A discrete system is described by the difference equation y(n)= 2.5y(n-1)-y(n-2)+3x(n)+3x(n-2) a. Using Z-transform, Determine all...

A discrete system is described by the difference equation y(n)= 2.5y(n-1)-y(n-2)+3x(n)+3x(n-2)

a. Using Z-transform, Determine all possible impulse responses h(n) and indicate the casuality and stability properties.

b.For the casual filter, determine the output y(n) if the input is x(n)=g(n)-2g(n-1) where g(n)=cos (pin/s)u(n).

Expert Solution

Manojponduru answered 1 year ago

For the following causal difference equation, given that y[-1] = 2, y[-2] = 3, and x[n]...

For the following causal difference equation, given that y[-1] = 2, y[-2] = 3, and x[n] = 3nu[n], solve using z-Transforms. (Hint: convert to delay operator form, find the z-Transform, use PFE to find the inverse z-Transform) y[n + 2] – 3y[n + 1] + 2y[n] = x[n + 1]

Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1]...

Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1] + y[n] = x[n] (for n = 0, 1, 2, 3)

For the following causal difference equation, given that y[-1] = 0, y[-2] = 1, and x[n]...

For the following causal difference equation, given that y[-1] = 0, y[-2] = 1, and x[n] = u[n], solve using z-Transforms. (Hint: convert to delay operator form, find the z-Transform, use PFE to find the inverse z-Transform) 4y[n + 2] + 4y[n + 1] + 2y[n] = x[n + 1]

Consider the following discrete-time system: y[n] = 100 x[n] cos(0.45πn + 0.5π) (a) Determine if the...

Consider the following discrete-time system: y[n] = 100 x[n] cos(0.45πn + 0.5π) (a) Determine if the system is linear, time-invariant, causal and stable. Justify your answers. (b) Find the impulse response h[n] for the system and sketch the waveform. (c) Draw the system block diagram using adder, multiplier and delay elements.

A SISO DT LTI system having input x[n] and output is described by the difference equation...

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Realize signal processing systems described by the difference equation: ?1(?)=1/2 [?(?)+?(?−1)] and ?2(?)=1/2 [?(?)−?(?−1)] using Matlab....

Realize signal processing systems described by the difference equation: ?1(?)=1/2 [?(?)+?(?−1)] and ?2(?)=1/2 [?(?)−?(?−1)] using Matlab. Assuming same input signal x(n)=sin(ωn) for various values of ω ={0,p/6 ,3p/2, 1.9p/2} applied to both systems find the following: a. Obtain stem plots and codes of y1(n) and y2(n) in each . b. Critically analyze y1(n) and y2(n) in terms of type of filter, maximum gain and cut off frequency. (Hint : The system can be tested by computing frequency response of the...

1. Determine forced and natural response for the following equation, where y[-1] =1, y[-2]=1 and x[n]...

1. Determine forced and natural response for the following equation, where y[-1] =1, y[-2]=1 and x[n] = delta[n]. y[n]+1/2 y[n-1] -1/4 y[n-2] = x[n] 2. find the impulse response of the system described below y[n]=1/2 y[n-1] + 2x[n]

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z...

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z = -1

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Number Theory Exercise 1 Prove that the equation 3x^2 + 2 = y^2 has no solution...

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