comprised of three components x t 1 2 cos \u03c0t 0 5 cos10 \u03c0t is illustrated here 2

# Comprised of three components x t 1 2 cos πt 0 5

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), comprised of three components, x ( t ) = 1 + 2 cos( πt ) + 0 . 5 cos(10 πt ) is illustrated here: 0 2 4 6 8 10 -4 -2 0 2 4 x(t) [INPUT SIGNAL] t [SEC.] This signal, x ( t ), is filtered with each of six different continuous-time LTI filters. The frequency response of each of the six systems are shown below. (For | ω | > 3 π , each frequency response has the value it has at | ω | = 3 π .) -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 1 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 2 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 3 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 4 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 5 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 6 ω The six output signals are shown below, but they are not numbered in the same order. 114
0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 1 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 2 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 3 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 4 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 5 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 6 t [SEC.] Match each output signal to the system that was used to produce it by completing the table. System Output signal 1 2 3 4 5 6 115
2.7.30 A signal x ( t ), comprised of three components, x ( t ) = 1 + 0 . 5 cos( πt ) + 2 cos(6 πt ) is illustrated here: 0 2 4 6 8 10 -4 -2 0 2 4 x(t) [INPUT SIGNAL] t [SEC.] This signal, x ( t ), is filtered with each of six different continuous-time LTI filters. The frequency response of each of the six systems are shown below. (For | ω | > 3 π , each frequency response has the value it has at | ω | = 3 π .) -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 1 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 2 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 3 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 4 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 5 ω -3π -2π 0 π 0 0.5 1 FREQUENCY RESPONSE 6 ω The six output signals are shown below, but they are not numbered in the same order. 116
0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 1 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 2 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 3 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 4 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 5 t [SEC.] 0 2 4 6 8 10 -4 -2 0 2 4 OUTPUT SIGNAL 6 t [SEC.] Match each output signal to the system that was used to produce it by completing the table. System Output signal 1 2 3 4 5 6 117
2.7.31 Each of the two continuous-time signals below are processed with each of four LTI systems. The two input signals, illustrated below, are given by: Input signal 1: 0 . 6 cos(3 πt ) + 2 cos(17 πt ) Input signal 2: 2 cos(3 πt ) + 0 . 6 cos(17 πt ) The frequency responses H f ( ω ) are shown below. Indicate how each of the output signals are produced by completing the table below (copy the table onto your answer sheet). Note: one of the output signals illustrated below will appear twice in the table (there are seven distinct output signals). Input signal System Output signal 1 1 1 2 1 3 1 4 2 1 2 2 2 3 2 4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -3 -2 -1 0 1 2 3 INPUT SIGNAL 1 TIME (SECONDS) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -3 -2 -1 0 1 2 3 INPUT SIGNAL 2 TIME (SECONDS) 118
ω - 20 π - 10 π 0 10 π 20 π H f 1 ( ω ) 1 ω - 20 π - 10 π 0 10 π 20 π H f 2 ( ω ) 1 1 ω - 20 π - 10 π 0 10 π 20 π H f 3 ( ω ) 1 ω - 20 π - 10 π 0 10 π 20 π H f 4 ( ω ) 1 1 119
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -3 -2 -1 0

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