0
What else can I help you with?
Is the fnction in fourier series periodic?
Yes, a Fourier series represents a periodic function. It decomposes a periodic function into a sum of sine and cosine terms, each of which has a specific frequency. The resulting series will also be periodic, with the same period as the original function. If the original function is not periodic, it can still be approximated by a Fourier series over a finite interval, but the series itself will exhibit periodic behavior.
Difference between power series and fourier power series?
A power series is a series of the form ( \sum_{n=0}^{\infty} a_n (x - c)^n ), representing a function as a sum of powers of ( (x - c) ) around a point ( c ). In contrast, a Fourier power series represents a periodic function as a sum of sine and cosine functions, typically in the form ( \sum_{n=-\infty}^{\infty} c_n e^{i n \omega_0 t} ), where ( c_n ) are Fourier coefficients and ( \omega_0 ) is the fundamental frequency. While power series are generally used for functions defined on intervals, Fourier series specifically handle periodic functions over a defined period.
How can you tell by looking at a graph its a function?
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)
What are the applicaton of fourier series?
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.
How do you graph x2 plus y2 equals 9?
Draw a circle with its center at the origin and a radius of 3.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
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.
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
What is physical significance of Fourier series?
Fourier series is series which help us to solve certain physical equations effectively
What is the difference between fourier series and discrete fourier transform?
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.
How do you find the inverse Fourier transform from Fourier series coefficients?
To find the inverse Fourier transform from Fourier series coefficients, you first need to express the Fourier series coefficients in terms of the complex exponential form. Then, you can use the inverse Fourier transform formula, which involves integrating the product of the Fourier series coefficients and the complex exponential function with respect to the frequency variable. This process allows you to reconstruct the original time-domain signal from its frequency-domain representation.
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Why was Joseph Fourier famous?
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.
Can a discontinuous function be developed in a Fourier series?
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
Can every function be expanded in fouriers series?
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
