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Frequency Domain Descriptions for Discrete Time Linear Time Invariant Systems

February 2, 2019 by 3200 Creative

Frequency Domain Descriptions for Discrete Time Linear Time Invariant Systems

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Question 1 of 3

1. Question
The phase response of a system shifts the phase of an input sinusoid.
- True
- False
Correct

Incorrect
Question 2 of 3

2. Question
The frequency response of a system is $H(e^{j\omega}) = 3/(1+0.5e^{-j\omega})$ . Identify the impulse response.
- $h[n] = 0.5(3)^n u[n]$
- $h[n] = -0.5(3)^n u[n]$
- $h[n] = -3(-0.5)^n u[n]$
- $h[n] = 3(-0.5)^n u[n]$
- $h[n] = 1.5(-1)^n u[n]$
Correct

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Question 3 of 3

3. Question
A system is described by the difference equation $y[n]-0.9 y[n-2] = 3x[n] + x[n-1]$ . Find the frequency response.
- $H(e^{j\omega})= \frac{1 -0.9e^{-j2\omega} }{3+e^{-j\omega}}$
- $H(e^{j\omega})= \frac{3+e^{-j\omega}}{1 -0.9e^{-j2\omega} }$
- $H(e^{j\omega})= \frac{1+3e^{-j\omega}}{-0.9 +e^{-j2\omega} }$
- $H(e^{j\omega})= \frac{-0.9+e^{-j2\omega} }{1+3e^{-j\omega}}$
- $H(e^{j\omega})= \left(3+e^{-j\omega}\right)\left(1 -0.9e^{-j2\omega} \right)$
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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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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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