Classify or characterize the following systems as homegeneous, additive, linearity, time-invariance, BIBO stability, causality, invertible and...
Classify or characterize the following systems as homogeneous, additive, linearity, time-invariance, BIBO stability, causality, invertible, and memoryless: (a) y(n) = Re(a(n)), (c) y(n-2(4n + 1) (d) y(n)=x(-n) (e) y(n) = 2(n-2)-22(n-8) (f) y(n) = nx(n) (g) y(n) = Even{x(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
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
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],
each of the following systems, determine if the system could satisfy the additivity property, the scaling property and/or the time-invariance property: e) f) g) y'(t)+ 2y(t) = 2x(t) y(t)= x(t)u(t) y(t) = tu(t)
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
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...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquist rate to get the sequence r[n]. (a) Sketch X(e) (b) If y[n] = [4n]. Sketch Y(e'"). (c) Is there any aliasing in the Fourier spectrum of yin]? Why or Why Not? (d) If z [n] = x-1, ketch the DTFT of z[n] (e) Is there any aliasing in the Fourier spectrum of [n]? Why or Why Not? 3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is...
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...