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### A#07_Solutions

Course: ECSE 2410, Spring 2009
School: RPI
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RPI - ECSE - 2410
Assignment #08 ECSE-2410 Signals &amp; Systems - Spring 2009 1(30). Perform the convolution, c(t ) = a(t ) b(t ) , where Due Fri 02/13/09a (t )1 tb(t ) 1t0101234(a) Use the graphical approach. Evaluate the integrals for each range
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #09 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Fri 02/20/09Using the properties and transform Tables (no integrations of the definition) find the Fourier transform, X ( ) , for the following signals: Look for symmetry properties. For
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #10 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Tue 02/24/09Use the properties and transform Tables (no integrations of the definition) to solve the following:x(t) 11(14). Find the Fourier transform ofand plot X ( ) vs. for4 t
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #11 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Fri 02/27/09Use the properties and transform Tables (no integrations of the definition) to solve the following: 1(10). Use duality to find the Fourier transform of x(t ) = 2(10). Find the
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #12 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Fri 03/06/091(32). Speech scramblers are designed to prevent electronic eavesdropping. The input voice, x(t ) , is , 1000 1 made unintelligible by altering the original spectru
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #13 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Tue 03/17/091(20). Consider the signal x(t)=3cos(t)+2cos(3t)+cos(4t). (a) Find the Nyquist sampling frequency, s, which guarantees that x(t) can be recovered from its samples. (b) Suppose
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #14 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Fri 03/20/091(24). Sketch the straight-line Bode Magnitude plot. Label all key magnitude, frequency and slope values. Check the slopes of H ( ) when 0 and when . (a) H ( ) =H
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #15 ECSE-2410 Signals &amp; Systems - Spring 2009 j 50 + 1 0.1 1(60). H ( ) = j j ( j + 1) + 1 50 (a) Sketch the straight-line Bode magnitude plot for. Label all key magnitude, frequency and slope values. (b) Sketch the approximate pha
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #16 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 1(25). For the circuits shown, (A) (B). Due Fri 03/27/09(a)(10). (b)(10). of (c)(5).Find H (s ) Sketch the general Bode straight-line magnitude diagram and indicate the general locatio
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #17 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 Read Section 6.5 and Sections 9.1 through 9.7, skipping 9.2. 1(28). For the following, sketch the pole-zero plot, find , n and determine if the system is undamped ( = 0) or underdamped (
RPI - ECSE - 2410
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #18 ECSE-2410 Signals &amp; Systems - Spring 2009 1(30). Given Y (s ) = (a) Find y(t )2 (s + 2 ) s + 4 (s + 1)22Due Fri 04/03/09(b) We know that y (t ) = y transient (t ) + y steady state (t ) . Show that the steady-state portion of y(t
RPI - ECSE - 2410
Assignment #19 ECSE-2410 Signals &amp; Systems - Spring 2009 1(20). Given the RLC circuit shown, (a)(5). Find H (s ) , , n , sketch pole-zero plot. (b)(5). Use MATLAB to plot the Bode magnitude and phase diagrams. x(t) C= 1 F 8 y(t) R=2 Due Tue 04/07/
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #20 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 1(30). Find the closed loop transfer function, (a)X (s )Due Fri 04/10/09 Y (s ) , in terms of the H ' s shown. X (s )H 2 (s ) Y (s )+ -+ -H 1 (s )H 3 (s )H 4 (s )(b)H 4 (s
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #21 ECSE-2410 Signals &amp; Systems - Spring 2009 Due Fri 04/17/091(30). Use the Routh array as discussed in class to determine the number of roots that the following polynomials have in the right half of the s-plane, if any. Note that (c) r
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #22 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 1(20). Find the closed loop system Y (s) transfer function, , expressed X ( s) in terms of transfer functions X(s) A( s ), B ( s ), C ( s ), D ( s ) . D(s) + + A(s) + Due Tue 04/21/09B(s
RPI - ECSE - 2410
RPI - ECSE - 2410
Assignment #23 p.1 ECSE-2410 Signals &amp; Systems - Spring 2009 1(10). The root locus shown represents a system with the closed-loop transfer function Y(s) K G(s) . The = X(s) 1 + K G(s) breakaway point is b = -4.44. Note: All the poles of G(s) have r