Please solve the following and show steps clearly
1-a casual LTI system is characterized by the following difference equation y[n]-3/4 y[n-1]+1/8 y[n-2]= 2 x[n]
find the impulse response, h[n], of this system
2-then find the response of the system to input x[n]= (1/4)^n u[n]
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Please solve the following and show steps clearly 1-a casual LTI system is characterized by the...
A causal LTI system is characterized by : y[n] - 3/4 y[n-1] + 1/8 y[n-2] =2x[n]. (a) Find the impulse response h[n] of this system (b) Find the response of the system to input x[n] = (1/4)^n * u[n]
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is 3. For following input/output system relationships, determine the...
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
please show detailed work/proof 3. The input and output of a causal LTI system satisfy the following difference equation (d.e.) y[n] = ayln-1] + x[n]-a"x[n-N], N > 0 a. Determine the impulse response h[n]. Hint: solve it iteratively starting from n=0, 1, , n=N+1; x[n] = δ[n] then think what is y[n] ? b. Sketch the impulse response h[n] c. Is this an FIR or an IIR system? d. For what values of the parameter a is the system stable?
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
For the LTI system described by the following impulse response: \(h(n)=n\left(\frac{1}{3}\right)^{n} u(n)+\left(-\frac{1}{4}\right)^{n} u(n)\)Determine the following:1) The system function representation,2) The Difference equation representation3) The pole-zero plot4) the output \(y(n)\) if the input \(x(n)\) is: \(x(n)=\left(\frac{1}{4}\right)^{n} u(n)\)
questions are connected. please show steps to all Consider the system characterized by the characteristic polynomial D2+4D+4. (0) Find the zero-input response go(t) of the system, such that vol(o) 0 and o(0) -1. Impulse Response and Zero-State Response 4 Consider the system characterized by the following diferential equation where z() represents the iaut and y(t) the output (D2 +4D+4) y(t) Da(t) (i) Determine the impulse response h(t) of the system. (i) Compute the convolution h r(t) for r(t) eu(t). Hint:...
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CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
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] +...