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The Fourier transforms of odd and even functions are very important. The reason is that they are computationally simpler than the Fourier transform. Let x(t) = e-ItI and y(t) = e-tu(t) - etu(-t).a. Plot x(t) and y(t), and determine whether they are odd or even.b. Show that the Fourier transform of x(t) is found from x(Ω ) = ∫ (xt )cos (Ωt )dt , which is a real function of Ω , thus its computational importance. Show that X( Ω) is also even as a function of (Ω ).c. Find x(Ω ) from the above equation (called the cosine transform).d. Show that the Fourier transform of y(t) is found from y( Ω) = -j ∫ (yt ) sin(Ωt )dt , which is the imaginary function of (Ω ), thus its computational importance. Show that Y( Ω) is also odd as a function of (Ω ).e. Find Y(Ω ) from the equation above (called the sine transform). Verify that your results are correct by finding the Fourier transform of z(t) = x(t) + y(t) directly and using the above results.f. What advantages do you see to the sine and cosine transforms> How would you use cosine and the sine transforms to compute the Fourier transform of any signal, not necessarily even or odd, explain.
A silicon p-n-p BJT was designed to have doping levels of 1020 cm-3, 1015 cm-3, and 1017 cm-3 in different parts. a. Identify which doping level was intended for the emitter, for the base, and for the collector.
What is the highest frequency of a triangle wave of 20V peak-to-peak amplitude that can be reproduced by an op amp whose slew rate is 10v/s. For a sine wave of the same frequency.
Design the circuit to establish a dc emitter current of 1mA and provide the highest possible voltage gain while allowing for a maximum signal swing at the collector of +-2V. Use +10V and -5V power supplies.
Brown and Vranesic. Problem 6.28 - Repeat Problem 6.26 using T flip-flops. Design a three-bit counterlike circuit controlled by the input w. If w = 1. then the counter adds 2 to its contents, wrapping around if the count reaches 8 or 9.
The parts of this problem refer to the reflection method of solving real transformer problems: A.What is the value of Zload projected into bus (Region) 2 B.What is the total impedance of bus 2 including the projection
If the concentration of free electrons is 10^29 electrons per cubic meter and if they are uniformly dispersed throught the wire, then what is the average velocity of an electron ?
If we want to correct the power factor to 0.9 lagging, what is the value of Q we need to inject.
A chopper is used to control the power flow from a dc source voltage of 125-V to a battery whose voltage is 240-V. The power transferred is 60 kW. Determine the duty cycle and the average input current.
If the machine is driven at a speed of 459rpm to act as a generator of real power, find the rotor current referred to the stator and the real and reactive power outputs of the induction machine.
The received power at a receiver antenna is -38 dBm. If the system impedance is 50 Ohms, what is the voltage at the receiver antenna
Charges +Q and +3Q are seperated by a distance 2m. A third charge is located such that the electrostatic system is in equilibrium. Find the location and the value of the third charger in terms of Q.
Once a week a wagon driver leaves his hut and drives his wagon to the river dock to pick up supplies for his town. At 4:05 PM, one-fifth of the way to the dock, he passes the Temple. At 4:15 PM, one-third of the way, he passes the Preetam-Da-Dhaba..
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