On Wed, Nov 16, 2011 at 2:24 PM, V G wrote: > 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 would be surprised what those kids are capable of (: >> 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. If you "truly" get the idea behind Dirac's work, you are ready to go. http://www.4shared.com/document/Zgg6tWo_/dirac_1926_dissertation.html Relevance to your situation ; there is no monochromatic signals ever because it would require infinite amount of energy. > , 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? If the signal is non-periodic than it can be expressed as sum of different frequency components (cos and sin). Thus FT of the signal will not be continuous consisting of discrete components (each component/spike corresponds to a frequency). >> 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 =A0=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*p= i*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? Break the signal into components and analyze since it's a linear addition (= sum). --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .