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lecture_06

# lecture_06 - MIT OpenCourseWare http/ocw.mit.edu 2.161...

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MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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1 0 W j W s x x x x x o o 1 Massachusetts Institute of Technology Department of Mechanical Engineering 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Lecture 6 1 Reading: Class handout: Sinusoidal Frequency Response of Linear Systems (Sec. 7). Class handout: Sinusoidal Frequency Response of Linear Systems (Sec. 6.1). Class handout: Introduction to Continuous Time Filter Design . Poles and Zeros of Filter Classes We can use the s -plane relationship between a ﬁlter’s poles and zeros and the frequency response function to make some general comments about the desgn of various classes of ﬁlters: (a) Low-Pass Filters: To ensure a high-frequency roll-oﬀ the number of poles must exceed the number of zeros, ie n>m . (In many low-pass ﬁlters m = 0.) ensure a ﬁnite low frequency gain there can be no poles or zeros at the origin. s - p l a n e | H ( j W ) | n > m n o p o l e s o r z e r o s a t t h e o r i g i n (b) High-Pass Filters ensure a constant high-frequency gain the number of poles must equal the number of zeros, ie n = m . ensure a low frequency gain that approaches zero, there must be one or more zeros at the origin. 1 copyright ± c D.Rowell 2008 6–1
1 0 W j W s W c x o o o x x 1 0 W s o o o x x x x x x s - p l a n e | H ( j W ) | n = m n z e r o s a t t h e o r i g i n (c) Band-Pass Filters To ensure a high-frequency roll-oﬀ the number of poles must exceed the number of zeros, ie n>m . ensure a low frequency gain that approaches zero, there must be one or more zeros at the origin. The band-pass characteristic is shaped by a group of poles clustered near the imaginary axis in the region of the passband, j W s l a n e | H ( j W ) | n > m p o l e s c l u s t e r e d n e a r t h e i m a g i n a r y a x i s i n r e g i o n o f t h e p a s s - p a n d o n e o r m o r e z e r o s a t t h e o r i g i n W c 1 W c 2 (d) Band-Stop Filters ensure a constant high-frequency gain the number of

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lecture_06 - MIT OpenCourseWare http/ocw.mit.edu 2.161...

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