Convolution Codes

Aug 04, 2014

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Convolution Codes. By: Eng. Jalal Al Roumy.

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Convolution Codes

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Convolution Codes By: Eng. Jalal Al Roumy

CHAPTER 3: Cyclic and convolution codes

CHAPTER 3: Cyclic and convolution codes. Cyclic codes are of interest and importance because They posses rich algebraic structure that can be utilized in a variety of ways. They have extremely concise specifications. They can be efficiently implemented using simple shift registers .

1.08k views • 30 slides

Convolution

Convolution. A mathematical operator which computes the pointwise overlap between two functions. Discrete domain: Continuous domain: . Discrete domain. Basic steps Flip (reverse) one of the functions. Shift it along the time axis by one sample.

489 views • 17 slides

Convolution

Convolution. A mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response .

1.21k views • 17 slides

Convolution Fourier Convolution

Convolution Fourier Convolution. Outline  Review linear imaging model  Instrument response function vs Point spread function  Convolution integrals • Fourier Convolution • Reciprocal space and the Modulation transfer function  Optical transfer function  Examples of convolutions

1.07k views • 36 slides

Introducing Convolution

Introducing Convolution. Is an operation between two tables of numbers, usually between an image and weights. Typically, if one table is smaller, it is on right of the operator * [ ] [ ] = ???. Image Weights. *. -1 +1 -2 +2. 0 2

1.45k views • 52 slides

Convolution

Convolution. A convolution operation is a cross-correlation where the filter is flipped both horizontally and vertically before being applied to the image: It is written: Suppose H is a Gaussian or mean kernel. How does convolution differ from cross-correlation?. Continuous filtering.

452 views • 12 slides

Convolution

Convolution. LTI: h(t). LTI: h[n]. g(t). g[n]. g(t)  h(t). g[n]  h[n]. Example: g[n] = u[n] – u[3-n] h[n] =  [n] +  [n-1]. Convolution methods:. Method 1: “running sum” Plot x and h vs. m Flip h over vertical axis to get h[-m] Shift h[-m] to obtain h[n-m]

507 views • 3 slides

Convolution

Basis beeldverwerking (8D040 ) d r. Andrea Fuster Prof.dr . Bart ter Haar Romeny dr. Anna Vilanova Prof.dr.ir . Marcel Breeuwer. Convolution. Contents. Spatial filtering Correlation Convolution Filters: Smoothing filters Sharpening filters Borders. Spatial filtering.

951 views • 49 slides

PARALLELIZED CONVOLUTION

PARALLELIZED CONVOLUTION. Convolution. Convolution is a mathematical operation on two functions A function derived from two given functions by integration that expresses how the shape of one is modified by the other. The Mathematical expression for basic two dimensional convolution is.

324 views • 18 slides

Convolution

Basis beeldverwerking (8D040) dr. Andrea Fuster dr. Anna Vilanova Prof.dr.ir . Marcel Breeuwer. Convolution. Contents. Spatial filtering Correlation Convolution Filters: Smoothing filters Sharpening filters Borders. Spatial filtering.

734 views • 49 slides

Convolution

Convolution. 3.1-3.2. An Integrator Circuit. Motivation. How does an integrator circuit respond to an impulse function ? How does an integrator circuit respond to a ramp input [ tu (t)] ?. Answer: Convolution Integral. * Signifies convolution. h() signifies impulse response.

600 views • 20 slides

Numerical Convolution

Numerical Convolution. EE 327. Numerical Convolution. Numerical evaluation of the convolution integral For difficult-to-solve convolution problems We will focus on the Matlab conv function. Discretizing the Time. Convolution Integral. Discretize the Time. n  sample value.

402 views • 8 slides

Convolution

Convolution. Why?. Image processing Remove noise from images (e.g. poor transmission (from space), measurement (X-Rays)). Edge Detection. e.g. could digitally extract brain for display could check if machined parts are correct. How does it work?. Lets use a grey image for ease

599 views • 19 slides

Convolution Operators

Convolution Operators. Spectral Representation Bandlimited Signals/Systems Inverse Operator Null and Range Spaces Sampling, DFT and FFT Tikhonov Regularization/Wiener Filtering. Convolution Operators. Definition :. FT. Spectral representation of a convolution operator :.

827 views • 26 slides

Convolution

Convolution. A mathematical operator which computes the pointwise overlap between two functions. Discrete domain: Continuous domain:. Discrete domain. Basic steps Flip (reverse) one of the functions. Shift it along the time axis by one sample.

2.85k views • 17 slides

Convolution codes （卷积码）

Chapter 8. Convolution codes （卷积码）. 李莉 . 信息机电学院 . SHNU. Linear codes: 1 infor. bit  1 codeword; (n,k)or [n,k,d] ， k-bit infor.  one n-bit codeword Convolution code: . 1 infor. bit  m codewords ; (n,k,m) k-bit infor.+ m previous infor.bits  1 n-bit codeword

666 views • 29 slides

Convolution

Convolution. 1D and 2D signal processing. Consider the delta function. Time-shift delta. Sample the input (it’s a convolution!). What does sampling do to spectrum?. What is the spectrum?. Fourier Coefficients. CTFT. Euler’s identity. Sine-cos Rep. Harmonic Analysis.

274 views • 15 slides

FFT Convolution

FFT Convolution. Michael Phipps Vallary S. Bhopatkar. Convolution theorem. Convolution theorem for continuous case: h(t) and g(t) are two functions and H(f) and G(f) are their corresponding Fourier Transform, then convolution is defined as

437 views • 16 slides

Convolution

Convolution. Convolution Properties. Commutative: f*g = g*f Associative: (f*g)*h = f*(g*h) Homogeneous : f*(  g)=  f*g Additive (Distributive): f*(g+h)= f*g+f*h Shift-Invariant f*g(x-x0,y-yo)= (f*g) (x-x0,y-yo). The Convolution Theorem. and similarly:. *. Examples.

269 views • 14 slides

Convolution

Convolution. CS474/674 – Prof. Bebis Section 3.4, 4.2. Output Image. Correlation - Review. K x K. Convolution – Review (cont’d). Same as correlation except that the mask is flipped both horizontally and vertically.

363 views • 28 slides

Convolution Operators

Convolution Operators. Convolution. Arguably the most fundamental operation of computer vision It’s a neighborhood operator Similar to the median and outlier processes we discussed last week Utilizes a pattern of weights defined over the neighborhood Also known as A filter A kernel.

503 views • 39 slides

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Convolution Codes

Convolution Codes

Presentation Transcript

CHAPTER 3: Cyclic and convolution codes

Convolution

Convolution

Convolution Fourier Convolution

Introducing Convolution

Convolution

Convolution

Convolution

PARALLELIZED CONVOLUTION

Convolution

Convolution

Numerical Convolution

Convolution

Convolution Operators

Convolution

Convolution codes （ 卷积码）

Convolution

FFT Convolution

Convolution

Convolution

Convolution Operators

Convolution codes （卷积码）