Assume a digital signal x[n] = 48[n] – 8[n − 2] is input into a filter system that can be described as: 4y[n] = b × y[n − 1] + y[n − 2] + x[n] + a × x[n − 1] − x[n − 2] Where a and b are tuneable coefficients used to change the design of the system. - - a. Find the transfer function of this filter system (keep a and b in the expression) b. To complete the design so the filter has two poles located at ±0.5 and two zeros at -1 ± √√2, what vales of a and b should be chosen?
Assume a digital signal x[n] = 48[n] – 8[n − 2] is input into a filter system that can be described as: 4y[n] = b × y[n − 1] + y[n − 2] + x[n] + a × x[n − 1] − x[n − 2] Where a and b are tuneable coefficients used to change the design of the system. - - a. Find the transfer function of this filter system (keep a and b in the expression) b. To complete the design so the filter has two poles located at ±0.5 and two zeros at -1 ± √√2, what vales of a and b should be chosen?
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![Assume a digital signal x[n] = 48[n] − 8[n − 2] is input into a filter system that can be
described as:
4y[n] = b × y[n − 1] + y[n − 2] + x[n] + a × x[n − 1] − x[n − 2]
Where a and b are tuneable coefficients used to change the design of the system.
a.
Find the transfer function of this filter system (keep a and b in the expression)
b. To complete the design so the filter has two poles located at ±0.5 and two zeros at
-1 ± √2, what vales of a and b should be chosen?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8dc8d95-1584-43f6-b330-b68de5a36493%2Fa4848f6f-22d1-46ce-90d5-6cdc54578f67%2F2nzw9uo_processed.png&w=3840&q=75)
Transcribed Image Text:Assume a digital signal x[n] = 48[n] − 8[n − 2] is input into a filter system that can be
described as:
4y[n] = b × y[n − 1] + y[n − 2] + x[n] + a × x[n − 1] − x[n − 2]
Where a and b are tuneable coefficients used to change the design of the system.
a.
Find the transfer function of this filter system (keep a and b in the expression)
b. To complete the design so the filter has two poles located at ±0.5 and two zeros at
-1 ± √2, what vales of a and b should be chosen?
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![c. Sketch the zero-pole plot and the direct form II diagram of the completed design out
of part b.
d. Calculate and sketch the output sequence after feeding x [n] into this system.](https://content.bartleby.com/qna-images/question/f8dc8d95-1584-43f6-b330-b68de5a36493/8eb49224-8318-49a7-a346-d6dc088d72cb/jovz9s_thumbnail.png)
Transcribed Image Text:c. Sketch the zero-pole plot and the direct form II diagram of the completed design out
of part b.
d. Calculate and sketch the output sequence after feeding x [n] into this system.
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