A system is designed for which an input signal emerges delayed by 1.0 second, followed by two echoes consisting of another copy of the same signal 1.0 second reduced to half amplitude and another copy of the same signal reduced to one quarter the original amplitude 1.0 second after that. Write an expression for the response function h(t) for this system. Make a sketch of h(t).
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A system is designed for which an input signal emerges delayed by 1.0 second, followed by...
Use MATLAB to: Design an Echo Filter. The output should be the original signal followed by three echoes with attenuations of 10%, 15 % and 25% respectively and the delays should be 0.9 sec, 1.4 sec, and 1.8 sec respectively for each echo. Hint: Based on this information the original signal appears at the output with the same amplitude, the first echo has amplitude 0.9 times the amplitude of the original (10% attenuation), the second echo has amplitude 0.85 (15%...
Only do question 2a. Please do it manually.
Signal processing theory: Input System impulse response in O 15 t 2 s t Question 1. Consider the figure above. An input signal has a square shape with a width of 1 s and amplitude of 1. The instrument impulse response has a square shape with a width of 2 s and amplitude of 1. Follow the example given in the lecture slides to manually calculate and plot the instrument's output in...
Question 13 For the control system shown below the input signal is x(C) and the output signal in ), the fransfer function is 10s +50 s +12s+ 100 10s +50 o HCs)--S-10s + 150 10s +50 s2 + 22s 101 10s+50 H(s) HS)2 + 22s 150 50 O H(s)- s2 +22s 150 For the control system shown below the input signal is X() and the output signal is VCt), the transfer function is H(S)- HS) 3 +252 +51 Question 1...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
Problem 1. (10 points) The signal x()u(-2) is applied to the input of an LTI system whose impulse response IS h(1)=-rect |- 4 (a) Sketch x(t), h(t) and x(r)h(t - 7) (b) Determine y)-x(i)* h() for all possible values of (interval by interval).
For Problems (9-10), use the continuous-time system depicted below which converts the input signal X(t) into the corresponding output signal y(t) = {x()} = 10 x(t) u(t - 3). system y(t) = $ { x(t) } = 10 x(t) · u(t – 3). (9) (10 points) (a) Compute the formula for the Ramp Response, yramp(t) = { r(t)}. (b) Plot the Ramp Response. Label both axes. Give key values of time and amplitude. (10) (10 points) (a) Compute the formula...
Digital Signal Processing
QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only)
QUESTION SIX A digital filter system has a transfer...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...