. [20%] Using the definition, compute the z-Transform, and find and sketch the poles and zeros...
3. (10 pts) Find the poles and zeros of the following function
and sketch them in an s-plane.
?(?) = 6?? + 7? + 2
6(?? + 9? + 14)(2? + 1)
3. (10 pts) Find the poles and zeros of the following function and sketch them in an s-plane. 6s2 + 7s + 2 H(S) 6(52 + 9 + 14)(2s + 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...
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write the formulas for its Z Transform, X(e), and Region of Convergence, RoCr (b) List the values of all poles and all zeros. (c) Sketch the pole zero diagram. Label both axes. Give key values along both axes. sin ( (-n))u-n]. (Hints: cos(π/3) (5) x1n] , 1/2, sin(π/3)-V3/2) ,"
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following:...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
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...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Question 1 10 points Using the definition of the transform, determine the transforms for each of the following signals. Sketch the pole-zero plot and indicate the region of convergence. (a) (5 points) (-3)"[n-2 () (5 points) "0(9) 15 points transforms for each of Question 2... Using 3-transform pairs and properties tables, determine the the following signals. (a) (5 points) un-un-2 (b) (5 points) -- [n - 2 (e) (5 points) nyin-1 ... 10 points Question 3 Find the inverse (a)...
please write neatly
Find Poles and zeros, sketch the magnitude (dB) and phase angle plot for the following transfer function with proper scales 400m s(s + 2n) A(S)s (s + 0.2n)2(s + 20m) (s + 200r) (convert to frequency, Hz, from radian frequency) Poles: Zeros: Draw the bode plots in scale, and mark all slopes and dB value for slope 0 (convert to frequency, Hz, from radian frequency) Freq(Hz) Freq(Hz) 80