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The Fast Fourier Transform Algorithm

February 2, 2019 by 3200 Creative

The Fast Fourier Transform Algorithm

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Question 1 of 3

1. Question
The term “fast Fourier transform” refers to
- A form of the Fourier transform that was first used in fuel control systems for race cars and jet airplanes
- A numerically efficient procedure for computing the DFT coefficients
- A numerically efficient procedure for computing the FT
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Question 2 of 3

2. Question
The number of numerical operations (additions and multiplies) required by the FFT algorithm to compute all $N$ DFT coefficients for a length- $N$ signal is proportional to
- $N^2$
- $N \log(2)$
- $N \log_2 (N)$
- $N^3$
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Question 3 of 3

3. Question
Which of the following properties or techniques are used to obtain the decimation-in-time FFT algorithm? Select all that apply. Let $W_N = e^{j2\pi/N}$ .
- The DFT of a longer signal is built using DFTs of smaller signals
- $W_N^2 = W_{N/2}$
- $W_N^{k(2r+1)} = W_N^k W_N^{2r}$
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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

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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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