ECE 485 Lesson 1

# ECE 485 Lesson 1 - ECE 485 Advanced Engineering Mathematics...

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ECE 485 Advanced Engineering Mathematics Lesson 1 Matrix Representation of Digital Filters Inner Product Matrix Multiplication

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2 Digital Filter Digital Filter h(n) δ (n) h(n) ( 29 = = 0 for 0 0 for 1 n n n δ Unit impulse sequence or unit sample Unit impulse response Unit sample response
3 FIR Digital Filters ( 29 ( 29 ( 29 ( 29 for 0 1 0 elsewhere for 0 1 0 elsewhere h x h n n N h n x n n N x n h - = - =

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4 Response of Digital Filter to x(n) ( 29 ( 29 1 0 ( ) 0,1,2, , 1 1 x N k y y x h y n h n k x k n N N N N - = = - = - = + - K
5 Special Case N h =3 and N x =2 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 3 1 4 0 0 0 1 1 0 0 1 2 2 0 1 1 3 2 1 y x h N N N y h x y h x h x y h x h x y h x = + - = + - = = = + = + =

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6 Inner or Dot Product ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 y h x h x x h h x x h h h x h x x y = + = = = + = h x h x h x
7 The Output Samples ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 1 1 2 2 3 3 0 0 0 1 0 1 2 1 2 0 2 3 h y h h y h h y h y = = = = = = = = h h x h

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