Think of it this way: Assume you have a sine wave with a period of 360 uS at 2V p-p. 30 degrees after a 0 crossing, the voltage will be .5V. At 45 degrees=20 it will be .707V, and at 60 degrees it will be .866V. This is the=20 definition of a sin wave. You can break it down further, and say that, for any 2 points (T1 and=20 T2), the voltage at T2 would be V2 =3D sin(T2) * (V1 / sin(T1)) If you have a different value of V2, then you don't have a sin wave,=20 even if it LOOKS like a sin wave. > Try this experiment: plot the function > v(t)=3Dsin(2*pi*t)+(1/3)*sin(2*pi*3*t)+(1/5)*sin(2*pi*5*t)+(1/7)*sin(2*pi= *7*t)....... > (you can try carrying this out to different numbers of terms following > this pattern) > =20 >Tried it. This is pretty cool. > What common waveform does that look like? > =20 >Sinusoidal? You should have gotten something approaching a square wave. You might want to pick up an ARRL Handbook (any year), it should explain=20 it fairly well. Pay particular attention to the 'keying' section. Kerry V G wrote: > On Wed, Nov 16, 2011 at 6:40 AM, Sean Breheny wrote: > =20 >> I can remember having this exact confusion once, too :) >> >> The concept of frequency here is that of a change of coordinates >> transformation - the Fourier Transform (for non-periodic signals) or >> Fourier Series (for periodic ones). >> =20 > > I looked it up. I wish I could study this in depth as the engineering > kids do (I'm in life sci where students don't even know what mmHg is, > much less anything about this kind of mathematics). So apparently "the > Fourier transform is a mathematical operation that decomposes a > function into its constituent frequencies". Got it. > > =20 >> You can fully describe a signal by means of a time-series (i.e. plot >> of voltage versus time) and that is referred to as the time domain >> representation of the signal. >> =20 > > Time domain representation. Got it. > > =20 >> You can also perform a change of coordinates so that you get a voltage >> versus frequency plot. The information is now in a different format >> but still represents the same information. You can convert back and >> forth between the two. >> =20 > > Fourier transform can be used to obtain a frequency domain plot. Got it. > > =20 >> The motivation behind this is that it is often easier to determine the >> effect which a circuit or a communications channel will have on a >> signal or signals by first representing them in the frequency domain, >> then multiplying by the frequency response of the channel/circuit, and >> then converting back to the time domain if needed. >> >> An individual discrete sinusoid of frequency f appears as two Dirac >> delta functions >> =20 > > Dirac delta function. Looked it up. Got it. > > , one at +f, the other at -f. This is the link between > =20 >> the simple definition of frequency as the inverse of the period, and >> this extended definition of frequency where you have a continuous >> function of amplitude versus frequency. >> =20 > > =20 >> It is only continuous for >> non-periodic signals - >> =20 > > Could you explain this again? > > =20 >> periodic ones will be a collection of different >> delta functions with different "weights" (the value you get when >> integrating around the immediate neighborhood of the delta function). >> =20 > > (According to wikipedia) - I thought that the integral of the delta > function =3D 1. > > =20 >> Try this experiment: plot the function >> v(t)=3Dsin(2*pi*t)+(1/3)*sin(2*pi*3*t)+(1/5)*sin(2*pi*5*t)+(1/7)*sin(2*p= i*7*t)....... >> (you can try carrying this out to different numbers of terms following >> this pattern) >> =20 > > Tried it. This is pretty cool. > > =20 >> What common waveform does that look like? >> =20 > > Sinusoidal? > > =20 >> This shows how a sum of >> sinusoids can make other waveforms (or conversely, how general >> waveforms can be converted into a collection of sinusoids - which then >> can be independently analyzed as they pass through a linear system - >> and then summed again) >> =20 > > Okay so signal can be decomposed into sum of signals via a Fourier > transform which can then be used to obtain a frequency domain plot > (spectrum analyzer). > > But I still can't visualize how AM radio has sidebands. I still see > only one pure sinusoidal frequency only of varying amplitude. > > I'm going to open up Mathematica and see if I can plot stuff out. > =20 --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .