1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show...
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. Start by assuming,x1[k]→y1[k], x2[k]→y2[k].
2) Determine if the discrete-time system,y[k] =x[k] +rk·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property.
3) For the system in part 1), if x[k] = 100·u[k−1] and y[k] = 0 for k<0, what is the range of values for r that makes this system BIBO stable? Show your work.
Homework Answers
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1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is
linear / time-invariant / causal / memoryless. Show...
Determine which of these properties (Memoryless, Time invariant, Linear, Causal, and Stable) hold and which do...
Determine which of these properties (Memoryless, Time invariant, Linear, Causal, and Stable) hold and which do not hold for each of the continuous-time system, y[n] = x [4n + 1]. Justify your answers. y(t) denotes the system output and x(t) is the system input
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify...
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify the properties of the given system. Select one: a. Non-linear, time invariant, BIBO stable, memoryless, and causal b. Non-linear, time invariant, unstable, memoryless, and non-causal c. Linear, time varying, unstable, not memoryless, and non-causal d. Linear, time invariant, BIBO stable, not memoryless, and non-causal e. Linear, time invariant, BIBO stable, memoryless, and non-causal 0
Q1. True / False Memoryless Causal Stable Time-invariant Linear y(t) = x(2t) – 1 rt-1 J-00...
Q1. True / False Memoryless Causal Stable Time-invariant Linear y(t) = x(2t) – 1 rt-1 J-00 y(t) = Sx() dt y[n] = 2 x[m] m =0
For the system described by y[n] = n2 x[n – 1],
For the system described by y[n] = n2 x[n – 1], determine whether it is a) Linear or not b) Time-invariant or not c) BIBO stable or not d) Causal or not and e) Memoryless or not
How can I determine whether a digital/analog signal system is linear, time invariant/variant, memoryless, causal, invertible,...
How can I determine whether a digital/analog signal system is linear, time invariant/variant, memoryless, causal, invertible, and stable? I am still a little bit confused after reading lecture notes on how to figure out the attributes of a signal system.
Problem 3 Determine whether each of the following system is memoryless, stable. Justify your answer time-invariant,...
Problem 3 Determine whether each of the following system is memoryless, stable. Justify your answer time-invariant, linear, causal or (a) y(t)r(t -2)+x(-t2) b) y(t) cos(3t)(t) (c) y(t) =ar(r)dT d) y(t)t/3) (e) y(t) =
Determine whether the summation operation defined by y[n] = Ek--- x[k], is Memoryless (11) Invertible (111)...
Determine whether the summation operation defined by y[n] = Ek--- x[k], is Memoryless (11) Invertible (111) Causal (iv) Stable Time invariant (vi) Linear
2. (a) For each sample of a discrete time signal x[n] as input, a system S...
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless?...
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless? Explain Is the system causal? Explain Is the system time invariant? Justify Is the system linear? Justify What is the impulse response h(t) of the system? Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below. ht=5e-tut-u(t-4)
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify the properties of the given system. Select one: a. Non-linear, time invariant, BIBO stable, memoryless, and causal b. Non-linear, time invariant, unstable, memoryless, and non-causal c. Linear, time varying, unstable, not memoryless, and non-causal d. Linear, time invariant, BIBO stable, not memoryless, and non-causal e. Linear, time invariant, BIBO stable, memoryless, and non-causal 0
Q1. True / False Memoryless Causal Stable Time-invariant Linear y(t) = x(2t) – 1 rt-1 J-00 y(t) = Sx() dt y[n] = 2 x[m] m =0
Problem 3 Determine whether each of the following system is memoryless, stable. Justify your answer time-invariant, linear, causal or (a) y(t)r(t -2)+x(-t2) b) y(t) cos(3t)(t) (c) y(t) =ar(r)dT d) y(t)t/3) (e) y(t) =
Determine whether the summation operation defined by y[n] = Ek--- x[k], is Memoryless (11) Invertible (111) Causal (iv) Stable Time invariant (vi) Linear
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
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