(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
(Bilinear transformation and all pass systems in the Laplace domain)
(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...
2. Investigate the stability of the following characteristic equation using bilinear transformation
$$ G(z)=\frac{(z+0.4)}{z^{3}-1.5 z^{2}+1.2 z-0.6} $$
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.
Find the time domain equations for the following frequency domain equation by using inverse Laplace transformation. 52 +55+6 (s+4)(s+1) 8(s+1)(s+3) s(s+2)(s+4) (3) 552 +7s+29 s(s2 +45+29) s(s+4)(s2 +65 +10)
Purpose: Use Laplace transforms to find the time domain response of a RLC band-pass filter to step and impulse inputs Vout Vin L=27 mH For the RLC circuit above Find the s-domain transfer function: Find the impulse response h(t) H(s) = Vout(s)/Vin(s) · These operations must be performed by hand using Laplace transforms, do not use MATLAB or a circuit simulator. We will verify your hand calculations in lab. Hints: To find the transfer function, find the equivalent impedance of...
(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
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;
What is the domain of the laplace transform
What is the domain of the Laplace transform L{t+ e-t sin(-3t) + 2e-2t} ? (A) (B) 8>0 -~<s<co (C) S>-1 (D) 8>-2
1. what condition signal can be transformed by laplace and fourier? 2. what is the weakness of transformation laplace in transform signal from time domain and frequence domain? 3. role of ROC in transformation laplace?
Complex Variables Problem Set :
If w_1 = w_1 (Z) = a_1 Z + b_1/C_1 Z + d_1, w_2 = w_2 (Z) = a_2 Z + b_2/C_2 Z + d_2, then w_1 w_2 (Z) = w_1 c w_2 (Z)) is also a bilinear transformation. if w_1 (Z), w_2 (Z), w_ (Z) are bilinear transformation, the w_1(w_2 w_3 (Z)) = (w_1 w_2) w_3 (Z) for any bilinear transformation w_1 (Z), there exists that w_1 (w_2 (Z)) = w_2 c w_1 (Z))...