Difference between revisions of "Math for Intelligence"
(→Fourier Transform (FT), Fourier Series, and Fourier Analysis) |
|||
| Line 79: | Line 79: | ||
== <span id="Fourier Transform (FT), Fourier Series, and Fourier Analysis"></span>Fourier Transform (FT), Fourier Series, and Fourier Analysis == | == <span id="Fourier Transform (FT), Fourier Series, and Fourier Analysis"></span>Fourier Transform (FT), Fourier Series, and Fourier Analysis == | ||
| + | [http://en.wikipedia.org/wiki/Joseph_Fourier Joseph Fourier] showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Joseph was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect. | ||
| + | |||
| + | * <b>Fourier Transform (FT)</b> decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. [http://en.wikipedia.org/wiki/Fourier_transform Fourier Transform | Wikipedia] | ||
| + | |||
| + | * <b>Fourier Series</b> is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time <i>Fourier transform</i> is an example of Fourier series. For functions on unbounded intervals, the analysis and synthesis analogies are <i>Fourier Transform</i> and inverse transform. [http://en.wikipedia.org/wiki/Fourier_series Fourier Series | Wikipedia] | ||
| + | |||
| + | * <b>Fourier Analysis</b> the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. [http://en.wikipedia.org/wiki/Fourier_analysis Fourier Analysis | Wikipedia] | ||
| + | |||
<youtube>ds0cmAV-Yek</youtube> | <youtube>ds0cmAV-Yek</youtube> | ||
<youtube>r18Gi8lSkfM</youtube> | <youtube>r18Gi8lSkfM</youtube> | ||
| + | <youtube>spUNpyF58BY</youtube> | ||
| + | <youtube>2hfoX51f6sg</youtube> | ||
Revision as of 11:52, 5 October 2019
YouTube search... ...Google search
- Statistics for Intelligence
- Finding Paul Revere
- Causation vs. Correlation
- Dot Product
- Animated Math | Grant Sanderson @ 3blue1brown.com
- Introduction to Matrices and Matrix Arithmetic for Machine Learning | Jason Brownlee
- Essential Math for Data Science: ‘Why’ and ‘How’ | Tirthajyoti Sarkar
- Gentle Dive into Math Behind Convolutional Neural Networks | Piotr Skalski - Towards Data Science
- Varient: Limits
- Google's Crash Course
- Neural Networks and Deep Learning - online book | Michael A. Nielsen
- Brilliant.org
- Convolution vs. Cross-Correlation (Autocorrelation)
- Bloomberg Lectures
- Quantum algorithms
- Fundamentals:
Contents
Getting Started
3blue1brown
Explained
Siraj Raval
Gilbert Strang (MIT) - Linear Algebra
Fourier Transform (FT), Fourier Series, and Fourier Analysis
Joseph Fourier showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Joseph was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect.
- Fourier Transform (FT) decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. Fourier Transform | Wikipedia
- Fourier Series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time Fourier transform is an example of Fourier series. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier Transform and inverse transform. Fourier Series | Wikipedia
- Fourier Analysis the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier Analysis | Wikipedia
