Finding an equation with given traits

[csmitty12]

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

Consider a function
f(x) = 0, 0 ≤ x < 1
and
f(x) = 1, 1 ≤ x < 2

What is the function and how did you find it? Please help it will be used for a Fourier Series project. I can get the Series stuff fine but I just don't remember how to find a function.

 

[robphy]

Can you draw it?
Here's a start:
http://www.wolframalpha.com/input/?i=Heaviside(x-1)-Heaviside(x-2)

 

[csmitty12]

Can you draw it?
Here's a start:
http://www.wolframalpha.com/input/?i=Heaviside(x-1)-Heaviside(x-2)

The thing is, is that it is supposed to be a periodic function with Period 2. I can't draw it that's all the info I've got.

 

[berkeman]

Consider a function
f(x) = 0, 0 ≤ x < 1
and
f(x) = 1, 1 ≤ x < 2

What is the function and how did you find it? Please help it will be used for a Fourier Series project. I can get the Series stuff fine but I just don't remember how to find a function.

The thing is, is that it is supposed to be a periodic function with Period 2. I can't draw it that's all the info I've got.

Welcome to the PF.

What you have specified is not periodic. As robphy indicates, you can use the addition of two step functions to generate the function that you have specified in your first post. There must be more to the problem statement than you have shown us so far.

BTW, is this for a schoolwork assignment or for something else?

 

[csmitty12]

Welcome to the PF.

What you have specified is not periodic. As robphy indicates, you can use the addition of two step functions to generate the function that you have specified in your first post. There must be more to the problem statement than you have shown us so far.

BTW, is this for a schoolwork assignment or for something else?

It is for a Fourier Series project. I can get the FS through MATLAB, my only question is how to get the function to use in the FS?

 

[berkeman]

It is for a Fourier Series project. I can get the FS through MATLAB, my only question is how to get the function to use in the FS?

Oh, that's different (now seeing the actual problem statement). They say to construct a periodic square wave out of that basic function. Do you know how to calculate the Fourier Series of a square wave with a DC offset?

 

[csmitty12]

Oh, that's different (now seeing the actual problem statement). They say to construct a periodic square wave out of that basic function. Do you know how to calculate the Fourier Series of a square wave with a DC offset?

So far we have only learned sinusoidal functions and complex representation. I'm not too sure how do do it with a square wave. Any idea where I can get started?

 

[berkeman]

Just Google the last part of my last post:

Fourier Series of a square wave with a DC offset

 

[csmitty12]

Just Google the last part of my last post:

Okay so now I understand how to get the equation for the series. Now I'm confused and stuck on the part where it says to calculate the first 30 terms for two cycles, x = -2 to 2. Any hints/suggestions?

 

[berkeman]

Okay so now I understand how to get the equation for the series. Now I'm confused and stuck on the part where it says to calculate the first 30 terms for two cycles, x = -2 to 2. Any hints/suggestions?

What happens when you google Gibb's Phenomenon?