Is it possible to split a square wave into its various harmonic components.?

Question

I know that by combining harmonic sinusoids together we can get a square wave.But i want to know whether we can split a square wave into its harmonic components.Its hard for me to believe a square wave(Lets say its being produced by a Battery Switched On & Off continuously) will contain sine waves.

Answer 1

It is actually IMPOSSIBLE to make a truely square wave.

You cannot instantly change the magnitude of a current in a circuit if there is any inductance present.

You cannot ....instantly change voltage if..capacitance...

All real-world circuits contain non-zero amounts of both inductance and capacitance. So when you think you have a square wave, you really have a very-rapid rate of rise (but non-infinite), a bit of 'ringing' (i.e. wiggling) where it levels off, etc

Even if you open a switch, there's a finite amount of time where the current is dropping, with a little bit 'jumping' the microscopic opening in the switch in the moment just after it opened.


To answer your actual question, if you run a square ('near-square') wave through a good low-pass filter (not enough room to describe, so Google it), you'll see some of the sinusoidal components. A good meter can describe the frequency components (Fourier transform)

Answer 2

It really does. It's called a Fourier series. You can only truly achieve the square wave by using an infinite series of sine and cosine functions, but you can get a pretty good approximation for most simple geometric patterns (square, sawtooth) by using the first four or five harmonics.

Answer 3

this could (or will possibly not) help. (permit ? be the sum over i = a million to 9) If ?x[i] = 9s, then (a million) ?(2s - x[i]) =?x[i] and (2) ?(x[i])² = ?(2s - x[i])² EDIT In different words, in case you come across a collection {a[i]} of 9 integers whose sum is 9s and whose sum of squares is 20049, then the sum of squares of the 9 integers {2s - a[i]} is likewise 20049. i don't understand, regardless of the undeniable fact that, if this form of sum exist. EDIT. ok now i understand. v = (-12, -eleven, 4, 7, 17, 50, sixty 3, eighty, eighty one) has a sum of 9*31 and a ssq of 20049 So s = 31. w = 2s - v = (seventy 4, seventy 3, fifty 8, fifty 5, 40 5,12, -a million, -18, -19) has a sum of 9*31 and a ssq of 20049 for this reason, it does not help through fact the two sums of squares have 12^2 in easy. yet, it would nonetheless be useful in different situations. EDIT. specific. This phenomenon happens a lot in magic squares. E.G. 8 3 4 a million 5 9 6 7 2 observe that 8²+3²+4² = 6²+7²+2² and eight²+a million²+6² = 4²+9²+2² there is no assure regardless of the undeniable fact that that this technique will produce thoroughly diverse numbers nor that it will produce numbers between a million and eighty one. greater generally, you need to to think of roughly what ameliorations of an integer vector produce yet another integer vector of an identical length. Checking this concept out with V's answer, I see that it is not useful.

Answer 4

It does and it doesn't. If you use a finite number of frequencies then it won't be exactly a square wave; if you use enough it will look like it though. Any periodic signal can be decomposed in terms of its Fourier Series, its just another way to write the function.

Answer 5

Yes it is possible.

You would have to use a separate band-pass filter for each of the fundamental and the first few of its odd harmonics and present the square wave to each one in turn.

(Remember than a square wave is composed of only odd harmonics and their amplitude is inversely proportional to their order; i.e. 3rd harmonic one 3rd of the fundamental's amplitude, 5th harmonic one 5th of the fundamental etc.)

Answer 6

Yes it does and lots of them. That is what a Fourier analysis will show. It is routine.