A filter has two poles at -0.6±0.8j and a zero at -1 on the
z-plane. The DC
gain is 1. What is the transfer function H(z)? Draw the pole-zero
plot.
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A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The...
A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The DC gain is 1. What is the difference equation of the filter in the time domain?
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
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)
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-...
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 (9-0) is 1, that is a. Note that H (θ) = H(z)IFeje and H(θ)le=0- 1 is equivalent to H(z)1-1 -1
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. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
a) List the relative attributes of using digital processing techniques compared to traditional analogue hardware for signal processing. [5 marks] b) Sketch a z-plane diagram including the unit circle. You have four Poles and two Zeros that you can place on the z-plane diagram. Place them in a position which would provide a digital band-stop filter characteristic with the 'notch' at a n/2 Justify your placement of the poles and zeros. 5 marks] c) The z-plane pole-zero plots of two...
7.7 A dynamic system has 0 as its zero; -1 (order three of multiplicity), -2 (order two of multiplicity) as poles, and a gain of 14. Use MATLAB to calculate the corresponding transfer function of this system then reconvert the obtained transfer function model into a zero-pole-gain model. 7.7 A dynamic system has 0 as its zero; -1 (order three of multiplicity), -2 (order two of multiplicity) as poles, and a gain of 14. Use MATLAB to calculate the corresponding...
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...