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Convolution circuits synthesis Perkowski

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FIR-filter like structure b4b3 b2b1 +++ a4000 a4*b4

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Think what you can do in all possible ways with two vectors of items (numbers)? 1. Dot product 2. Convolution (polynomial multiplication) 3. Cartesian Product 4. Kronecker Product 5. Other? Think what you can do in all possible ways with two matrices of items (numbers)?

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Convolution Perhaps the most important operation on data. Not related to operators that operate on items. It is a pattern of moving data and operating on them Although first systolic processors were not for convolution, it is the standard and common object of systolic, cellular and parallel design of algorithms and hardware. Every image processing project such as Hadamard, Fourier, Hough or other transform includes convolution – like circuit/system design in one way or another. This part of design is truly creative.

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I have two vectors A=(a1,a2,a3,a4) and B=(b1,b2,b3,b4) b4b3 b2b1 +++ a400 a4*b4 a3 a3*b4+a4b3

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b4b3 b2b1 +++ a3a40 a4*b4 a2 a3*b4+a4b3 a4*b2+a3*b3+a2*b4

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b4b3 b2b1 +++ a2a3a4 a4*b4 a1 a3*b4+a4b3 a4*b2+a3*b3+a2*b4 a1*b4+a2*b3+a3*b2+a4*b1

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b4b3 b2b1 +++ a1a2a3 a4*b4 0 a3*b4+a4b3 a4*b2+a3*b3+a2*b4 a1*b4+a2*b3+a3*b2+a4*b1 a1*b3+a2*b2+a3*b1

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We insert Dffs to avoid many levels of logic b4b3 b2b1 +++ a4a2a3 a4*b4 a4*b3 a4*b2a4*b1

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b4b3 b2b1 +++ a3a1a2 a4*b4 a4*b3+a3b4 a4*b2+a3b3 a4*b1+a3b2 a3b1

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b4b3 b2b1 +++ a20a1 a4*b4 a4*b3+a3b4 a4*b2+a3b3+a2b4 a4*b1+a3b2+a2b3 a3b1+a2b2 a2b1 The disadvantage of this circuit is broadcasting

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We insert more Dffs to avoid broadcasting b4b3 b2b1 +++ a4a2a3 a4*b4 0 00 000

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b4b3 b2b1 +++ a3a1a2 a4*b4 a3b4 a4b3 0 a400 0 Does not work correctly like this, try something new….

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b4b3 b2b1 a3a1a2 a4*b4 a3b4a4b3 0 a400 0 a2b4 a1b4 a3b3 a2b3 a1b3 00 0 0 a4b2 a3b2 a2b2 a1b2 0 0 0 a4b1 a3b1 a2b1 First sum Second sum

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FIR-filter like structure, assume two delays b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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b4b3 b2b1 +++

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Week 10. Chapter 9 1.Convolution sum & integral 1.Kronecker delta and Dirac delta 2.Impulse response and convolution 2.Impulse response & frequency response.

Week 10. Chapter 9 1.Convolution sum & integral 1.Kronecker delta and Dirac delta 2.Impulse response and convolution 2.Impulse response & frequency response.

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