Problem 1. Let f(x) = e¬™x and inductively define f2(x) = f * f(x) f3(x) = f * f2(x) = f * f * f(x) %3D %3D fn(x) = f * fn-1(æ) = { ***** f (x). %3D n convolutions Find a simple pre-calculus expression for fn(x). (Hint: use Fourier transforms.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 1.
Let f(x)
and inductively define
= e
f2(x) = f * f(x)
f3(x) = f * f2(x) = f * ƒ * f(x)
fn(x) = f * fn-1(x) = [ * **** f (x).
n convolutions
Find a simple pre-calculus expression for fn(x). (Hint: use Fourier transforms.)
Transcribed Image Text:Problem 1. Let f(x) and inductively define = e f2(x) = f * f(x) f3(x) = f * f2(x) = f * ƒ * f(x) fn(x) = f * fn-1(x) = [ * **** f (x). n convolutions Find a simple pre-calculus expression for fn(x). (Hint: use Fourier transforms.)
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