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 Apr19 comment Definition of Sinc function @J.M.: I guess it was really not needed to state both. I could of just stated the one of preference (or of matter here). But I just included for others who may be only familiar with one definition over the other. Apr19 comment Definition of Sinc function @J.M.: Please see here: en.wikipedia.org/wiki/Sinc_function Apr19 comment Definition of Sinc function @J.M.: What do you mean by using one name for two different functions? I'm more so used to the normalized form. Apr19 asked Definition of Sinc function Mar25 comment Integral Transform @Mathlover: where does the $e^t$ go, that's on the outside of the integral on the RHS of the equation? Mar24 comment Integral Transform @Tpofofn: Thanks, I realized that. But I need the function $w(t)$ to determine the output to another system with $w(t)$ being the input. This is why I needed to integrate or use properties to transform $W(f) \leftrightarrow w(t)$. Mar23 comment Integral Transform @Mathlover: Ah hah, I knew that integral looked familiar. I do not have a book handy, but is this a transform pair I believe or property? I just remember seeing it sometime ago, but haven't used it before. Which now makes more sense in terms of what functional constructs that has infinite amplitude, such as the dirac. Thank You! Mar23 comment Integral Transform @Mathlover: I didn't get what you meant by that. It would be in terms of $f$ correct because its indefinite and its whats the independent variable is for that case, right? So would our $w(t) = e^t\int_{-\infty}^{\infty} j\pi f e^{j2\pi ft} df$? Mar23 comment Integral Transform @Mathlover: Exactly is what I get. I had done: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)=\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$, because I know the integral would not converge, but when doing: $\frac{d}{dt}(w(t)e^t)=\frac{d}{dt}(\int_{-\infty}^{\infty} \! \frac{j\pi f}{1+j2\pi f}e^{(j2\pi f+1)t} df)$, it equal to what you have. So, for this last integral equation, this would be what $w(t)$ is? That's pretty interesting, for it to be in terms of a definite integral. Mar23 comment Integral Transform @Mathlover: Thanks. So when doing this, I get for the right hand side before evaluating the limits is: $\frac{e^{t+2 i \pi f t} (2 \pi f t+i)}{4 \pi t^2}$. Now, plugging in limits, the integral will not converge on $[-\infty,\infty]\,$. How do we go from here to fully obtain the inverse of $W(f)$? Mar23 comment Integral Transform @Tpofofn: Thanks, I just realized I did not need to find the inverse to get $w_1(t)$ because it was only asking for the frequency spectrum. But, how would I find the inverse of $W(f)$ to get what $w(t)$ is. Either using the definition which I started, or transform properties. I managed to get this from using the properties but not sure if it is correct: $w(t)= 1/2e^{-t}\frac{\mathrm{d}w}{\mathrm{d}t} u(t)\,$ where $u(t)$ is the unit step function. Mar23 asked Integral Transform Mar22 accepted Computing Coefficients of Complex Form Fourier Series Mar20 awarded Yearling Mar5 asked Computing Coefficients of Complex Form Fourier Series Feb27 comment Nice proofs of $\zeta(4) = \pi^4/90$? I wondering what does the $\zeta$ represent? Is that of any significance or just a variable? Feb18 accepted Sifting out Solutions to Differential Equations Feb18 comment Sifting out Solutions to Differential Equations Hey Julian, This is a really well thought out response and helpful to know for future reference and work/research. Thank You. Feb17 asked Sifting out Solutions to Differential Equations Jan13 accepted Error When Using Mathematica To Solve Differential Equation