fourier series applet etc.

[PG1995]

Hi

I was playing around with this applet. I was using square wave. Please help me with these queries, **broken link removed** and **broken link removed**. Thank you.

Regards
PG

 

[MrAl]

Hi,

Q1, 2, 3:

The playing sound appears to be the base frequency. So that's the frequency used to show the wave, ie the fundamental frequency.

The 'bars' allow you to play only one harmonic, or to mute one harmonic so the sound should change. What i didnt like was it doesnt seem to remove that harmonic from the wave shape if you mute it. To mute click on a top bar, to use only that one harmonic click on the bottom bar.

The phase sticks are showing the phase of that harmonic. So if you see one that is at -1 that means the phase shift is -1 for that harmonic (in radians most likely). You get this view when you click Magnitude and Phase View which they call "Mag/Phase View". otherwise you get sine and cosine view.

 

[PG1995]

Thank you, MrAl.

Could you please help me with these queries, **broken link removed** and **broken link removed**? Thank you.

Regards
PG

 

[MrAl]

Hi again,


I didnt say that the phase shift was "one radian", i said they were giving the phase shift in units of radians. But to be more exact, they are using units of radians but the graduations are probably pi/2 units apart for the vertical axis. So if you see a stick where the head is near the first graduation down, then it is probably near -pi/2 so the phase shift is -pi/2. You could verify this doing a few calculations.

But also when you do that and for your other query you should first note that the application is not anything near what we could call perfect. Some of the calculations are not very exact at all. For example, the app stats that the base frequency is 220Hz, yet when it calculates the 2nd harmonic it comes out with a result of 441Hz which is pretty tacky if you ask me. Who cant calculate what twice 220 is with even the simplest of calculators? So that's why you are coming up with some of these questions. If the calculations (as simple as they are he he) were more exact i think you might be more happy. So when you see something like 0.0023 cos(9x-1.564) it could really mean 0.000000000*cos(9x-1.564) which of course is zero, and furthermore that 1.564 could really be pi/2 because the calculations in that applet just are not that exact.
But it does show the basics of how these things work so it's not too bad of an example, but maybe someone should write to the author and inform them that there are pretty silly errors that mess up the beauty of the app.

The best way to go about proving this is to sit down and roll your sleeves up and do a few calculations of your own. You'll see how it all fits together that way. You can start with the Fourier Series and go from there. If you dont know how to calculate this right now, myself or someone else can go through an example if you are interested enough to see how the Fourier Series works. The square wave is a good example and that's often a starting point for students.

One thing you can glean from the app is that the more terms you have, the higher the accuracy of the reconstructed wave.

You can also note that a very good program im sure you know, the LT spice simulator, does the same thing except it's more accurate. Sometimes when it finds an amplitude it will be non zero when theoretically it is truly zero. This isnt to much of a problem however because when we see an amplitude of 1.2 for the fundamental frequency and an amplitude of 0.003 for the amplitude of some harmonic, we know that 0.003/1.2=0.0025 so that means the harmonic is just 0.25 percent of the fundamental, which is usually considered negligible.

You'll sometimes find that if you want really good accuracy you have to calculate it yourself. That's ONE of the reasons why you're learning all this and not simply using applets for everything, so when a problem comes up with someone else's software you know what you have to do