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Andrew M
Andrew M
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So I'm trying to get some sample time-series data from pink noise (PSD: $S(w) = 1/f$$S(f) = 1/f$). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

So I'm trying to get some sample time-series data from pink noise (PSD: $S(w) = 1/f$). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

So I'm trying to get some sample time-series data from pink noise (PSD: $S(f) = 1/f$). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

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lennon310
lennon310
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So I'm trying to get some sample time-series data from pink noise (PSD: S(w) = 1/f$S(w) = 1/f$). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

So I'm trying to get some sample time-series data from pink noise (PSD: S(w) = 1/f). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

So I'm trying to get some sample time-series data from pink noise (PSD: $S(w) = 1/f$). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?

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Andrew M
Andrew M
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Deriving Time-Series Data from PSD when the Inverse Fourier Transform doesn't converge

So I'm trying to get some sample time-series data from pink noise (PSD: S(w) = 1/f). However, when I try to evaluate the Inverse Fourier Transform integral

$\int \frac{1}{\omega} e^{j \omega t} dt$

from negative infinity to positive infinity, I get a non-converging integral. I tried a Taylor Expansion, but I'm running into the same issue. Is there some other way around this?