2. Investigate the stability of the following characteristic equation using bilinear transformation
$$ G(z)=\frac{(z+0.4)}{z^{3}-1.5 z^{2}+1.2 z-0.6} $$(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation F:C→C is a mapping from the z-domain to the Laplace domain, defined as s唔倫-1) without loss of generality, let us 7 17-) Without loss of generality, let us Td 1+z-1 assume that the scaling factor Ta is not important here, so we can choose 1-z-1 Ta = 2 to simplify our discussions; hence, s(z) =-. 1+z-1 (a) Show that the transformation maps the unit circle in the...
Problem # 1 . Topics: Bilinear Transform Assuming parameter k-1.2 and using the Bilinear Transform, map the following poles in the s-plane to the z-plane. Give z-plane. magnitude and angle for the corresponding poles in the S=-0.5 +0.5j → z=
Problem #2: Transform the following characteristic equations into the bilinear plane and use the Routh Array to determine stability. 2. A(Z)-4-0.97.3-0.23% + 0.222+0.05
9. The following causal IIR digital transfer functions were designed using the bilinear transformation method with T = 0.5. Determine their respective parent causal analog transfer functions. 4-2 +3z + 4) (a) G() = 10-2 + 4z + 6 5473 +62-2 +262 +18 (b) G(2) = (32 + 1)(1222 – 4z +8)
Given an RC lowpass filter with R=200K and C=4uF and the bilinear transform equation as shown: 2 (1 – z-1) S=T. (1 + z-1) Calculate a discrete filter approximation using a bilinear transformation in terms of 7;
(a) Find the bilinear transformation that maps the point (0), (1), (i) into the point (1+i), (-i), (2-1). (b) Show that the function sinhz is an analytic function. 42-3 Where C is the circle such that Evaluate the integral Sc(2-2) (1) C:Z1 = 1 (2) C:[Z= 1 (3) C:Z) = 3 200
control systems 1) Using Routh Hurwitz Stability Criteria, determine whether the following system of equation is stable or not. a) S4+253+3S2+45+5=0 2) Using the Routh Hurwitz stability criterion, determine the range of K for stability of the following characteristic equation. a) s4+2s8+(4+K)s2+9s+25=0 3)Sketch the root-locus of the following systems a) G(s)H(s) = s(s+1)(s+2) b) G(s)H(s) = 52(8+3.6) K(5+1)
A digital low pass IIR filter is to be designed with Butterworth approximation using the Bilinear transformation technique having the following specifications:(i) Passband magnitude is constant within 1 dB for frequencies below 0.2 π.(ii) Stopband attenuation is greater than 15 dB for frequencies between 0.3 π to π. Determine the order of the filter, cutoff frequency, poles location and transfer function of digital filter in order to meet the above specifications.
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai passos frequencies up to f,, 12K1Iz with ınaximiin kxz; ofǎ_ (1,1A and stops frequences from, fs-24KHz with a minimum loss of δ2-0.3. The sanpling frequency isf 100KHz. Find the Butterworth Filter Order(N), 3-dB Cutoff frequency and the numerator and denominator coefficients of the H(z) by hand-calculation. Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai...
1. Find the critical load Pcr using the bifurcation approach. 2. Investigate the stability behavior of the asymmetric spring-bar model. Please provide me with detailed solutions.... 1. Find the critical load Per using the bifurcation approach. 0.5L 0.51 0.5 k,t s2 2. Investigate the stability behavior of the asymmetric spring-bar model ks 45" 1. Find the critical load Per using the bifurcation approach. 0.5L 0.51 0.5 k,t s2 2. Investigate the stability behavior of the asymmetric spring-bar model ks 45"