
#1
Jan2713, 10:29 AM

P: 3

This is not a homework problem, but a problem in the textbook that is not required. I am doing this to get a handle on the topic.
I am evaluating a Fourier transform, without tables, and need to evaluate this integral: [tex] \int e^{t} * sin(2 \pi f_c t) * e^{j2 \pi ft} dt [/tex] I have tried two methods: 1) integration by parts, and 2) integration after expressing the sine function as a complex exponentials. I get stuck in both cases. The asterisks are there to assist with clarity of spacing. Thanks for any help you can provide, J 



#2
Jan2713, 04:06 PM

Sci Advisor
P: 5,941

Use Euler formula to get exp(t)*trig function. This is a standard integral (find in table).
Trig function: sin(at), integral = a/(1 + a^{2}) cos(at), integral = 1/(1 + a^{2}) (a > 0 for both) 



#3
Jan2713, 06:49 PM

P: 3

Thanks, I did try Euler's formula but then worked the integral out manually (attempted to...)
So this integral I would find in the table exclusively, and never try without a table? The way the drill is stated in the book (not a homework problem.), I wonder if I am to work it out without a table. Thanks, J 



#4
Jan2813, 02:32 PM

Sci Advisor
P: 5,941

Help with integral
You can integrate by parts twice to get an equation involving the original integral.
I(exp(t)cos(at)) = 1 + aI(exp(t)sin(at)) = 1  a^{2}I(exp(t)cos(at)) Similarly for sin(at) integral. 



#5
Jan2813, 04:22 PM

P: 3

Thank you



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