The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above definition, find the Fourier transform F(w) of the following function: f(t) = e=t + (t – 1)e-2t Ost<∞ b) Write down expressions for the modulus and the phase of F(@). c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
Problem 91E
icon
Related questions
Question
The Fourier transform of a function f(t) is defined by
00
F(@) =
f(t)e-jutdt
-0-
a) Using the above definition, find the Fourier transform F(w) of the following function:
f(t) = e-t + (t – 1)e-2t
Ost<∞
b) Write down expressions for the modulus and the phase of F(@).
c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.
Transcribed Image Text:The Fourier transform of a function f(t) is defined by 00 F(@) = f(t)e-jutdt -0- a) Using the above definition, find the Fourier transform F(w) of the following function: f(t) = e-t + (t – 1)e-2t Ost<∞ b) Write down expressions for the modulus and the phase of F(@). c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Laplace Transformation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning