoulli.
	en.wikipedia.org /wiki/Fourier_series (2340 words)

	A Fourier Series Solution for the Temperature Distribution on Convection Cooled Plates with Discrete Heat Sources
		This article is about a Fourier series solution to the problem of calculating the temperature distribution on a convection cooled plate with discrete heat sources.
		It is basically a Fourier series in which the coefficients are given by another Fourier series.
		These series can be made to model just about any function but their drawback is that the fit only is perfect if an infinite number of terms are included.
	www.frigprim.com /articels/analsolv_1.html (1965 words)

	Fourier Series (Site not responding. Last check: )
		Fourier series are made up of sinusoids, all of which have frequencies that are integer multiples of some fundamental frequency.
		A great thing about using Fourier series on periodic functions is that the first few terms often are a pretty good approximation to the whole function, not just the region around a special point.
		Fourier series are used extensively in engineering, especially for processing images and other signals.
	mathforum.org /key/nucalc/fourier.html (191 words)

	Fourier series
		Named after Joseph Fourier, the expansion of a periodic function as an infinite sum of sines and cosines of various frequencies and amplitudes.
		Fourier series are used a great deal in science and engineering to find solutions to partial differential equations, such as those in problems involving heat flow.
		The study and computation of Fourier series is known as harmonic analysis.
	www.daviddarling.info /encyclopedia/F/Fourier_series.html (223 words)

	KR Mathematics: Fourier Transformations (Site not responding. Last check: )
		A fourier series works on the idea that any wave function, such as a wave pulse can be constructed by a combination of pure frequency waves, such as a sine or cosine.
		However, a fourier series has a limitation in that the function being examined must be made of discrete frequencies.
		Doing Fourier Transformations by hand can be very tedious, but with the invention of computers programs and algorithms were developed to preform fourier transformations at a quicker rate.
	www.kopernekus.com /math/fourier.asp (729 words)

	Basic Concept on Fourier Series (Site not responding. Last check: )
		Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components.
		Basically, fourier series is used to represent a periodic signal in terms of cosine and sine waves.
		Fourier series is a method to represent that periodic signal that we can manage it easily with simple trigonometry skills.
	www-ee.eng.hawaii.edu /~sasaki/Undergrad/WaveCalc/ZeLi/fourier.html (320 words)

	Fourier Analysis and FFT
		Fourier Analysis is based on the concept that real world signals can be approximated by a sum of sinusoids, each at a different frequency.
		The two series are identical except that the magnitude generated by the exponential series are half the value of the trigonometric series.
		The magnitudes are corrected for the trigonometric series and therefore use the same units as the input signal.
	www.astro-med.com /knowledge/fourier.html (2529 words)

	Fourier series Summary
		The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short.
		Fourier series serve many useful purposes, as manipulation and conceptualization of the modal coefficients are often easier than with the original function.
		Fourier series and Fourier transforms usually used in signal processing then become special cases of this theory and are easier to interpret.
	www.bookrags.com /Fourier_series (2697 words)

	Examples of Fourier Series
		Fourier series are used to represent periodic functions.
		This is partially due to the finite length of the series, but also due to an intrinsic imperfection in Fourier series.
		This effect, discovered by J.W. Gibbs in 1899, shows that even if Fourier series can be accurate approximations in some regions of the independent variable, they may be inaccurate in the neighborhood of discontinuities.
	hesperia.gsfc.nasa.gov /~schmahl/fourier_tutorial/node2.html (209 words)

	Fourier series examples (Site not responding. Last check: )
		The Fourier series coefficients are shown on the plot labeled "Frequency domain".
		For the square wave, the peak error of the approximation (the maximum difference between the red and blue curves) does not appear to decrease as the number of terms in the approximation is increased.
		The peak error does not decrease to zero as the number of terms in the Fourier series is increased to infinity.
	ptolemy.eecs.berkeley.edu /~eal/eecs20/week8/examples.html (372 words)

	Fourier - Wikipedia, the free encyclopedia
		Joseph Fourier (1768-1830), a French mathematician and physicist
		The Fourier transform, a generalisation of the fourier series
		Peter Fourier (1565-1640) a French saint in the Roman Catholic Church and priest of Mattaincourt
	en.wikipedia.org /wiki/Fourier (118 words)

	Fourier Series Example #2
		All three forms of the Fourier series (trig, cosine, and exponential) will be computed, beginning with the trig form.
		When the complete series is used, the series converges to the exact value of the signal at every point in time where the signal is continuous and converges to the midpoint of the discontinuity wherever the signal is discontinuous.
		The signal x(t) can be approximated by using a truncated form of the Fourier series, that is, stopping the summation after a finite number N of terms.
	ece.gmu.edu /~gbeale/ece_220/fourier_series_02.html (1049 words)

	IV. Calculating Fourier Series
		The Fourier series is converging nicely to the function except at the end-points of the interval, which are places where the full periodic saw-tooth function has jumps, and we saw something similar with the square pulse.
		In both cases we see numerical evidence for the theorem that the Fourier series converges to f(x) where f(x) is continuous, and where it has a jump, the Fourier series converges to the average of the upper and the lower value at the jump.
		Notice that the Fourier series is not bothered by the corners in the function at -1,0, and 1.
	www.mathphysics.com /pde/ch4wr.html (2142 words)

	Introduction to Fourier Series at nOnoscience (Site not responding. Last check: )
		A light color Math-warning flag is hoisted, but if you are curious about the Fourier series and how it was used in the analytical description of heat diffusion in solids, perhaps a peek into these posts should rouse your interest.
		The series which goes by his name nowadays appeared in Chapter 3 of Fourier’s classic “The Analytical Theory of Heat”, which appeared in print in 1822 for the first time.
		Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it is said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics…Fourier is a mathematical poem.
	www.nonoscience.info /2006/11/15/introduction-to-fourier-series (1349 words)

	FourierTransform
		The Fourier transform is commonly used to transform a problem from the continuous "time domain" into the continuous "frequency domain." The Fourier transform may be viewed as the continuous analog of the Fourier series decomposition, which expresses a periodic function as a superposition of exponential or trigonometric functions.
		The plot of the truncated series is similar to that of the function.
		Likewise, the (infinite sum) Fourier exponential series can be thought of as an inverse transform from the discrete frequency domain into the continuous time domain.
	documents.wolfram.com /v5/Add-onsLinks/StandardPackages/Calculus/FourierTransform.html (591 words)

	III. Fourier series, Introduction
		There are very similar theorems for the Fourier sine series and the Fourier cosine series series, which are based, respectively, on the orthogonal sets (2.5) and (2.7).
		If you look at the various Fourier series that are plotted in the next chapter, you will see that the crazy phenomenon of Example 2 doesn't happen.
		What we see from the examples is that where a function has a discontinuity, the Fourier series, when truncated to a large but finite number of terms, takes on a value between the right and left limits.
	www.mathphysics.com /pde/ch3wr.html (1847 words)

	Fourier Series Expansions
		Fourier series are used to expand periodic functions in the trigonometric form.
		The pattern we have for the Fourier trigonometric polynomials are given by the following summation which we can check out for the case where 5 terms are added in the sum.
		The pattern we have for the Fourier trigonometric polynomials are given by the following summation which we can check out for the case where 3 terms are added in the sum.
	math.fullerton.edu /mathews/N310/projects3/e24.htm (328 words)

	Fourier Series Simulation
		Fourier series, which is a method of expressing an arbitrary periodic function as a sum of cosine terms.
		In other words, Fourier series can be used to express a function in terms of the frequencies (harmonics) it is composed of.
		The function is displayed in white, with the Fourier series approximation in red.
	licencera.free.fr /fourier_simulation/fourier_series_simulation.htm (714 words)

	Discrete Fourier Transform
		A continuous, periodic signal can be decomposed into an infinite set, called the Fourier series, of harmonically related frequencies, the fundamental frequency being equal to the inverse of the period.
		The Fourier series in Equation 6 then needs to be modified by changing the summation to integration and the discrete frequency nω0 to continuous frequency ω.
		The representation through samples of the Fourier transform is in effect a representation of the finite-duration sequence by a periodic sequence, one period of which is the finite-duration sequence we wish to represent.
	rfdesign.com /mag/radio_understanding_discrete_fourier (2000 words)

	Chapter 3: Fourier Analysis of Discrete Functions
		Fourier, who is credited with resolving this issue, was interested in the theory of heat.
		This horizontal line is the Fourier series for this case of D=1 samples and the parameter m is called a Fourier coefficient.
		Again, since the squared amplitudes of the Fourier coefficients are associated with the energy in the model, this equation says that the variance of a set of data points may also be thought of as a measure of the amount of energy in the signal.
	research.opt.indiana.edu /Library/FourierBook/ch03.html (4038 words)

	Fourier Series
		This series is called the Fourier series and the coefficents are called the Fourier coefficients.
		The Fourier series expansion of a continuous and periodic waveform provides a means of expanding a function into its major sine / cosine or complex exponential terms.
		The first figure is the approximation of a square wave using 2 fourier series terms, and the second figure is the approximation when 16 terms are included.
	www.cage.curtin.edu.au /mechanical/info/vibrations/tut1.htm (436 words)

	Fourier Series Applet
		This java applet demonstrates Fourier series, which is a method of expressing an arbitrary periodic function as a sum of cosine terms.
		In other words, Fourier series can be used to express a function in terms of the frequencies (harmonics) it is composed of.
		The function is displayed in white, with the Fourier series approximation in red.
	www.falstad.com /fourier (117 words)

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