Turn on thread page Beta

Fourier series/ Gibb's phenomena/ accuracy of approximations watch

    • Thread Starter
    Offline

    11
    ReputationRep:
    Hello.

    I am approximating a sinusoidal signal modulated by a gaussian envelope defined over the interval x=[-L/2,L/2]. However my question is more general:

    If you have a function which is continuous across the boundary at x=-L/2 and x=L/2, what other reasons, apart from discontinuity of the function across the boundary, would you have for the approximation (i.e. when you rebuild the function from the calculated fourier co-efficients, but only using a finite number of them) becoming less good at the boundaries.

    I'm aware I probably haven't described my problem very well.... to put in simple terms, if you look at my graph i've attached, I want to know why the yellow line gets big at the edges, even though the function is continuous everywhere (in the zeroth derivative).

    Cheers
    Attached Images
     
    Offline

    4
    ReputationRep:
    I'm not sure what you want to know, but basically there are bound to be problems when approximating a discontinuous function with a continuous one...
 
 
 
The home of Results and Clearing

1,531

people online now

1,567,000

students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.