MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 003 Signals and Systems Fall 2002 Tutorial for the week of November 25th November 29th Alex s O ce Hours Monday 3 5pm Important Due Dates Problem Set 9 due on Wednesday Today 1 Pole Zeros to Bode Plot example 2 Z Transform stu 1 More on CT Frequency response You should feel comfortable understanding how a system is characterized in many di erent forms 1 System Function H s eg 1 s 1 H s 2 Impulse response h t Re s 1 h t e t u t 3 Graph of impulse response or step response Impulse Response 1 0 9 0 8 0 7 Amplitude 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 6 Time sec 4 Bode plot Bode Diagram 0 Magnitude dB 5 10 15 20 25 Phase deg 0 45 90 1 0 10 1 10 10 Frequency rad sec 5 Pole zero diagram Im 2 1 2 1 1 1 2 2 2 Re Example All the fun you can have with pole zero diagrams and bode plots Match the pole zero diagrams on this page with the the frequency response plots on the next page b a Im s Im s 3 3 Re s 10 c d Im s 10 Re s 1 Im s Re s 1 10 e 1 Re s f Im s Im s 100j 100j Re s 0 1 Re s 1 100j 100j 3 b 20 14 5 25 Magnitude dB Magnitude dB a 15 14 13 5 30 35 13 40 12 5 45 90 180 Phase deg Phase deg 45 135 90 45 45 0 0 90 0 1 10 10 2 0 10 c d Magnitude dB Magnitude dB 60 80 40 60 80 100 120 100 0 0 45 45 Phase deg Phase deg 2 10 20 40 90 135 90 135 180 2 10 Frequency rad sec 3 0 10 1 10 10 2 10 Frequency rad sec e f 40 20 25 60 Magnitude dB Magnitude dB 10 Frequency rad sec 20 180 1 10 1 10 Frequency rad sec 80 100 30 35 40 120 45 0 30 Phase deg Phase deg 45 90 60 135 180 1 10 90 2 10 Frequency rad sec 3 0 10 1 10 10 Frequency rad sec 4 2 10 Example Given the z transform pair z z 2 4 use z transform properties to determine the z transform of the following signals x n z2 a y n 2n x n b y n x n 1 x n 1 c y n x n x n x n m times d y n n 3 x n 2 5 Work Space 6 Example Determine all possible signals that can have the following z transforms with the given conditions a 1 1 32 z 1 12 z 2 b 2 32 z 1 3 1 1 2 1 2 z 2 z c 3 1 10 z 1 z 2 3 d 1 12 z 1 1 12 z 1 causal stable right handed 7 Work Space 8
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