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# Lesson%20170 - Lesson17 Challenge16...

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Lesson 17 Lesson 17 Challenge 16 Lesson 17:  z-transform (Introduction) Challenge 17

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Lesson 17 Challenge 16 An 51 st  order MA filter is presented with a cosine wave at frequency  ω   What is the smallest positive baseband frequency that will result in a +90 °   output signal phase shift?
Lesson 17 Challenge 16 The first occurrence of a +90 °  phase shift corresponds to an unwrapped -270 °   or 3 π /2 radian phase shift.  The phase response of the filter is  H(e j ω ) = - 25  ω  = 3 π /2, or  ω  = 3 π /50 which corresponds to f=3f s /100. - π /25 π /25 2 π /25 ... =-25 90 ° f=1/50 f=1/25 -270 °

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Lesson 17 Z-Transform The author’s provide an ad-hoc presentation of z-transforms.
Lesson 17 Z-Transform Given The z-transform of x[n] is  defined  to be: The z-operator represents a positional delay: z -1  = one clock delay; z -K  = K clock delays  [ ] [ ] k n k x n x K N k - = = δ 0 ] [ ( 29 [ ] k N k z k x z X - = = 0

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Lesson 17 Z-Transform Example Suppose a discrete-time signal has a sampled response: x[k]={1, 2, 3, 4, 3, 2, 1} The z-transform of the signal is: X(z) = 1z -0  + 2z -1  +3z -2  +4z -3  +3z -4  +2z -5  +1z -6
Lesson 17 Z-Transform Example , 0 all for 1 ] [ ] [ . 1 1 = = k k u k x 1 0 0 1 2 3 4 5 6 7 x 1 [ k ] =u [ k ] The  z -transform of the step function  x 1 [ k

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Lesson%20170 - Lesson17 Challenge16...

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