https://github.com/dgcnz/fourier
Final project of Analysis and Design of Algorithms @UTEC, Perú
https://github.com/dgcnz/fourier
analysis-algorithms fourier fourier-transform signal-processing
Last synced: 7 months ago
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Final project of Analysis and Design of Algorithms @UTEC, Perú
- Host: GitHub
- URL: https://github.com/dgcnz/fourier
- Owner: dgcnz
- Created: 2019-05-28T13:03:22.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2020-03-26T04:29:35.000Z (over 5 years ago)
- Last Synced: 2025-01-28T00:17:25.539Z (9 months ago)
- Topics: analysis-algorithms, fourier, fourier-transform, signal-processing
- Language: C++
- Homepage:
- Size: 115 MB
- Stars: 0
- Watchers: 2
- Forks: 1
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# Fourier Transform
## Instructions
```zsh
cd code
# To build image containing OpenCV and other dependencies (only run it one time)
./script/pre_build
# To compile project
./script/build
# To execute project
./script/run
```
## Useful resources
+ [3blue1brown. _But, what is a Fourier Transform?_](https://www.youtube.com/watch?v=spUNpyF58BY)
+ For an intuition of Fourier Transforms (recommended by dgcnz).
+ [Osgood, Brad. _The Fourier Transform and its Applications_](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf)
+ Tremendously comprehensive lecture notes from MIT's Brad Osgood.
+ [Math.StackExchange. _How is the Fourier Transform Linear?_](https://math.stackexchange.com/questions/140788/how-is-the-fourier-transform-linear)
+ For a discussion on what it means to be a linear transform and how can a Fourier Transform be considered one.
+ Spoiler alert: If it satisfies two conditions, namely, additivity (addition) and homogeneity (multiplication by scalar).
+ [Charles Van Loan. _Computational Frameworks for the Fast Fourier Transform_, 1992.](https://dl.acm.org/citation.cfm?id=130635)
+ For understanding of FFT and the mathematics of multidimensional FFTs (recommended by CLRS).
+ [Alan V. Oppenheim and Ronald W. Schafe, with John R. Buck. _Discrete-Time Signal Processing_, 1997.](https://dl.acm.org/citation.cfm?id=1795494)
+ For an introduction to signal processing and handling case when `n` is not power of 2 (recommended by CLRS).
+ [Rafael C. Gonzalez and Richard E. Woods. _Digital Image Processing_, 1992](https://dl.acm.org/citation.cfm?id=573607)
+ For a discussion in multidimensional Fourier Transforms and their use in image processing (recommended by CLRS).
+ [Brilliant.org. _Roots of unity_](https://brilliant.org/wiki/roots-of-unity/)
+ Useful intuition for FFT key concept.
## Literature
```txt
├── dgcnz
│ ├── graphs
│ │ ├── Are There Approximate Fast Fourier Transforms On Graphs? - Magorau - 2016.pdf
│ │ ├── Big Data Analysis with Signal Processing on Graphs - Sandryhaila - 2014.pdf
│ │ └── The Emerging Field of Signal Processing on Graphs - Shuman - 2013.pdf
│ ├── misc
│ │ └── Some Topics in Analysis of Boolean Functions - O'donell - 2008.pdf
│ ├── music
│ │ ├── Applications of Fourier Analysis to Audio Signal Processing: An Investigation of Chord Detection Algorithms - Lensen - 2013.pdf
│ │ ├── Design and Evaluation of a Simple Chord Detection Algorithm - Hausner - 2014 [Thesis].pdf
│ │ └── ON THE MATHEMATICS OF MUSIC: FROM CHORDS TO FOURIER ANALYSIS - Lensen - 2013.pdf
│ ├── theoretical
│ │ ├── Fourier Transforms and the Fast Fourier Transform (FFT) Algorithm - Heckbert - 1995.pdf
│ │ └── Recent Developments in the Sparse Fourier Transform: A compressed Fourier transform for big data - Gilbert - 2014.pdf
│ └── voice
│ └── Mathematical Methods for Voice Transformation - Lilla - 2017.pdf
├── jotarios
│ ├── books
│ │ └── Digital Image Processing for Medical Applications - See at page 232 onwards - 2009.pdf
│ ├── papers
│ │ ├── fft
│ │ │ ├── A Sparse Multi-Dimensional Fast Fourier Transform with Stability to Noise in the Context of Image Processing and Change Detection - 2016.pdf
│ │ │ ├── An Algorithm for the Machine Calculation of Complex Fourier Series - Cooley Tukey - 1965.pdf
│ │ │ ├── Fast Fourier transform using matrix decomposition - 2014.pdf
│ │ │ ├── Reduction of speckle in digital holography by discrete fourier filtering - 2007.pdf
│ │ │ ├── applications
│ │ │ │ ├── Diagnosis of Epilepsy in Patients Based on the Classification of EEG Signals Using Fast Fourier Transform - 2015.pdf
│ │ │ │ ├── Fast Fourier Transform for Feature Extraction And Neural Network for Classification of Electrocardiogram Signals - 2015.pdf
│ │ │ │ └── The Fast Fourier Transform and Its Applications - 1968.pdf
│ │ │ └── parallel-gpu
│ │ │ └── cusFFT: A High-Performance Sparse Fast Fourier Transform Algorithm on GPUs - 2016.pdf
│ │ ├── noise reduction - audio
│ │ │ └── Suppression of Acoustic Noise in Speech Using Spectral Subtraction - 1979.pdf
│ │ └── noise reduction - image
│ │ ├── Fourier Transform based Windowed Adaptive Switching Minimum Filter for Reducing Periodic Noise from Digital Images - 2015.pdf
│ │ └── Noise reduction algorithms using Fibonacci Fourier transforms - 2008.pdf
│ └── parts in books
│ └── Fast Fourier Transform (FFT) on GPUs - Chapter 16 - 2014.pdf
│
│
│
├── martin-carrasco
│ ├── fft
│ ├── An Omega((n log n)R) Lower Bound for Fourier Transform Computation.pdf
│ ├── On Computing the FFT.pdf
| |
│ └── Sparse Fourier Transform in Any Constant Dimension with Nearly-Optimal Sample Complexity in Sublinear Time.pdf
│ └── images
│ ├── An Accurate Nonuniform Fourier Transform for SPRITE Magnetic Resonance Imaging Data.pdf
│ ├── Determining Image Orientation using the Hough and Fourier Transforms.pdf
│ ├── High-quality Motion Deblurring from a Single Image.pdf
│ ├── Image Motion Estimation from Motion Smear - A New Computational Model (1996).pdf
| |
│ └── With J Fast Fourier Transforms and Removing Motion Blur.pdf
│
└── ramirez
├── FrationalFourierTransform.pdf
├── FrationalFourierTransform.pdfNoise removal in speech signal using fractional fourier transform-2017 .pdf
├── HarmonicAnalysus-1978.pdf
└── paper.md
```