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

If 6 more black balls are put in the box find x, A box contains 12 balls ou...

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put i

Karatsubas algorithm, Consider the following two polynomials in F 17 [x] ...

Consider the following two polynomials in F 17 [x]   (a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials. (b) Use the FFT algorithm, by hand, to

Linear programming, Maximize P=3x+2y Subject to ...

Maximize P=3x+2y Subject to x+y =6 x =3 x =0,y =0

Mean and standard deviation, Q. Mean and Standard Deviation? Ans. ...

Q. Mean and Standard Deviation? Ans. The normal distribution is totally described if we know the average and standard deviation. - the population mean of the distribu

find the slope and the y intercept of the line - geometry, 1. Find the slo...

1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin

Find the sum of a+b and a-b, Find the sum of a+b, a-b, a-3b, ...... to 22 t...

Find the sum of a+b, a-b, a-3b, ...... to 22 terms. Ans:    a + b, a - b, a - 3b, up to 22 terms d= a - b - a - b = 2b S22 =22/2 [2(a+b)+21(-2b)] 11[2a + 2b - 42b] =

Precalculus, describe the end behavior of the following function using Limi...

describe the end behavior of the following function using Limit notation f(x)= 2x-1/x-1

#rounding off, I am the least two digit number which round off to 100?

I am the least two digit number which round off to 100?

Perimeter and Area, A farmer has a rectangular field of length 100m and bre...

A farmer has a rectangular field of length 100m and breadth 70m. He leaves a path of 1m all along the boundary inside it. He decides to apply a manure to the remaining part of the

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