is the system y(n)=x(n)+0.1x(n-1) a bounded-input bounded output stable
is the system y(n)=x(n)+0.1x(n-1) a bounded-input bounded output stable
A system is BIBO (bounded-input, bounded-output) stable if every bounded input X(t) yields a bounded output y(t). A system is NOT BIBO stable if there exists any bounded input that results in an unbounded output. By "bounded", we mean that the magnitude of the signal is always less than some finite number. (The signal x(t)=sin(t) would be considered a bounded signal, but X(t)t would not be a bounded signal.) Signals that are infinite in time, but with a magnitude that...
Memory less ?
Causal ?
Bounded input bounded output stable ?
Is the system invertible ?
Linear ?
Time invariant?
Question (1) ls the system S, given by (6 Marka y(t) = 3x(t-1)-2 a) Memoryless?
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense?...
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.
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
Consider the discrete-time system with input x[n] and output y[n] described by : y[n]=x[n]u[2-n] Which of the following properties does this system possess? Justify your answer in each case. Do not use Laplace transforms a) Memoryless b)Time-invariant c) Linear d)Casual e) Stable
The output of a discrete-time system is related to the input by Y(n) x(n is 1 1) = - a. Find the transfer function of the system. b. If the input X(n) is stationary with E(X(n)) = 0 Rxx(k) = { 1, for k = 0 for k 0 0 find Sy(f) and EfY'(n) γγ
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
(Convolution DT) consider the following LTI system with input x[n] and output y[n]: (a) sketchbthe input signal x[n] = (1/2)^n(u[n])
Consider a DT system with input x[n] and output y[n] described
by the difference equation 4y[n+1]+y[n-1]=8x[n+1]+8x[n]
73 Consider a DT system with input xin and output yin] described by the difference equation (a) What is the order of this system? (b) Determine the characteristic mode(s) of the system (c) Determine a closed-form expression for the system's impulse response hln].
73 Consider a DT system with input xin and output yin] described by the difference equation (a) What is the order...