(1) A binary PCM signaling uses on-off signaling to transmit symbols 1 and 0 (symbol 1 is represented by a rectangular pulse of amplitude A and duration Tb; symbol 0 is represented by no pulse transmission for period Tb). The additive noise at the receiver input is white and Gaussian with zero mean and PSD of N_{0}/2. Find an expression for the average probability of error with matched filtering assuming symbol 1 and 0 occur with equal probability.

(2) An analog signal was sampled, quantized and encoded into a binary PCM wave. The sampling frequency was 10 kHz and the number of representation levels was 256. The PCM signal streamed over a baseband channel. How many digits are used to represent each sample? What is the bit rate? How long does it take to transmit one sample? What is the minimum required transmission bandwidth?

(3) The combination of the transmitter and channel produces a pulse with its amplitude spectrum defined by G(f)H(f) = e^{-|f|Tb}. Determine the spectrum of the of the ideal receiver filter that would eliminate intersymbol interference. Assume ideal Nyquist channel.

(4) In a single parity-check code, a single parity bit is appended to a block of k message bits (m_{0}, m_{1}, m_{k-1}). This single parity bit, b_{1}, is chosen so that the codeword satisfies the even parity rule: m_{0} + m_{1} +.......+ m_{k-1} + b_{0} = 0 (mod 2). For k = 3, set up the 2^{k} possible codewords in the code defined by this rule.

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Find an expression for the average probability of error : Find an expression for the average probability of error with matched filtering assuming symbol 1 and 0 occur with equal probability. |

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Where does the energy for the light come from : Consider an experiment where you produce waves on a string by moving one end up and down with your hand. What is the relationship between the frequency of your hand (ie. the number of times per second you move your hand up and down) and the freque.. |

## Obtain the z transform and find the z transformObtain the z transform and find the z transform - solve the problem for the first 30 samples. Plot both analytical and the numerical results in the same figure. |

## Write a 4-bit up counter with an asynchronous clearWrite a 4-bit up counter. Your counter has a asynchronous clear and when the clear is activated, the counter is reset to 3. The count range is from 3 to 9. |

## How many joules of energy are stored in the batteryA double-A (AA) rechargeable battery is rated at 1.2V, 2100mAh (mili-amp hours) 1- how many coulombs of charge can this battery hold 2- how many joules of energy are stored in the battery |

## Determine the relative probability of finding the electronDetermine the relative probability of finding the electron at the distance (a) 12 A beyond the barrier, and (b) 48 A beyond the barrier, compared to the probability of finding the incident particle at the barriers edge. Plot the wave function for .. |

## Calculate the value of the thermal voltageCalculate the value of the thermal voltage, VT at -400C, 00C, +400C and +1500 C. At what temperature is VT exactly 25mV |

## Determine what is the bandwidth of the output signalA device with input x(t) and output y(t) is characterized by: y(t) = x2(t).An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5kHz is applied to this device. What is The bandwidth of the output signal. |

## Derive a hazard-free realization of the functionDerive a hazard-free realization (and show that it is hazard-free), of the function AC+BCD+A'B'D' using only 2-input NAND gates, assume inputs are available uncomplemented and complemented. |

## Why the circuit must have a high input impedanceI)Design a circuit that gives you the following relation between input and output Vout = 2.17Vin + 5 Here are the constraints you need to work with: 1) Only one power supply that gives ±12V is available 2) Available op-amps run on ±12V |

## Design a butterworth digital filter using bilinear transformThe specificationof the desired low pass filter are A min=23 dB, A max=5dB, P=02and S=0.6. Design a Butterworth digital filter using bilinear transformation. |

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## Find resistance of copper conductor of equal cross sectionIn a toaster the heating unit is a Nichrome wire whose resistance is 660 micro-ohm-CM/ft and resistance is 20 ohms.Determine the resistance of copper conductor of equalcross-section, but 10 times as long as the Nichrome wire. |

## What will the pressure be if the temperature is raisedA rigid container holds hydrogen gas at a pressure of 3.0 atm and a temperature of 2.0° C. What will the pressure be if the temperature is raised to 10° C |

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