Re: question about integration of spectrum

On 28 Sep, 19:25, "mcyoung" <diaoyip...@xxxxxxx> wrote:
hi all,
i want to get a integral spectrum, i have two choices:

1:do integration to time domain then do fft to get the spectrum
2:do integration to fft spectrum directly

i do not know which is better, can anyone give me some advices.

and if we do integration to a spectrum ( multiply 1/(j*w) ), how can we
deal with 0 Hz?

So you want to integarte a function which is represented by
its spectrum?

The time-domain and frequency-domain approaches are *formally*
equaivalent, but the technicalities are different.

In time domain, the integral is easy:

X[0] = x[0]
X[n] = X[n-1]+x[0]

In frequency domain you need to handle the DC component
specifically, as the integral of a DC component is a ramp
function. Due to technicalities about the definition of the
Fourier Transform (the infinite integral must be bounded
for the FT to exist) it is not at all obvious if (or how)
the DC component should be handled.

So my advice is that you avoid a lot of trouble by doing
your integration in time domain.

Rune
.

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