'Circular convolution' presentation slideshows

Lecture 2

Lecture 2. Variational Methods for Image Restoration. Digital Images. Digital image comes from a continuous world (continuum). Common pixel representations are unsigned bytes (0 to 255) and floating point. Image can be vector- or manifold- valued

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Outline of chapter seven

Outline of chapter seven. Discrete-Time Fourier Transform Discrete Fourier Transform Properties of the DFT System Analysis via the DTFT and DFT FFT Algorithm Applications of the FFT Algorithm. Discrete-Time Fourier Transform (DTFT) ???????????.

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Fast Fourier Transform

Fast Fourier Transform. A bunch of smart people. Outline (hopefully). Finite discrete signals Linear shift-invariant filters Impulse responses Circular convolutions Discrete Fourier Transform The Fast Fourier Transform. Continuous signals. Finite signals.

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Chapter 8. The Discrete Fourier Transform

Chapter 8. The Discrete Fourier Transform. 8.1 Laplace, z-, and Fourier Transforms 8.2 Fourier Transform 8.3 Fourier Series 8.4 Discrete Fourier Transform (DFT) 8.5 Properties of DFS/DFT 8.6 DFT and z-Transform 8.7 Linear Convolution vs. Circular Convolution

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Chapter 8. The Discrete Fourier Transform

Chapter 8. The Discrete Fourier Transform. 8.1 Laplace, z-, and Fourier Transforms 8.2 Fourier Transform 8.3 Fourier Series 8.4 Discrete Fourier Transform (DFT) 8.5 Properties of DFS/DFT 8.6 DFT and z-Transform 8.7 Linear Convolution vs. Circular Convolution

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Lecture 6 : DFT

Lecture 6 : DFT. Xiliang Luo 2014/10. Periodic Sequence. Discrete Fourier Series. For a sequence with period N, we only need N DFS coefs. Discrete Fourier Series. DFS. Synthesis. Analysis. Example. DFS of periodic impulse. DFS Properties. Linearity:. Shift:. DFS Properties.

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EEE-752 Emerging Wireless Networks OFDM

EEE-752 Emerging Wireless Networks OFDM. Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan. Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 1. OFDM. FDM

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Block Convolution: overlap-save method

CIRCULAR CONVOLUTION. LINEAR CONVOLUTION + ALIASING. Block Convolution: overlap-save method. Input Signal x [ n ] : arbitrary length Impulse response of the filter h [ n ] : lenght P Block Size: N ? we take N samples of x [ n ]

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Block Convolution: overlap-save method

CIRCULAR CONVOLUTION. LINEAR CONVOLUTION + ALIASING. Block Convolution: overlap-save method. Input Signal x [ n ] : arbitrary length Impulse response of the filter h [ n ] : lenght P Block Size: N ? we take N samples of x [ n ]

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CSC2535: Computation in Neural Networks Lecture 12: Representing things with neurons

CSC2535: Computation in Neural Networks Lecture 12: Representing things with neurons. Geoffrey Hinton. Localist representations. The simplest way to represent things with neural networks is to dedicate one neuron to each thing. Easy to understand. Easy to code by hand

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Fourier Transform of the Shah Function

Fourier Transform of the Shah Function. The Sampling Theorem. Discrete Fourier Transform. Insight of Discrete Fourier Transform. Formula of Discrete Fourier Transform. Zero-Padding of DFT. Circular Convolution in the Discrete Case. Convolution Theorem in the Discrete Case.

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Digital Image Processing Lecture 8: Fourier Transform

Digital Image Processing Lecture 8: Fourier Transform. Prof. Charlene Tsai. Introduction. The Fourier Transform is generally used to decompose a signal into various sinusoidal components.

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Lecture 3

Lecture 3. Linear filtering based on the DFT Advanced Digital Signal Processing Dr Dennis Deng Department of Electronic Engineering, La Trobe University 1998,1999. Contents. Linear filter and circular convolution Overlap and save method Overlap and add method Self test exercises.

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DFT properties

DFT properties. Note: it is important to ensure that the DFTs are the same length If x1(n) and x2(n) have different lengths, the shorter sequence must be padded with zeros in order to make it the same length as the longer sequence . . Circular shift . Circular shift of a Sequence

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Wavelet Based Image Coding

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APPLICATION of the DFT: Convolution of Finite Sequences .

zero when . APPLICATION of the DFT: Convolution of Finite Sequences . In filtering applications we need to implemenent a linear convolution between the input signal and the impulse response of the filter. zero pad. zero pad.

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We have the FT pairs (the relationship is symmetric)

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We have the FT pairs (the relationship is symmetric)

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