![of the following irrational z transforms. (a) x(z) = ea, Izl > 0, o)X(z)log (1- az), zl < 1/lal. . 1 Show the following p roperties for the z transforms of even and odd 6.7 discrete-time functions. (a) If x[n] is even, that is, x[n-x(-n], then X(z) = X(z-1) (b) If x[n] is odd, that is, x[n] =-x|-n], then X(z)--X(2-1). (c) If x[n] is odd, then there is a zero in X(z) at z 1.](http://img.homeworklib.com/questions/eb1e6160-9669-11eb-a44d-59e63d70031c.png?x-oss-process=image/resize,w_560)
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6.6a b
6.7c d e
of the following irrational z transforms. (a) x(z) = ea", Izl...
3) Compute the Z-Transforms of the following time series: (a) x(n)k2"u(n) (b) + 1) x(n) =...
3) Compute the Z-Transforms of the following time series: (a) x(n)k2"u(n) (b) + 1) x(n) = u(-n (c) x(n) -k2"u-1) (d) x(n) 0.5%1(n) + 3"11(-n) (e) x(n) = 4-nu(n) + 5-nu(n + 1) In the above, u(n) stand for the unit step signal in the discrete time domain. Also, if you can in each case determine the region of convergence of the Z-Transform you obtain.
please answer them indetail. thanks 4. Let x(n) be a causal sequence. a) b) what conclusion...
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
2. Circle the causal BIBO stable ROC below. a) 1.1<\리<1.2 b) Izk1/201zP1/2 d) 0.5<Izl<0.9 e) none...
2. Circle the causal BIBO stable ROC below. a) 1.1<\리<1.2 b) Izk1/201zP1/2 d) 0.5<Izl<0.9 e) none above 3. A linear time-invariant IIR system is always BIBO stable a) True b) False 4. If a fiter has z-transform H(z)05, then the fiter s ;z>0.5, then the filter is zz-0.5z a) Nonlinear b)FIR )R d) two-sided e) none above 5. The discrete-time frequency o in rad/ sample of the sinusoid hin] below is d) T2 e) none above hIn] -1
Please solve for part (b) and (c) thank you! 1. Consider the function f(x) = e-x...
Please solve for part (b) and
(c) thank you!
1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (...
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12
Problem 3: Let x(n) be an...
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
Discrete Structures Name: Problem 2. Prove the following theorem using P Theorem. Let x, y e...
Discrete Structures
Name: Problem 2. Prove the following theorem using P Theorem. Let x, y e Z. If c-y is odd, then 1 em using proof by contrapositive. yis odd, then ris odd or y is odd.
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 the z-transforms of the following sequences: (a) x = [3, 0, 5, 6, 0,...
1. Determine the z-transforms of the following sequences: (a) x = [3, 0, 5, 6, 0, 1] (b) x = [1, 0, 0, 4] 2. Compute the transfer fuctions for the following impulse responses: (a) h = [1, −5, 4, 0, 5] (b) h = [1, −0.5, 0.25, −1.125] 3. If h(n) = 3^ -n for n ≥ 0, express H(z) as a ratio of polynomials. 4. Find the 10 roots of unity, that is, solve z^10 − 1 =...
2. Give the asymptotic running time of each the following functions in e notation. That is,...
2. Give the asymptotic running time of each the following functions in e notation. That is, write down a recurrence relation for each recursive function below and solve it. Show your work def Pow(x, n): 2 if n-0: 3 return 1 end 5 e f Pow(x, [n/2]) 1 # n is even if n % 2-0: 9 return f f 10 end #nis odd 12return r*f*.f 13 end
3) Compute the Z-Transforms of the following time series: (a) x(n)k2"u(n) (b) + 1) x(n) = u(-n (c) x(n) -k2"u-1) (d) x(n) 0.5%1(n) + 3"11(-n) (e) x(n) = 4-nu(n) + 5-nu(n + 1) In the above, u(n) stand for the unit step signal in the discrete time domain. Also, if you can in each case determine the region of convergence of the Z-Transform you obtain.
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
2. Circle the causal BIBO stable ROC below. a) 1.1<\리<1.2 b) Izk1/201zP1/2 d) 0.5<Izl<0.9 e) none above 3. A linear time-invariant IIR system is always BIBO stable a) True b) False 4. If a fiter has z-transform H(z)05, then the fiter s ;z>0.5, then the filter is zz-0.5z a) Nonlinear b)FIR )R d) two-sided e) none above 5. The discrete-time frequency o in rad/ sample of the sinusoid hin] below is d) T2 e) none above hIn] -1
Please solve for part (b) and
(c) thank you!
1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12
Problem 3: Let x(n) be an...
Discrete Structures
Name: Problem 2. Prove the following theorem using P Theorem. Let x, y e Z. If c-y is odd, then 1 em using proof by contrapositive. yis odd, then ris odd or y is odd.
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...
2. Give the asymptotic running time of each the following functions in e notation. That is, write down a recurrence relation for each recursive function below and solve it. Show your work def Pow(x, n): 2 if n-0: 3 return 1 end 5 e f Pow(x, [n/2]) 1 # n is even if n % 2-0: 9 return f f 10 end #nis odd 12return r*f*.f 13 end
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