# Square waves sine waves etc(signal propagation)

1. Dec 27, 2007

### smack_whore

err probably skin too many q's but anyway....
what type of waves are made from naturall sources?eg then sun etc....are theren any square waves...im just wandering ifn theres any weirdness or differences when using square waves as a carrier wave in transmitting...if u know any good info sources thatd be a help....
srry that was garbage lol.....im lookin for info on transmitting signals ...mostly intrested in a certAIN subject..:r naturally ocuring waves sinusoidL OR CAN THEY BE Square waves etc and if artificially made square waves for transmitting really the same thing as naturally ocuring waves .....hard to say what i want lol...think its the big gap in my head where maths ability should be hahaha...
thnks in advanxce if u can offer help...even would like a point in another direction (of subjec t)....gotta lot of time hahahahhaa
SRRY FOR POSTING TWICE TWAS ACCIDENTAL I SWEAR LOL

<< Edit by berkeman -- I merged the two threads >>

Last edited by a moderator: Dec 28, 2007
2. Dec 27, 2007

### smack_whore

hi ,
a weird novelty driven q.....
anyone have sources or own knowledge that can describe the difference properties etc of sine waves vs square waves ....are square waves (ie a signal beiong propagated from a simple on/off/on/off signal generator) the same thing/replacable for , a sinusoidal wave signal?>
any good sources on waves for someonb of tyhe maths ability i have...(AS level B student)
errr yeah trhnks any help will be thankfull fo9r....
ps...in an inductor....
current flows and makes a field , cu?rrent stops an d field collapses...induces current.....is this current in the same direction...????
thinks hahahhahaa im ****

3. Dec 27, 2007

### ranger

But any periodic signal (no matter how weird it may look) can be mathematically expressed as a sum of sine waves. For example, the Fourier series expansion of a square wave can be expressed as an infinite sum of odd harmonic sine waves.

Look at Lenz's Law.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c2

4. Dec 28, 2007

### Kevinh

Fundamentally all waves can be represented as series of sine waves ( Fourier ). A square wave is no exception and it has its own spectrum. To me the most natural wave is a sine and anything else has been polluted with harmaonics.
I am not sure what you are trying to do, but you may benefit by examining techniques that take you from time domain to frequency domain (or somewhere in between). You can Google FFT (fast fourier transform) and Wavelets to start.

5. Dec 28, 2007

### Staff: Mentor

Just to add a little to ranger's explanation. Once you express your square wave (or whatever waveshape) as a sum of sin and cos waves, you can look at the propagation of those components separately. Depending on the medium (EM waves in air, or sound waves in air, or water waves on a lake, etc.), you will get more or less "dispersion" of the components as they propagate. Dispersion expresses the variation in propagation velocity versus wavelength. A media that is very dispersive will cause a square wave (or a pulse) to get spread out and rounded as it propagates, since the various frequency copmonents that make up the original sharp waveform are moving at different propagation speeds. Check out this wikipedia.org article about the dispersion of water waves for more info:

http://en.wikipedia.org/wiki/Dispersion_(water_waves)

6. Jan 3, 2008

### seang

Can you express a sinusoid as an infinite sum of square waves? I feel that you could, but I don't really have the math skills to prove it.

7. Jan 3, 2008

### ranger

Thats an excellent question!

I haven't managed to get my hands dirty as yet with some math. But by just thinking about it, I feel that you cannot. You have to be able approximate any given continuous segment of the function, but with square waves its impossible. Well its true that we can do this for points, but not for segments. Square waves have jump discontinuities, and thus as we introduce more and more square waves to approx. a segment, we'll only be introducing more discontinuities.

Using a "fourier series", you won't be able to get a pure sinusoidal wave. You can picture the resultant wave as a sine wave with lots of high frequency noise. But I'll play around with this later on and see what comes of it.

Edit: It should also be noted that this really isn't a fourier series, because such a series uses sines and cosines. My apologies for mixing my terms up.

Last edited: Jan 3, 2008
8. Jan 3, 2008

### seang

Yep, that's the catch I think. But, creating a perfect discontinuity out of sinusoids seems just as unlikely at first glance IMO, but Fourier found a way to do it!

I kind of envision a circle displayed on a computer screen, you know? The pixels are square, but if we let the number of pixels go to infinity, would the circle displayed on the screen be perfect?

Also, given that a square wave has its own Fourier series, the question could be restated as, can you make sinusoid from an infinite sum of sinusoids? The answer here seems to be yes.

What would you vary in a square wave to make it nearly a sine wave? I guess the duty cycle and amplitude?

good times on winter break : )

9. Jan 3, 2008

### ranger

Just hold on there. Why do you think pixels are square? Is it because when you zoom into a graphic, you see "squares"? IMHO, this is a naive view of something more abstract. Instead one should think of it as a sample. Sampling is the sense of representing a continuous signal by a discrete signal. In the context of sampling, the "square" model does not shown up at all. The article below should clear some things up:

http://www.cs.princeton.edu/courses/archive/spr06/cos426/papers/smith95b.pdf
Are you taking about a single square wave? I'm not sure what you can vary with a single wave. But if we were fortunate enough to be able to sum up an infinite amount of squares, we would most likely keep the same period but varying the phase and sign of the amplitude to get an approximation of a sinusoidal.

10. Jan 5, 2008

### deakie

you can't use square waves to build a sine because the square waves themselves would have to be a composed of sines anyway and most likely to include the sine you are building.
Better you filter out the sine you need.....or like stated....sampling and smoothing.

in terms of switching, your switch would have to operate much faster than your sine to produce a bunch of squares. Reminds me of the chopper circuit....;)

if you are thinking about transmitting, squares are okay if you start thinking of packet data....but then you have the added complication of reception and mathematics to decipher the components of your packets.....