×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Periodic rectangular function

Periodic rectangular function

Periodic rectangular function

(OP)
Question...

Can anybody tell me what happens to this equation when:

1. tau->0
2. T->infinity

http://en.wikipedia.org/wiki/Pulse_wave

I'm talking about the Fourier Series... The answer is not zero I guess. But I don't know what it is...

Please help!

RE: Periodic rectangular function

(OP)
Thank you very much! BUT!!!

I wasn't saying tau~0 and T-> infinity at the same time :(

Plus I'm not talking about the FFT but the Fourier Series!

RE: Periodic rectangular function

What prompts you to ask? Is there an application or are you just curious? You have to admit, it looks a bit like homework...

To understand what happens in (1) and (2) (which are equivalent after timescaling), consider the parts of the FS equation:

1) the DC component, tau/T, goes to zero because the average content of the signal gets small as the pulse width gets small.

2) the cosine amplitudes, (2/n*pi)*sin(pi*n*tau/T), flatten out and get smaller. Plot the amplitude, replacing n with x and varying tau to see this happening - the graph will be continuous but the FS amplitudes are at periodic points on this line. As Greg indicates, the spectral components are "smearing" out to a flat line.

3) the cosines, cos(2*pi*n*t/T), are simply shifted to lower frequencies the bigger T is.

 

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login



News


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close