stest1-2005

# stest1-2005 - t u(2-t(a Determine whether x t is a power...

This preview shows pages 1–2. Sign up to view the full content.

Name BME 171, Spring 2005 - TEST #1 1. Consider an LTI system with delay, whose output to an input x ( t ) = 6 u ( t ) is y ( t ) = 3(1 - e - 5( t - 2) ) u ( t - 2) . (a) What is the impulse response of this system? Compute and make a sketch. (b) Without using convolution, compute the response of this system to the input x 1 ( t ) = - 12 u ( t - 8). Sketch both the input and the response. Do not forget to label the axes and to indicate all pertinent features. 2. The filter is given by the block diagram shown below (left): n z -1 z -1 z -1 + + x[n] y[n] y[n] (a) Find and sketch impulse response h [ n ] of this filter. Determine the type and the order of this filter. (b) Consider an input x [ n ] = 2 u [ n + 2] u [2 - n ]. The response y [ n ] of the filter to this input is shown above (right) but the axes are incomplete. Show how you can determine the position of the vertical axis, the support of the output, and the scale of the vertical axis. Then complete the plot of y [ n ].

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. An LTI system has an impulse response: h ( t ) = 3 e - t u ( t ) . The input to this system is
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( t ) u (2-t ). (a) Determine whether x ( t ) is a power signals, an energy signal, or neither. (b) Determine whether the system is BIBO stable. What can you conclude regard-ing the response of this system to x ( t )? (c) The response to input x ( t ) can be computed by evaluating the convolution integral: y ( t ) = Z ∞-∞ x ( λ ) h ( t-λ ) dλ. (1) Draw a sketch indicating the position of the two functions inside the convo-lution integral at time t = 0 . 5. Carefully label all pertinent features on the graph. 4. Consider a sinusoidal signal x ( t ):-8-6-4-2 2 4 6 8-4 4 t x(t) (a) Write this signal in the form of a rotating phasor, ¯ x ( t ) = X e jωt , where X is a complex number. (b) Assuming that x ( t ) was sampled with frequency f s = 2 Hz, determine a sinu-soidal signal x a ( t ) that will be represented by the same samples as x ( t ) due to aliasing. 2...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern