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Convolution circuits synthesis

Convolution circuits synthesis. Perkowski. FIR-filter like structure. a4. 0. 0. 0. b2. b1. b4. b3. +. +. +. a4*b4. 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

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Convolution circuits synthesis

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  1. Convolution circuits synthesis Perkowski

  2. FIR-filter like structure a4 0 0 0 b2 b1 b4 b3 + + + a4*b4

  3. 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)?

  4. 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.

  5. I have two vectors A=(a1,a2,a3,a4) and B=(b1,b2,b3,b4) a3 a4 0 0 b2 b1 b4 b3 + + + a4*b4 a3*b4+a4b3

  6. a2 a3 a4 0 b2 b1 b4 b3 + + + a4*b4 a3*b4+a4b3 a4*b2+a3*b3+a2*b4

  7. a1 a2 a3 a4 b2 b1 b4 b3 + + + a4*b4 a3*b4+a4b3 a4*b2+a3*b3+a2*b4 a1*b4+a2*b3+a3*b2+a4*b1

  8. 0 a1 a2 a3 b2 b1 b4 b3 + + + a4*b4 a3*b4+a4b3 a4*b2+a3*b3+a2*b4 a1*b4+a2*b3+a3*b2+a4*b1 a1*b3+a2*b2+a3*b1

  9. We insert Dffs to avoid many levels of logic a2 a3 a4 b2 b1 b4 b3 + + + a4*b4 a4*b3 a4*b2 a4*b1

  10. a1 a2 a3 b2 b1 b4 b3 + + + a4*b4 a4*b3+a3b4 a4*b2+a3b3 a3b1 a4*b1+a3b2

  11. 0 a1 a2 b2 b1 b4 b3 + + + a4*b4 a4*b3+a3b4 a4*b2+a3b3+a2b4 a4*b1+a3b2+a2b3 a2b1 a3b1+a2b2 The disadvantage of this circuit is broadcasting

  12. We insert more Dffs to avoid broadcasting a2 a3 a4 0 0 0 b2 b1 b4 b3 + + + a4*b4 0 0 0

  13. a1 a2 a3 a4 0 0 b2 b1 b4 b3 + + + a4*b4 a3b4 a4b3 0 0 Does not work correctly like this, try something new….

  14. a1 a2 a3 a4 0 0 b2 b1 b4 b3 0 0 a1b2 a2b1 0 a1b3 a2b2 a3b1 a1b4 a2b3 a3b2 a4b1 a2b4 a3b3 a4b2 0 a3b4 a4b3 0 0 Second sum a4*b4 0 0 0 First sum

  15. FIR-filter like structure, assume two delays b2 b1 b4 b3 + + +

  16. b2 b1 b4 b3 + + +

  17. b2 b1 b4 b3 + + +

  18. b2 b1 b4 b3 + + +

  19. b2 b1 b4 b3 + + +

  20. b2 b1 b4 b3 + + +

  21. b2 b1 b4 b3 + + +

  22. b2 b1 b4 b3 + + +

  23. b2 b1 b4 b3 + + +

  24. b2 b1 b4 b3 + + +

  25. b2 b1 b4 b3 + + +

  26. b2 b1 b4 b3 + + +

  27. b2 b1 b4 b3 + + +

  28. b2 b1 b4 b3 + + +

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