Discrete transforms

Discrete transform

In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency. Many common integral transforms used in signal processing have their discrete counterparts. For example, for the Fourier transform the counterpart is the discrete Fourier transform. In addition to spectral analysis of signals, discrete transforms play important role in data compression, signal detection, digital filtering and correlation analysis. The discrete cosine transform (DCT) is the most widely used transform coding compression algorithm in digital media, followed by the discrete wavelet transform (DWT). Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete-time Fourier transform and the Z-transform, from discrete time to continuous frequency, and the Fourier series, from continuous time to discrete frequency, are outside the class of discrete transforms. Classical signal processing deals with one-dimensional discrete transforms. Other application areas, such as image processing, computer vision, high-definition television, visual telephony, etc. make use of two-dimensional and in general, multidimensional discrete transforms. (Wikipedia).

Video thumbnail

The Two-Dimensional Discrete Fourier Transform

The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequen

From playlist Fourier

Video thumbnail

Introduction to the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor

From playlist The z-Transform

Video thumbnail

The Discrete Fourier Transform

This video provides a basic introduction to the very widely used and important discrete Fourier transform (DFT). The DFT describes discrete-time signals as a weighted sum of complex sinusoid building blocks and is used in applications such as GPS, MP3, JPEG, and WiFi.

From playlist Fourier

Video thumbnail

Fourier Transforms: Discrete Fourier Transform, Part 3

Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 3 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

Video thumbnail

Discrete Fourier Transform - Example

We do a very simple example of a Discrete Fourier Transform by hand, just to get a feel for it. We quickly realize that using a computer for this is a good idea...

From playlist Mathematical Physics II Uploads

Video thumbnail

Discrete Fourier Transform - Introduction

An introduction to the Discrete Fourier Transform (DFT) and its interpretation.

From playlist Mathematical Physics II Uploads

Video thumbnail

The Discrete Fourier Transform: Sampling the DTFT

http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files.

From playlist Fourier

Video thumbnail

Fourier Transforms: Fast Fourier Transform, Part 1

Data Science for Biologists Fourier Transforms: Fast Fourier Transform Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

Video thumbnail

The Discrete Fourier Transform (DFT)

This video introduces the Discrete Fourier Transform (DFT), which is how to numerically compute the Fourier Transform on a computer. The DFT, along with its fast FFT implementation, is one of the most important algorithms of all time. Book Website: http://databookuw.com Book PDF: http

From playlist Fourier

Video thumbnail

Lec 8 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 8: The discrete Fourier series Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

Video thumbnail

Lec 9 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 9: The discrete Fourier transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

Video thumbnail

Lecture 19 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood demonstrates aliasing by showing the class what happens when you under sample music. The Fourier transform is a tool for solving physical probl

From playlist Lecture Collection | The Fourier Transforms and Its Applications

Video thumbnail

Lecture 21 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the properties of discrete Fourier transforms. The Fourier transform is a tool for solving physical problems. In this

From playlist Lecture Collection | The Fourier Transforms and Its Applications

Video thumbnail

Lecture 20 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on the Discrete Fourier Transform. The Fourier transform is a tool for solving physical problems. In this course the emph

From playlist Lecture Collection | The Fourier Transforms and Its Applications

Video thumbnail

Aliasing and the Sampling Theorem Simplified

http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. A presentation of aliasing, the sampling theorem, and the Fourier transform representation of a sampled s

From playlist Sampling and Reconstruction of Signals

Video thumbnail

Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters | MIT RES.6.007

Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6.007 Signals and Systems, 1987

Video thumbnail

Lec 18 | MIT RES.6-008 Digital Signal Processing, 1975

Lecture 18: Computation of the discrete Fourier transform, part 1 Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES.6-008 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-008 Digital Signal Processing, 1975

Video thumbnail

Lecture 11, Discrete-Time Fourier Transform | MIT RES.6.007 Signals and Systems, Spring 2011

Lecture 11, Discrete-Time Fourier Transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6.007 Signals and Systems, 1987

Video thumbnail

The Fourier Transform and Derivatives

This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow

From playlist Fourier

Related pages

Detection theory | Discrete wavelet transform | Signal processing | Z-transform | Correlation | Fourier transform | Integral transform | Discrete-time Fourier transform | Discrete cosine transform | Fourier series | Digital filter | Discrete Fourier transform