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Important Discrete Fourier Transform Properties

February 2, 2019 by 3200 Creative

Important Discrete Fourier Transform Properties

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Question 1 of 4

1. Question
If $x[n]$ is a real-valued signal, the DFT $X[k]$ is real valued.
- True
- False
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Question 2 of 4

2. Question
Let $x[n] \longleftarrow DFT;N \longrightarrow X[k]$ . Identify all of the following statements that are true.
- $X[k]$ is purely imaginary
- $X[k]$ has period $N$
- $x[n]$ has period $N$
- $x[n]$ has even symmetry
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Question 3 of 4

3. Question
The DFT of a sum of signals is the sum of the DFTs of the individual signals.
- True
- False
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Question 4 of 4

4. Question
Shifting a signal in time causes what operation on the DFT coefficients of the signal?
- The DFT coefficients are unchanged
- The DFT coefficients are convolved with themselves
- The DFT coefficients are multiplied by a complex sinusoid in the frequency domain
- The DFT coefficients are shifted in frequency
- The imaginary part of the DFT coefficients is set to zero
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Course Lessons

Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform
Important Discrete Fourier Transform Properties
Fast Fourier Transform (FFT) Algorithm
Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform
Circular Convolution Property of the Discrete Fourier Transform
Filtering with the Discrete Fourier Transform
The Discrete Fourier Transform Approximation to the Fourier Transform
The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform
Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range
An Example of Approximating the Fourier Transform with the Discrete Fourier Transform
Jupyter Notebook: Explore the Windowed DFT
The Short-Time Fourier Transform and the Spectrogram
Jupyter Notebook: Explore the Spectrogram
A Matrix Interpretation of the Discrete Fourier Transform
A Matrix Interpretation of the Fast Fourier Transform Algorithm

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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