Consider the following discrete-time systems: T[x(n)] = 2x(n) T[x(n)] = 3x(n) + 4 T[x(n)] = x(n)...
Consider the following discrete-time systems:
- T[x(n)] = 2x(n)
- T[x(n)] = 3x(n) + 4
- T[x(n)] = x(n) +2x(n − 1) – x(n − 2)
- Use (2.12) to determine analytically to see whether these systems are time-invariant?
- Let x1(n) be a uniform distributed random sequence and x2(n) be a Gaussian distributed random sequence with mean 0 and variance 10 over 0 ≤ n ≤ 100. Test time-invariant of 3rd system only. Choose any values for a1 and a2.
Homework Answers
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Consider the following discrete-time systems:
T[x(n)] = 2x(n)
T[x(n)] = 3x(n) + 4
T[x(n)] = x(n)...
solve using MatLab please. HW - 1 Use a cover page Word file attached for the...
solve using MatLab please.
HW - 1 Use a cover page Word file attached for the homework solution. Solve all questions using Word and the Matlab output should be copied into the Word file. All questions and answers should be numbered HW1.1 Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function. 1- x(n) = n°[u(n+5] – u(n-6) + 105(n) + 20(0.5)* [u(n-4)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
How do you show this? 1.2.12. Accept the following definition. Discrete random variables X1, X2,.. ,...
How do you show this?
1.2.12. Accept the following definition. Discrete random variables X1, X2,.. , Xn, taking values in Ai, A2,..., An, are said to be independent if (1) P(Xi = ai , . . . ,x, = an) =11P(X, = a.) 仁1 for all ai E A1,., an E An. Then prove that random variables in any subsequence of a finite sequence of independent random variables are independent.
13. Let X1, X2, ...,Xy be a sequence of independent and identically distributed discrete random variables,...
13. Let X1, X2, ...,Xy be a sequence of independent and identically distributed discrete random variables, each with probability mass function P(X = k)=,, for k = 0,1,2,3,.... emak (a) Find the expected value and the variance of the sample mean as = N&i=1X,. (b) Find the probability mass function of X. (c) Find an approximate pdf of X when N is very large (N −0).
In x[n] = sin(w*T*n), 'w' and 'T' are both constant, is the discrete-time sequence x[n] =...
In x[n] = sin(w*T*n), 'w' and 'T' are both constant, is the discrete-time sequence x[n] = sin(w*T*n) peroid?
7. Consider the discrete time systems G : y[n] = x[n]-x[n-1] For each of the combined...
7. Consider the discrete time systems G : y[n] = x[n]-x[n-1] For each of the combined systems below, determine the output y[n]. Then determine which systems are equivalent, ie., produce the same output y[n] GHy FHy
5. A stationary random process X[n] is input to a discrete time LTI system with frequency...
5. A stationary random process X[n] is input to a discrete time LTI system with frequency response j“)-10 zero mean given as A(e nmay be expressed as where Wnlis a zero mea a-HS1 unit variancei.i.d. (independent identically distributed) Gaussian sequence and c, d are constants. Let Yl be the output random a)Determine the mean function for the output random sequence Yn in terms ofa, c and d b) Determine S7 (e), the power spectral density ofthe output random sequence Yn]...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed white The sample functions of...
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed white The sample functions of this process is filtered according to the n( zn-1)+x(n) (5 points). Write the MATLAB code for the computation of autocorrelation of the processes X(n) and Z(n) by repeating the experiment 100 times. (5 points). b.
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed...
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show...
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. Start by assuming,x1[k]→y1[k], x2[k]→y2[k]. 2) Determine if the discrete-time system,y[k] =x[k] +rk·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. 3) For the system in part 1), if x[k] = 100·u[k−1] and y[k] = 0 for k<0, what is the range of values for r that makes this system BIBO stable? Show...
solve using MatLab please.
HW - 1 Use a cover page Word file attached for the homework solution. Solve all questions using Word and the Matlab output should be copied into the Word file. All questions and answers should be numbered HW1.1 Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function. 1- x(n) = n°[u(n+5] – u(n-6) + 105(n) + 20(0.5)* [u(n-4)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
How do you show this?
1.2.12. Accept the following definition. Discrete random variables X1, X2,.. , Xn, taking values in Ai, A2,..., An, are said to be independent if (1) P(Xi = ai , . . . ,x, = an) =11P(X, = a.) 仁1 for all ai E A1,., an E An. Then prove that random variables in any subsequence of a finite sequence of independent random variables are independent.
13. Let X1, X2, ...,Xy be a sequence of independent and identically distributed discrete random variables, each with probability mass function P(X = k)=,, for k = 0,1,2,3,.... emak (a) Find the expected value and the variance of the sample mean as = N&i=1X,. (b) Find the probability mass function of X. (c) Find an approximate pdf of X when N is very large (N −0).
7. Consider the discrete time systems G : y[n] = x[n]-x[n-1] For each of the combined systems below, determine the output y[n]. Then determine which systems are equivalent, ie., produce the same output y[n] GHy FHy
5. A stationary random process X[n] is input to a discrete time LTI system with frequency response j“)-10 zero mean given as A(e nmay be expressed as where Wnlis a zero mea a-HS1 unit variancei.i.d. (independent identically distributed) Gaussian sequence and c, d are constants. Let Yl be the output random a)Determine the mean function for the output random sequence Yn in terms ofa, c and d b) Determine S7 (e), the power spectral density ofthe output random sequence Yn]...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed white The sample functions of this process is filtered according to the n( zn-1)+x(n) (5 points). Write the MATLAB code for the computation of autocorrelation of the processes X(n) and Z(n) by repeating the experiment 100 times. (5 points). b.
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed...
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