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

Evaluate the integral, Example:   If c ≠ 0 , evaluate the subsequent integr...

Example:   If c ≠ 0 , evaluate the subsequent integral. Solution Remember that you require converting improper integrals to limits as given, Here, do the integ

Example of negative number, Q. Example of negative number? If you take ...

Q. Example of negative number? If you take an elevator 8 stories  down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories  up .

Find ad, A circle is inscribed in a triangle ABC having sides 8cm, 10cm and...

A circle is inscribed in a triangle ABC having sides 8cm, 10cm and 12cm as shown in the figure. Find AD, BE and CF.

BASIC MATHEMATHICS :AN APPLIED APPROACH BY RATHUS, FIRST OF ALL I WANNA KN...

FIRST OF ALL I WANNA KNOW THECHNIQUES, I CAT DIVIDE BIG BIG NUMBERS , EVERYTHING IN MATH IIS VERY HARD FOR ME I HOPE YOU CAN HELP ME

Steps for radio test - sequences and series, Steps for Radio test Assum...

Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i

Level curves or contour curves - three dimensional space, Level Curves or C...

Level Curves or Contour Curves Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are t

Mass-Spring-Damper -- Underdamped System, us consider the following mass-sp...

us consider the following mass-spring-damper system: md2xdt2+cdxdt+kx=0 with m=5 kg as the mass of the body, k=1.6N/m as the spring constant and two different values of c.

Times fractons, In a garden, 1/8 of the flowers are tulips. 1/4 of the tuli...

In a garden, 1/8 of the flowers are tulips. 1/4 of the tulips are red. What fraction of the flowers in the garden are red tulips?

How much wrapping paper will needed, Barbara is packing a wedding gift that...

Barbara is packing a wedding gift that is contained within a rectangular box 20 by 18 by 4 in. How much wrapping paper will she require? a. 512 in 2 b. 1,440 in 2 c. 1,0

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