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?
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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 transfer function H(z)? Draw the pole-zero plot.
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
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-...
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...
What kind of filter has poles in the imaginary left half plane? (Low pass, high pass, band pass, or band reject). A brief explanation of the transfer function(s) would be great, I am having a hard time understanding the concept behind this. Thank you.
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)
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...
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...
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...
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain of 1. Find the difference equation for this system. Show all work. Z - plane 0.5 -0.5 0.5e
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain...