Draw a graph of a given curve in the xoy plane. Now draw a vertical line so that it cuts the graph. If the vertical line cuts the graph in more than one ordinate then given graph is not a function. If it cuts the graph at a single ordinate such a graph is a function.(is called vertical line test)
It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.
Draw a circle with its center at the origin and a radius of 3.
Find the domain of the relation then draw the graph.
because you have to show your work and make shore its right
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
Fourier series and the Fourier transform
what are the limitations of forier series over fourier transform
yes a discontinuous function can be developed in a fourier series
no
Yes. For example: A square wave has a Fourier series.
Fourier series is series which help us to solve certain physical equations effectively
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Joseph Fourier was the French mathematician and physicist after whom Fourier Series, Fourier's Law, and the Fourier Transform were named. He is commonly credited with discovering the greenhouse effect.
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.