Function expansion, Mathematics

Assignment Help:

The functions

{sinmx; cosmx}; m = 0,....∞

form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have

883_FUNCTION EXPANSION.png

To show that the above holds for x = 1, study the di erence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (di erence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.


Related Discussions:- Function expansion

Find out the maximal elements of a poset, Refer the poset  ({1}, {2}, {4}, ...

Refer the poset  ({1}, {2}, {4}, {1,2}, {1,4}, {2,4}, {3,4}, {1,3,4}, {2,3,4}, ≤ ). (i)  Find out the maximal elements. (ii)  Find out the minimal elements. (iii)  Is ther

Analysis of algorithm running time - undirected graph, Problem. You are giv...

Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1, 2, . .

Trigonometry, Prove: cotA/2.cotB/2.cotC/2 = cotA/2+cotB/2+cotC/2

Prove: cotA/2.cotB/2.cotC/2 = cotA/2+cotB/2+cotC/2

Communicating the meaning of addition, COMMUNICATING THE MEANING OF ADDITIO...

COMMUNICATING THE MEANING OF ADDITION :  One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on

Basic Mathematics, Distinguish between Mealy and Moore Machine? Construct a...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''''s encountered is even or odd.on..

Coefficient of determination, Coefficient of Determination It refers t...

Coefficient of Determination It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The s

Sum of a number of terms in a.p., We know that the terms in an ...

We know that the terms in an A.P. are given by a, a + d, a + 2d, a + 3d, ........ a + (n - 2)d, a + (n -  1)d The sum of all t

Second order differential equation, Write the subsequent 2nd order differen...

Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0  y (3) = 6  y′ (3) = -1  We can wri

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd