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The Discrete Time Fourier Transform

February 2, 2019 by 3200 Creative

The Discrete Time Fourier Transform

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Question 1 of 4

1. Question
The primary role of the discrete-time Fourier transform (DTFT) in signal processing is computation of frequency response and the spectral content of signals.
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- False
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Question 2 of 4

2. Question
A discrete-time signal is defined as $x[n] = \left\{ \begin{array}{cc} 1, & |n| \le 10\\ 0,& |n| > 10 \end{array} \right.$ . Which is the correct DTFT? (Hint: use the result derived in the video.)
- $X(e^{j\omega}) = \frac{1}{1-10e^{-j\omega}}$
- $X(e^{j\omega}) = 21$
- $X(e^{j\omega}) = \frac{\sin(21\omega/2)}{\sin(\omega/2)}$
- $X(e^{j\omega}) = \frac{\sin(11\omega/2)}{\sin(\omega/2)}$
- $X(e^{j\omega}) = 10\delta(\omega)$
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Question 3 of 4

3. Question
The DTFT can be used to analyze the interaction between a discrete-time system and a discrete-time periodic input signal.
- True
- False
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Question 4 of 4

4. Question
The DTFT of a signal is $X(e^{j\omega}) = \frac{1}{1+0.5 e^{-j\omega}}$ . Which is the correct time domain signal? (Hint: use the result derived in the video.)
- $x[n] = 0.5 u[n]$
- $x[n] = (-0.5)^n u[n]$
- $x[n] = (0.5)^n u[n]$
- $x[n] = \frac{\sin(0.5 n)}{\pi n}$
- $x[n] = 0.5 \delta[n]$
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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

Courses

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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