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The Fourier Transform

February 2, 2019 by 3200 Creative

The Fourier Transform

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Question 1 of 5

1. Question
The primary role of the Fourier transform in signal processing is computation of frequency response and the spectral content of signals.
- True
- False
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Question 2 of 5

2. Question
A signal is defined as $x(t) = \frac{\sin(2t)}{\pi t}$ . Which is the correct Fourier transform? (Hint: use the result derived in the video.)
- $X(\Omega) = \left\{ \begin{array}{cc} 1, & |\Omega| < 2\\ 0,& |\Omega| > 2 \end{array} \right.$
- $X(\Omega) = \left\{ \begin{array}{cc} 2, & |\Omega| < 1\\ 0,& |\Omega| > 1 \end{array} \right.$
- $X(\Omega) = \frac{2\sin(2\Omega)}{\Omega}$
- $X(\Omega) = \frac{1}{2+j\Omega}$
- $X(\Omega) = 2\delta(\Omega)$
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Question 3 of 5

3. Question
The Fourier transform of a signal is $X(\Omega) = \frac{1}{4 +j\Omega}$ . Which is the correct time-domain signal? (Hint: use the result derived in the video.)
- $x(t) = 4$
- $x(t) = 4\sin(t)/(\pi t)$
- $x(t) = 4e^{-t}u(t)$
- $x(t) = 4 \delta(t)$
- $x(t) = e^{-4t}u(t)$
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Question 4 of 5

4. Question
Which of the following signals is likely to have the broadest Fourier transform, that is, whose Fourier transform spans the broadest range of frequencies.
- $x(t) = 1$
- $x(t) = 5\sin(t)/(\pi t)$
- $x(t) = 3e^{-t}u(t)$
- $x(t) = 3e^{-100t}u(t)$
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Question 5 of 5

5. Question
The Fourier transform exists for any possible signal.
- True
- False
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Course Lessons

The Fourier Series: Continuous-Time Periodic Signals
Square Wave Fourier Series and the Sinc Function
Fourier Series Properties
The Fourier Transform: Linking Time and Frequency Domains
Properties of the Fourier Transform
The Discrete-Time Fourier Transform
Discrete-Time Fourier Transform Properties
Fourier Transforms and Discrete-Time Fourier Transforms for Periodic Signals
Frequency-Domain Descriptions for Continuous-Time Linear Time-Invariant Systems
Frequency-Domain Descriptions for Discrete-Time Linear Time-Invariant Systems
Two-Dimensional Signal Processing: Continuous Space

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Foundations
Time Domain LTI Systems
Fourier Series and Transforms
Sampling and Reconstruction
The DFT and Applications
The Z-Transform
Intro to Filter Design
IIR Filter Design
FIR Filter Design
Random Signal Characterization
Basis Representations of Signals
Estimation of Power Spectra and Coherence
Introduction to Signal Estimation and Detection Theory
MMSE Filtering and Least-Squares Problems

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