[sdiy] Dirac deltas

[Aaron Lanterman]

>> But a sudden dc shift has a broadband frequency spectrum!
>
> A single sudden DC shift contains no frequencies. It is just an 
> integrated dirac delta, but if you analyse it on the jw axis you have no 
> energy, but you will experience a temporary rise before it fades out.
>
> It is when you have repeating occurances that we can talk about 
> frequencies.

Your ear won't perceive it as such, but you _can_ certainly talk about 
frequencies associated with a single DC shift.

A dirac delta x(t) = delta(t) has a flat spectrum X(j omega) = 1. Its 
integral, a unit step function x(t) = u(t), would have a spectrum of X(j 
omega) = 1/(j omega). (Uhm, sort of: u(t) doesn't have a finite absolute 
integral, so it doesn't technically have a Fourier transform per se - 
notice the spectrum blows up as omega -> infinity. But it works 
operationally).

But your brain doesn't really perceive it as a sum of sine waves... it's 
just a mathematical trick that you can do that.

- Aaron

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