Classify or characterize the following systems as homogeneous, additive, linearity, time-invariance, BIBO stability, causality, invertible, and...
Classify or characterize the following systems as homegeneous, additive, linearity, time-invariance, BIBO stability, causality, invertible and memoryless (a) y(n)= Re(z(n)), (b) y(n) = Re(ejiHz(n)) (e) y(n)=x(4n +1) e) y(n)r(n -2) - 2x(n - 8) (g) y(n) Evenfx(n - 1))
Examine the properties (memory, stability, casuality, linearity, and time-invariance) for the following systems (a) y(t) = 2*log x(t) (b) y[n] = (1/n) x(n-1) (c) y[n] = 3x [2n-1] (d) y[n] = |x[n]|
Classify each in terms of linearity, time invariance, memory (static/dynamic), & causality (a) y’’(t) + 3y’(t)=2x’(t) + x(t) (b) y’’(t) + 3y(t)y’(t)=2x’(t) + x(t) (c) y’’(t) + 3tx(t)y’(t)=2x’(t) (d) y’’(t) + 3y’(t)=2x2 (t) + x(t+2) (e) y(t) + 3 = 2x2 (t) + 2x(t) (f) y(t) = 2x(t+1) + 5 (g) y’’(t) + e-ty’(t) = | x’(t-1) | (h) y(t) = x2 (t) + 2x(t+1) (i) y’’(t) + cos(2t)y’(t) = x’(t+1) (j) y(t) +t y(t)dt = 2x(t) -infinit,i
system #1 is described by y(t) = ramp(x(t)) and system #2 is described by y(t) = x(t) ramp(t). Classify both systems as to BIBO stability, linearity, invertibility and time invariance.
1.30. Determine if each of the following systems is invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output. (a) ya)-x(t - 4) (c) y[n] nx[n] (b) y(t) = cos(x(t)] x[n - 11, n z 1 In], (e) yIn]-0, ns-1 (g) y[n] x[1 -n] G) y(t) dxt (1) V(f) = X(20) n 0 (k) vini =lx(n+1],
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
Please answer all of the questions. 6. Consider three systems with the following input-output relationships: { 0, odd System 1: yn 피[핑], n even System 2: y[nx[n] - 10xr[n + 2] + 3xr[n - 1 System 3: yn x[3n] The interconnection diagram is at follows: y System 3 System System 2 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal) 6. Consider three systems with the following input-output...
Consider three systems with the following input-output relationships 6. Consider three systems with the following input-output relationships: { 4 0, odd System 1: y[n n even r[n] 10ar(n 2]3r[n - 1 System 2: yn + + System 3: yn x[3n] The interconnection diagram is at follows: System 1 System 2 System 3 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal). 6. Consider three systems with the following...
Signal system question. EEGR 221 Signals and Systems Homework 3 Determine whether the following systems are (i) Memoryless (ii) Invertible (ii) Casual (iv) Stable (v) Time invariant (vi) Linear (a) y(t)-5x(2t +4) (b) y(t)-7 x(2t 1) +3 (c) y(t)e4x(c) (d) y(t)-sin (x(t + 1)) (e) y(t) x(t)l (1) y() log(x(t)) Your answer must have 3 components for each property 1) Definition of the property 2) Yes or NO 3) Justification and the test that you have done to give the...
Dasi 1. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, and (5) memoryless: (a) 7(x[n]) = g[n]X[n] with g[n] given (b) (x[n]) = x=no x[k] n20 (c) 7(x[n]) = (d) T(x[n]) = x[n - nol + x[k] (e) T(x[n]) = ex[n] (f) T(x[n]) = ax[n] + b (g) T(x[n]) = x[-n] (h) T(x[n]) = x[n] + 3u[n + 1).