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 = 0.
5. What are the values of a1 and b1 for the sine function filter we created running at 8 kHz that will produce a 750 Hz sine wave?
Homework Answers
Add Answer to:
1. Determine the z-transforms of the following sequences:
(a) x = [3, 0, 5, 6, 0,...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
3.96 Determine the z-transforms of the following sequences and their respective ROCs: (a) x1[n] = -a"u[-n-1],...
3.96 Determine the z-transforms of the following sequences and their respective ROCs: (a) x1[n] = -a"u[-n-1], (b) x2[n] = "Min + 1], and (c) x3[n] = "u-n).
Using the following two finite-length sequences: x = {0, 1, 7, 6, 1, 2, 0, 7, 1, 0, 3, 4}; h = {1, 1, -1}
Using the following two finite-length sequences: x = {0, 1, 7, 6, 1, 2, 0, 7, 1, 0, 3, 4}; h = {1, 1, -1}; a Obtain the linear convolution of the two sequences. b Obtain the circular convolution of the two sequences. c Obtain the linear convolution of the two sequences using the overlap-and-add method with a partition size of 4. d Obtain a factor of two interpolation of the sequence x with filter h using: (i) upsampling followed by filtering, (ii) the...
Determine the z-transform of the following sequences and their ROCs: a) x(n) = (0.5)" for n>...
Determine the z-transform of the following sequences and their ROCs: a) x(n) = (0.5)" for n> 5, and zero for all other values of n; b) x(n)= (0.5)"[u(n) - u(n-7)]; c) x(n)=(-1)"a"u(n), 0 <a<1.
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.
Problem 4: (a) and (b): Find the z-transform including the ROC for each of the following...
Problem 4: (a) and (b): Find the z-transform including the ROC for each of the following waveforms: [n] 3(금)"u[n] Xa | 지 = (c) Find the z-transfor by m of the impulse response hn] of an LTI system, when h[n] is given h[n] = 5(을)"u[n]. (d) and (e): Using z-transforms, find the responses (yan] and yb[n]) of the system described in part (c) to the inputs (an andn] described in parts (a) and (b
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
a) The transfer function of an ideal low-pass filter is and its impulse response is where...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
6.6a b 6.7c d e of the following irrational z transforms. (a) x(z) = ea", Izl...
6.6a b
6.7c d e
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.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convol...
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the...
3.96 Determine the z-transforms of the following sequences and their respective ROCs: (a) x1[n] = -a"u[-n-1], (b) x2[n] = "Min + 1], and (c) x3[n] = "u-n).
Determine the z-transform of the following sequences and their ROCs: a) x(n) = (0.5)" for n> 5, and zero for all other values of n; b) x(n)= (0.5)"[u(n) - u(n-7)]; c) x(n)=(-1)"a"u(n), 0 <a<1.
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.
Problem 4: (a) and (b): Find the z-transform including the ROC for each of the following waveforms: [n] 3(금)"u[n] Xa | 지 = (c) Find the z-transfor by m of the impulse response hn] of an LTI system, when h[n] is given h[n] = 5(을)"u[n]. (d) and (e): Using z-transforms, find the responses (yan] and yb[n]) of the system described in part (c) to the inputs (an andn] described in parts (a) and (b
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
6.6a b
6.7c d e
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.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
Most questions answered within 3 hours.
-
What is the significance of the constraints in a physical model?
What part do distinct constraints...
asked 1 hour ago -
a student was diagnosed with myopia (nearshightedness). He can
comfortably read a newspaper when it is...
asked 41 minutes ago -
Consider a 3m x 3m window in a house. The thermal conductivity
is reported to be...
asked 1 hour ago -
Why has California been the favorite destination of large number
of secondary migrants?
asked 1 hour ago -
Do not neglect the old for the new. The existing business must
not lose priority simply...
asked 4 hours ago -
Kylie is a single mom with two dependent children,
Tanner, age 7 and Olivia, age 11....
asked 6 hours ago -
Phosphorous + bromine = phosphorous tribromide. If 35.0 g of
bromine are reacted and 27.9 grams...
asked 7 hours ago -
Derive the long wavelength limit of the Planck energy density
distribution
asked 7 hours ago -
Calculate the pH of each of the following solutions.
0.50 M HBr
3.1×10−4 M KOH
4.2×10−5...
asked 11 hours ago -
For the year ended December 31, Depot Max’s cost of merchandise
sold was $85,600. Inventory at the...
asked 11 hours ago -
Week 10 - Professional Memo Assignment
Professional Memo Assignment
Your mission for this week, should you...
asked 11 hours ago -
Write a Python program that stores the data for each
player on the team, and it...
asked 11 hours ago