Skip to main content
5 votes

For the square wave signal, why does a narrower square wave correspond to more spread in the frequency domain?

Think of what happens when you play back a recording at 2x speed: each frequency of the sound doubles. When you make the pulse narrower, that's equivalent to speeding it up in the time domain. ...
jpa's user avatar
  • 763
3 votes

For the square wave signal, why does a narrower square wave correspond to more spread in the frequency domain?

One way to view this concept is from energy conservation. With proper scaling, the Fourier transform is energy conserving. In order to use up its energy in a short window, the signal has to expel its ...
Baddioes's user avatar
  • 1,135
3 votes
Accepted

Magnitude and phase spectrum of a periodic signal

For magnitude and phase you need the complex Fourier coefficients: $$c_n=\frac{1}{T}\int_{0}^Tx(t)e^{-j2\pi nt/T}dt\tag{1}$$ I think your Fourier series is correct, so you can directly determine them ...
Matt L.'s user avatar
  • 90.5k
3 votes
Accepted

The utility electric power signal is periodic or not?

will I get an exact repeating pattern ?? No. You will get a repeating pattern but it's not exact. No physical signal can be "exactly" periodic. There will always be some amount of noise, ...
Hilmar's user avatar
  • 45.9k
1 vote

Recovering a quasi-periodic signal subject to amplitude modulation and additive noise

Okay, just FYI I've done this with audio signals. I have posted here the sufficient mathematics, but no code. Here's the comb filter stuff. Here is how to do precision delay. Here is how to do pitch ...
robert bristow-johnson's user avatar
1 vote

Fourier series - finding its period from frequency representations

HINTS: Note that the given numbers are not indices but actual angular frequencies. So your result should be a number, not just a multiple of the unknown quantity $\omega_0$. In point 2, there's one ...
Matt L.'s user avatar
  • 90.5k
1 vote
Accepted

What function can be used to describe periodicity of the signal

You are sampling, then resampling, then (essentially) filtering. Everything that you see can be explained because of the combination of these effects. You're starting with a signal at 100Hz: $x(t) = \...
TimWescott's user avatar
  • 12.9k
1 vote

The utility electric power signal is periodic or not?

A fundamental of engineering practice is that you look for some way of taking the messy real world, and describing it in terms that are easy to solve mathematically. Is utility electric power -- or ...
TimWescott's user avatar
  • 12.9k

Only top scored, non community-wiki answers of a minimum length are eligible