5 Simplify the following Boolean function F, together with the don't-care conditions d, and then express the simplified function in sum of products: (a) F (x, y, z) = E(0, 1, 2, 4, 5) %3D d (x, y, z) = E(3, 6, 7) (b) F (A, B, C, D) = E(0, 6, 8, 13, 14) %3D d (A, B, C, D) = E(2, 4, 10) (c) F (A, B, C, D) = E(1, 3, 5, 7, 9 15) d (A, B, C, D) =E(4, 6, 12, 13)
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- a) Y(ω) = 1/(5+jω) The expression above defines the frequency domain signal Y(ω) from a time domain signal y(t) i) Determine the imaginary & real parts of Y(ω). ii.Determine the signal y(t) that produced the signal Y(ω). b)What are the 3 areas of application of i.Signals ii.Systems c) Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.Draw a circuit that performs the function given by the following truth table: Please write clearly, and include K-map, function expression, and explain component choice(s). A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1I need help with the question below Consider a causal LTI continuous system described by the differential equation y′′(t) + 3y′(t) + 2y(t) = x(t) where y(t) is the system output and x(t) is the input.1. Find the transfer function H(s) of the system.2. Find its poles and zeros. From its poles and zeros, determine if the system is BIBO stable or not.3. If x(t) = u(t) and initial conditions are zero, determine the steady-state response yss(t)4. If the initial conditions were not zero, would you get the same steady state?. Explain
- Calculate the range of values K will take for the steady-state error to be ??? ≤ 0.04 when the input of the system is ?(?) = ?. Calculate the range of values K will take for the damping ratio to be 1>ξ ≥(1/2√6). Calculate the damping rate ξ and the undamped natural frequency ?? so that ? = 0.5Examine the stability of the system given by the characteristic polynomial Δ(s)=2s^3+4s^2+ s+1 using the Routh-Hurwitz criterion.: If F(s) = s 4+ 5s3+20s 2 + 40s + 50 , Investigate the stability of this system
- a) get the equation of motion by drawing the free body diagram of the given system.b) get the transfer function of the system. Ɵ(s)/T (s) = ?Show all decals in detail.A)Perform the N=5 point circular convolution of x and h using DFT. B)Perform the N=5 point circular convolution of x and h in time-domain.1-)Examine the graphs of the DSB (t) and VSB (t) signals in the time space. What are the differences?2-)How many sine waves does the resulting VSB signal contain? What are the frequencies of these signals?
- A continuous time signal, x(t) = sin(20πt) + cos(40πt), is sampled uniformly at intervals of T to obtaina discrete time signal,x(n) = sin(πn/5) + cos(2πn/5).a) What is the value of T assuming no aliasing has occurred?b) Assume both frequency components have been aliased. In this case, is your choice of T unique? If not,specify some choices of T consistent with the information given1. A real value signal x[n] is said to be antisymmetric ifa. x(n) =x(−n)b. x(n) = x(−n)c. x(n) =−x(n)d. nothing is right 2. If x(n)={....0,0,2,−1,3,7,?,2,−3,0,0........... .............} and y(n)= {....0,0,1,−1,2,−2,?,1,−2,5,0, 0 ............................} then the cross correlation x(n) and y(n) is? a. {10,9,19,36,−14,33,0,?,13,−18,16,7,5,−3} b. {10, −9,19,36, −14,33,0, ?, 13, −18,16, −7,5, −3} c. {10,9,19,36,14,33,0, −?, 13, −18,16, −7,5, −3} d. {10,−9,19,36,−14,33,0,−?,13,18,16,7,5,−3} 3. What is the relationship between the analog signal frequency F and the digital signal frequency f? (T is the period of the sampling period)a. F =f∗Tb. F = F*Tc. No connectiond. Nothing is right 4. If the signal x(t)=cos(2∗pi∗40∗t) is sampled with a sampling frequency of 20 Hz, what signal will be produced?a. cos(pi * n)b. cos(2*pi*n)c. cos(4*pi*n)d. cos(8*pi*n) 5. What is the minimum sampling frequency that must be used to sample the signal x(t) = 3cos(50 * pi * t) + 10sin(300 * pi * t)…Derive the expression of the equivalent circuit. (R1;=5 kΩ ,R2=10 ΚΩ, rπ, =10 kΩ)