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Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (...
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 causal, linear-phase, real-valued FIR filter has zeros at z = 0.5, z = 1, and z-ej2, a) Supp...
Digital Signal Processing
:) A causal, linear-phase, real-valued FIR filter has zeros at z = 0.5, z = 1, and z-ej2, a) Suppose the gain factor for this filter is po 1. Specify the impulse response of this filter assuming the length of the filter needs to be as small as possible. b) What is the type of this FIR filter? A causal, linear-phase, real-valued FIR filter has zeros at z - 0.25e 3 and z - 2 a Assuming...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
Please solve the following with full steps. 2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three no...
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the pole zero diagram of this filter. 2) Sketch magnitude and phase spectrum (not decibels) 3) Could you comment on the type of filter (LP, HP, BP or BS) and justify your answer?
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the...
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (8-0) is 1, that is, a. Note that H (θ)-H(z)IFeje and H(θ)18-0-1 is equivalent to H(z)IF1-1 b. Plot the pole-zero diagram. c. Plot the magnitude response |H(6) d. Plot the phase response H(6) e. Find yin) as a function of x(n), x(n-1), x(n-2), x(n-3),x(n-4), x(n-5),x(n-6),x(n-7)
5. The z transform is a very useful tool for studying difference equations. Often difference and ...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z...
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1- +2-2) a. Draw the pole/zero diagram for H(z), noting any pole/zero cancellations. b. Sketch the magnitude response H'(o). c. Show that H(z) is FIR by finding h(n) for all n. d. Find the dc gain of the filter.
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1-...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
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...
Digital Signal Processing
:) A causal, linear-phase, real-valued FIR filter has zeros at z = 0.5, z = 1, and z-ej2, a) Suppose the gain factor for this filter is po 1. Specify the impulse response of this filter assuming the length of the filter needs to be as small as possible. b) What is the type of this FIR filter? A causal, linear-phase, real-valued FIR filter has zeros at z - 0.25e 3 and z - 2 a Assuming...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the pole zero diagram of this filter. 2) Sketch magnitude and phase spectrum (not decibels) 3) Could you comment on the type of filter (LP, HP, BP or BS) and justify your answer?
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (8-0) is 1, that is, a. Note that H (θ)-H(z)IFeje and H(θ)18-0-1 is equivalent to H(z)IF1-1 b. Plot the pole-zero diagram. c. Plot the magnitude response |H(6) d. Plot the phase response H(6) e. Find yin) as a function of x(n), x(n-1), x(n-2), x(n-3),x(n-4), x(n-5),x(n-6),x(n-7)
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1- +2-2) a. Draw the pole/zero diagram for H(z), noting any pole/zero cancellations. b. Sketch the magnitude response H'(o). c. Show that H(z) is FIR by finding h(n) for all n. d. Find the dc gain of the filter.
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1-...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
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