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# Electrical Engineering

### Analysis of discrete time waveforms in z domain

A discrete time domain signal x(n) - u(n) - u(n-10) is decomposed and plotted. It is then examined in the z domian by appropriate transformation and algebraic manipulation. From the z transform representation the poles and zeros are determined and plotted in the z domain

### From a given z transform X(z) = {1- z^-10}/{1 - z^-1} the discrete time domain form x(n) is deduced using complex manipulation and inverse transforms to arrive at x(n) = x(n-1) + u(n) - u(n-10) The second part shows how to convert the given X(z) into a polynomial in z as X(z) = 1 + z^-1 + z^-2 + .... + z^-9 Finally the third part goes on to show the poles and zeros of X(z) and plot these in the complex z plane as zeros , z(n) = 0.2n*pi, magnitude 1, Poles at 0

From a given z transform X(z) = {1- z^-10}/{1 - z^-1} the discrete time domain form x(n) is deduced using complex manipulation and inverse transforms to arrive at x(n) = x(n-1) + u(n) - u(n-10) The second part shows how to convert the given X(z) into a polynomial in z as X(z) = 1 + z^-1 + z^-2 + .... + z^-9 Finally the th

### Mapping of Poles Into Complex Z and W (Laplace) Planes

Given poles(in complex notation) are mapped to both the z and s (Laplace) planes. The transforms between the different planes are developed and the mappings grpahically shown for a number of examples. See the attached file.

### Safety, and Reliability Concerns and Risk

1(a) Are safety and reliability concerns more or less important in an embedded application when compared to a non-embedded system? Why or why not? 1(b) What is risk? Give several examples of low and high risk embedded applications. Identify several embedded applications that may either be high or low risk depending on their o

### Digital Circuits in Counters

a) A 4 bit binary up/down counter is set to zero. if the down mode is selected and five clock pulse applied, the counter value will be? b) A production plant has a requirement for a counter that will count 4,000 times before recycling and starting over. How many flip flpos are required?

### Damping factor, Damped frequency, Natural frequency

For the waveform shown in attached figure, estimate (a) the damping factor, (b) the forced or damped frequency of oscillation, and (c) the natural or undamped frequency.

### Pseudo Code

Write the pseudocode for a program that does the following: The user is prompted to enter an integer between 1 and 1000. When the user enters the integer, the program uses a repetition control structure to validate whether the integer is within the proper range; otherwise, the prompt is continuously redisplayed to the user un

### Sampling rate, Systems function, Region of convergence

** Please see the attached file for the complete problem description ** 1. If the -3dB cut-off point for the filter shown (in the attachment) occurs for a real frequency of 200Hz then what should be the sampling rate (samples per sec)? 2. The difference equation for a digital filter is given by: y(n) = 2y(n-1) + y(n-2) + x

### Bode magnitude plot

Please provide a step-by-step solution showing all the working. 1. Which of the following systems has the bode magnitude plot shown below? 2. Which of the following systems has the unit step response shown below? 3. Which of the following systems has the bode plot shown below? Please see the attachment for the respec

### Methods used to eliminate noise from a spatio-temporal signal

Name and describe, in detail, 2 methods used to eliminate noise from a (spatio-temporal) signal. This question requires a clear, detailed explanation of the methods. Mathematical equations can/should be minimized. The application under consideration are signals from an EEG or MEG reading.

### S-R flipflops have a forbidden state that makes them hard to use.

S-R flipflops have a forbidden state that makes them hard to use. Some designers switched to the following flipflop instead. Fill in the timing diagram shown. Then, describe what the flipflop does in each of the cases of M and N (i.e explain what the output does for each combination of the inputs). Note that filling in this timi

### This is a Java application that prints out numbers.

Write a Java application that prints out numbers 2, 4 and 6 in row 1, numbers 3, 5 and 7 in row 2, numbers 8, 10 and 12 in row 3 and numbers 9, 11 and 13 in row 4. There should be an underline followed by a row of numbers that adds the numbers in the respective columns. The program should print out the information as follows:

### Three Fourier analysis of systems problems

Fourier Analysis of Systems: 1. A linear time-invariant continuous-time system has the frequency response function H(Ï?)=5cos(2Ï?), compute the system's impulse response h(t): 2. A signal with the highest frequency component at 10 kHz is to be sampled. To reconstruct the signal, the sampling must be done at a minimum f

### System analysis and design

Elmwood College Situation: The school is considering a new system that will speed up the registration process. As a systems analyst, you are asked to develop a plan for fact-finding. a. List all the possible techniques that you might use. b. Describe an advantage for each technique. c. Suppose the development budget is t

### Transfer Functions of Simple Filters

Recall that the general formula H(w) = Vout(w) / Vin(w) can be used in several ways: for example, from the known transfer function and the output, you can calculate the input signal of the circuit. Part 1. In the circuit shown in the diagram, R = 1 kOhm and C = 50 nF; at 10 kHz, the output signal amplitude equals Vout = 5 Vp

### Z-Transform of the Sequence & Indicate the Region of Convergence

The z-transform of x(n) is X(z) = 1 / (1 + 0.5 z^-1), |z| <= 0.5 . Determine the z-transform of the following sequence and indicate it's region of convergence. x1(n) = x(3-n) + x(n-3). See the attached file.

