Question

21. Find the Fourier transform of $f(x) = e^{-x^2/(2\sigma^2)}$. Hint: Complete the square in the \\ x terms in the exponent and make the change of variable $y = x + \sigma^2 i\alpha$. Use tables \\ or computer to evaluate the definite integral.

          21. Find the Fourier transform of $f(x) = e^{-x^2/(2\sigma^2)}$. Hint: Complete the square in the \\
x terms in the exponent and make the change of variable $y = x + \sigma^2 i\alpha$. Use tables \\
or computer to evaluate the definite integral.

21. Find the Fourier transform of f(x) = e^-x^2/(2σ^2). Hint: Complete the square in the

x terms in the exponent and make the change of variable y = x + σ^2 iα. Use tables

or computer to evaluate the definite integral.

Added by Joseph V.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Umar Sohail Qureshi

Step 1

You mentioned terms in the exponent, so I assume you have an integral of the form: ∫ e^(f(x)) dx Step 2: Make the change of variable Next, we need to make the change of variable y = f(x). In this case, you mentioned y = +oia. So, we substitute y = +oia into the Show more…

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Please do it step by step. 21. Terms in the exponent and make the change of variable y=+oia. Use tables or a computer to evaluate the definite integral.