On Wed, Nov 16, 2011 at 6:40 AM, Sean Breheny wrote: > 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). 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. > 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. Time domain representation. Got it. > 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. Fourier transform can be used to obtain a frequency domain plot. Got it. > 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 Dirac delta function. Looked it up. Got it. , one at +f, the other at -f. This is the link between > 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. > It is only continuous for > non-periodic signals - Could you explain this again? > 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). (According to wikipedia) - I thought that the integral of the delta function =3D 1. > 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) Tried it. This is pretty cool. > What common waveform does that look like? Sinusoidal? > 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) 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 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .