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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?

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?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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?
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.
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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