> On Wed, Nov 16, 2011 at 6:40 AM, Sean Breheny <
spamBeGoneshb7spamBeGonecornell.edu> 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 = 1.
>
>
>> Try this experiment: plot the function
>> v(t)=sin(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.