By John R. Buck
Designed to increase better figuring out of the rules of signs and structures. makes use of MATLAB workouts to actively problem the reader to use mathematical suggestions to actual international difficulties.
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Additional info for Computer Explorations in Signals and Systems Using MATLAB
Convolve x1[n]with hSeries[n] to get the output yd2[n]. Compare y d l [n]and Yd:! [n]. Did you get the same results when you process X I [n]with the individual impulse responses as when you process it with hSeries[n]? / Intermediate Problems (e). Suppose two LTI systems have impulse responses hel = hl [n]and he2[n]= hl [n- no], where hl [n]is the same signal defined in Part (a) and no is an integer. Let yel [n]and y,z[n] be the outputs of these systems when x[n]is the input. Use the commutative property to argue that the outputs will be the same if you interchange the input and impulse response of each system.
For what values of t does yl approximate y(t)? Plot the valid elements of yl with a correctly labeled time axis. Is yl a close approximation to the analytic expression you found in Part (a)? (e). 01 on the time interval 0 5 t 5 6 using vectors x2 through x4. Define h2 through h 4 to represent hA(nA) on the same interval with the same sampling periods. Compute y2 through y4 using conv and the appropriate inputs and impulse responses. In each case, the output signal is valid over the same range of t, but because A is different for each output, this corresponds to a different set of samples.
This is a reasonable model for an echo resulting from the signal reflecting off of an absorbing surface like a wall. If a microphone is placed in the center of a room, and a person is speaking at one end of the room, the recording will contain the speech which travels directly to the microphone, as well as an echo which traveled across the room, reflected off of the far wall, and then into the microphone. Since the echo must travel further, it will be delayed in time. Also, since the speech is partially absorbed by the wall, it will be decreased in amplitude.
Computer Explorations in Signals and Systems Using MATLAB by John R. Buck