6) Find Nodal matrix and find Vo(t) for t> 0 using Laplace transformer. 10 www 3u(t) A CO5F 2023 10(1) 10u(t) V
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- write any five properties of Laplace transformer? required name, rule,proof, an example in each propertiesWhat are the limitations of z-transformQUESTION 3 (a) There are 4 different types of transform (i to iv), can be used to represent a continuous and discrete time signal. The chosen types of transfom are selected based on the finite or infinite duration and also the generated signal either periodic or aperiodic. In the table, fill in the blanks with i, ii, iii or iv depending on which transform(s) can be used to represent the signal described. i- Contimuous-time Fourier Series (CTFS) Discrete-time Fourier Series (DTFS) 11- ii- Contimuous-time Fourier Transfom (CTFT) iv- Discrete-time Fourier transform (DTFT) Signal description Transform Continuous time Infinite duration Periodic Discrete time Infinite duration Aperiodic
- Explain the Z-Transform Properties including the Convolution property and Linearity property.transform formula to prove thès -9t e cs Scanned with CamScannerHome Works The - Transform Show. that.Z XcA-m) }. assumeZer Ic 1. show that Z. E ,(m) f Ck-m) 2. Find 2.Tof .. the following a) % { sin wn s b).. Z. cos wn.- c) %{ coihwn} 3. sin wn e Ans: .a). 2_sin w./_C. 2-2 2. com W +.)... 2*-2. cosw/ ( 22- 2 2 copes + 1 ) zz.cosh w./(2?2Z coshw. + 1. d) Zea sin w./ (z²c^ - 22 ea cosw. +. 1.2. Find xin). using. partial. fraction method ·; a . XC2) =. b). X(Z)=. 2 +1 3(2-)(2-) c) Xcz)= lo 5. Use discrete.comvelution to solve . ycz) n= 0, 1, 2, 3 and K= {, 2,5 (z-1) (Z-ē) Plot ycn) vs. n using Graphical method 8 Tabular methed. 6. Write the. difference epuation and realize the system" %3D X(2).: 2. + 5. z+ 22. the diffrences siuation for the systems shown below. -A: rite
- 1. Determine the Canonical form (Standard SOP) for AB + BC 2. Determine the Canonical form (Standard POS) of (A + B)(B+C) 3. Sketch the circuit diagram for a circuit that checks for odd prime numbers for the first 9 numbers ranging from 0 to 8. Use K map method for the simplification of the expression. 4. Use K map method to simplify the following expressions D+ A.C + B.C40 Complete the following exercises in complex arithmetic. a. Find the complex conjugate of (4 +j4), (2 –78), (-5+j2). b. Convert the following to polar form by multiplying the numerator and denominator by the complex conjugate of the denominator and then performing the cpnversion to polar coordinates: 1+l j4 4+j4 2- 8 -5+j2 c. Repeat part b but this time convert to polar coordinates before performing the division.Discuss Phasor algebra / complex number types (rectangular and polar) conversion complex algebra