1. Determine y(n) of the given LTI Difference equation y(n)=1.2 y(n-1) -0.32 y(n-2)+10x(n) +6x(n-1) a. x(n)...
Problem 2 Given is the LCC difference equation that represents some LTI system: y(n)y(n 2) = x(n) +;x(n- 1) 2 Draw a Direct- I and Direct Il block diagram representations of the system Find the impulse response of the system a) b)
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1] + x[n]. a) Derive the impulse response of the system. (2 pt) b) Determine if the system is BIBO stable. (1 pt) c) Assuming initial conditions yl-1) = 1, derive the complete system response to an input x[n] = u[n] - u[n-2), for n > 0.(2 pt) d) Derive the zero-state system response to an input z[n] = u[n] - 2u[n - 2] +...
(a) Determine the difference equation relating the input (x[n]) and outpt (y[n]) for an LTI system whose impulse response is given by: h(n) = (1/4){δ(n) + δ(n - 1) (b) Find and plot the amplitude and phase response of the above LTI system. Indicate what kind of filter this system represents.
Determine the impulse response h[n] of the LTI system described by the difference equationy[n] - 0.35y[n-1] = x[n]
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...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
a causal discrete time LTI system is implemented using the difference equation y(n)-0.5y(n-1)=x(n)+x(n-1) where x(n) is the input signal and y(n) the output signal. Find and sketch the impulse response of the system
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
For the LTI system with the difference equation y[n] = 0.25x[n] +0.5x[n-1] + 0.25x[n-2] a. Find the impulse response h[n] (this is y[n] when x[n] = δ[n] ) b. Find the frequency response function H(?^?ω). Your result should be in the form of A(?^?θ(?) )[cos(αω)+β]. Specify values for A, ?(?), α,and β c. Evaluate H(?^?ω) for ω = π , π/2 , π/4, 0, -π/4, - π/2, -π d. Plot H(?^?ω) in magnitude and phase for –π < ω <...
Please show full Calculations for part C) 1. Consider the following causal LTI systems with difference equations (a) yIn]+3 y[n-1]+2y[n-2] - x[n] + 2xln-1] (b) y[n] +0.8 y[n-21 x[n-1]. (c) y[n] -0.5 yln-2 2x[n] -xln-21]. In each of cases a,b and c i) Find and sketch the impulse response, hin) by recursive solution. ii) Is the system FIR or IIR ? ii) Find and sketch the corresponding step response, s[n] iv) Draw the direct form & direct-form Il structures for...