I am doing a Fourier Transform for the function $f(t)=(1/9)^t\cdot \text{UnitStep}(t+9)$. $$\int_{-9}^{+\infty} (1/9)^t*e^{-j\Omega t}\, dt$$ but I don't know how to continue.
2026-04-13 21:15:50.1776114950
Fourier Transform of $(1/9)^t$?
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Using the fact that $$\left(\frac{1}{9}\right)^t = e^{t\cdot\ln\left(\frac19\right)}=e^{-t\ln 9}$$ helps you transform the expression into $$\int_{-9}^{+\infty} e^{-t(\ln 9+j\Omega)}dt$$ which should help you.