### Find and Express the Z Transform as a Rational Function

For the following expression: x(n) = 3 (0.75)^n cos(0.3 pi n)u(n) + 4 (0.75)^n sin(0.3 pi n) u(n), Please calculate and express the Z transform as a rational function Z^-1 and work out the ROC.

### Routh Hurwitz stability criterion is used here to determine stability of the system.

Question 1: Determine if the following characteristic equation represents a stable system: s^3 + 4 s^2 + 8 s + 12 = 0 Question 2: Determine if the following characteristic equation represents a stable or unstable system: s^3 + 8 s^2 + 14 s + 24 = 0

### Design of a PD controller for a double integrator system

The block diagram of a control system is given in the attachment.The inner loop is positive feedback, i.e. Ks>0, and hence the system is unstable. Adding a P-D controller on the forward channel and a unity negative feedback, one can stabilize the system. Find: 1. The conditions of Kc and Tc to stabilize the system. 2. T

### Twenty voice signals are to be multiplexed and transmitted over twisted pair.

Twenty voice signals are to be multiplexed and transmitted over twisted pair. What is the bandwidth required (in bps) if synchronous time division multiplexing is used, along with the standard analog-to-digital sampling rate, and each sample is converted into an 8-bit value?

### Impulse response using inverse discrete-time Fourier transform.

An ideal low-pass filter is described in the frequency-domain by H_d(e^(jw)) = 1 . e^(-jaw) , |w| <= w_c 0 , w_c < |w| <= PI where w_c is called the cutoff frequency and a (denoting symbol alpha) is called the phase delay. Determine the ideal impulse response h_d(n) using the

### CMRR, RC-lag circuit, Bode plot, Open-loop midrange gain

4. A certain op-amp has an open-loop voltage gain of 100,000 and a common mode gain of 0.2. Determine the CMRR in dB. 5. Find the open loop gain and phase shift for an RC-lag circuit at the following frequencies: (i) 1 Hz (ii) 10 Hz (iii) 100 Hz (iv) 1000 Hz (v) 10000 Hz. Plot the curve of phase shift versus frequency curve i

### Electrical Engineering: Op-Amp

1. Show that gain rolls-off at -6 dB/octave for a passive LP filter. 2. (a) Write down the expression for the frequency-dependent open-loop gain of an operational amplifier. Sketch the magnitude of the open-loop gain of an operational amplifier as a function of frequency. Explain what is meant by a `single-lag' response of an

### Design a synchronous counter using J-K flip-flops

Design a synchronous counter using J-K flip-flops that will count from 0010 to 1101 repetitively. a) Construct the "present state - next state" truth table. b) Complete the required K-maps for the design. c) Derive the minimised Boolean expressions for the J-K inputs. d) Draw the logic diagram for the counter.

### Slew rate, CMRR, Bandwidth, Critical frequency, Closed-loop gain

Please refer to the attachment for the figures mentioned in these questions. 1. When a pulse is applied to an op-amp, the output goes from -40 V to +5 V in 0.6 microseconds. What is the slew rate? 2. A certain diff-amp (differential amplifier) has a differential voltage gain of 1500 and a common-mode gain of 0.5. Determine

### Block diagram and equations for control system water fill

Develop a control system to fill a container with water after it is emptied through a stopcock at the bottom. The system must automatically shut off the water when the container is filled. Please show a block diagram explaining the operation of the developed control system.

### Laplace transform, Fourier transform, Unit-pulse response, Impulse response, DTFT, Differential equation

Please see the attachment for all the questions with proper symbols/notations. 1. Compute the Laplace transform of e^(-10t)cos(3)u(t) . 2. Compute the z-transform of the discrete time signal defined by: x[n] = &#948;[n] + 5&#948;[n - 1] 3. Compute the inverse Laplace transform of X(s) = (s+2) / (s^2+7s+12) . 4.

### Gain of compensator, steady-state error and range of gain

Please see the attachment for complete questions. 5. Find the gain (K) of the compensator so that overall closed-loop response to a unit step input has a maximum overshoot of 25%, and a 2% settling time of 0.1 sec. 7. Given the plant or process for a unity feedback system, find the steady state error for the given input.

### Use Laplace transforms to compute the solution to the differential equation.

Please walk me through these problems step by step. 1. Compute the Laplace transform of e^(-10t) = u(t). 2. Compute the inverse Laplace transform of: X(s) = (3s^2+2s+1) / (s^3+5s^2+8s+4) 3. Use Laplace transforms to compute the solution to the differential equation given in the attachment.

### Write down an expression for the voltage waveform, and sketch the waveforms of the harmonic components.

An a.c. voltage, V, comprises of a fundamental voltage of 100 V rms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging. (i) Write down an expression for the voltage waveform. (ii) Sketch the waveforms of the harm