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a) Show (prove) that the signal 3^j2t is an eigenfunction of any LTI system, and nd the formula for the eigenvalue. That is, use the convolution integral and simplify to show that if you input 3^j2t into an LTI system with impulse response h (t ), then the output is 3^j2t multiplied by some scalar that does not depend on time (this scalar is the eigenvalue corresponding to this eigenfunction).
b) What is the formula for the eigenvalue from part (a)?
c) If h (t ) = d(t - 7) + d(t + 7), calculate the eigenvalue for the system, putting your answer in the form a cos(b ).
Consider a network with a driving-impedance Z. (1) Find expression for P and Q. (2) Find p(t) in terms of P and Q. (3) Suppose that the network is a series RLC. Interpret the result in part (2).
A random variable X is normally distributed with mean u = 10 and standard deviation sigma = 1.5. Find the following probabilities: A. P(8 or equal 8.5).
1. Find the transfer function 2. Find the Laplace transformation of the output when x(t)=sin(t)u(t) 3.Find the output by taking the inverse Laplace transform of part 2.
A 1.0 dc voltage source is connected across a 10 ohm resistor. What is the current through the resistor if (a) the voltage source is ideal (b) the voltage source has internal resistance 0.1 ohm (c) internal resistance 1.0 ohm
Explain briefly from what you notice about the digital output values in (a) why a digital output value of an A/D converter is rarely the exact same digital value as the analogue input value.
An input signal of 10 sin (2pi 1592t+0degrees) is applied to a series RC circuit with resistor R =1000ohm and capacitor C= 0.1 uF. The current flow through the capacitor is a. 10mApk angle 90 degrees b. 5mApk angle 45 degrees
find a minimal two-level NAND realization for each of the following switching functions. a) f(A,B,C) = sum m(0,2,3,7) b) f(A,B,C,D) = sum m(0,2,8,10,14,15) c) f(A,B,C,D,E) = sum m(4,5,6,7,25,27,29,31)
What functions must the communications stations perform? Repeat for ring and star.
A shunt regulator utilizing a zener diode is biased on through a 100 resistor. Determine the change in the regulated output voltage for the two situations below: a) VI changes +2.0 V, ILoad constant b) ILoad changes +100 mA, VI constan..
A (3V, 300mA) flashlight bulb is to be used as the dial light in a 120V radio. What is the resistance of the resistor that should be connected in series with the flashlight bulb to limit the current
A PWM is used in 8-bit mode to produce a signal with a 1 msec period and 60% duty cycle. Determine the value required for any pre-scaling, and the values for the period, and duty cycle registers. The E-clock is 24 MHz.
A linear CW product detector local oscillator has a 500 Hz error while detecting an AM signal. What will the receiver's output sound like What if the receiver is listening to a DSB or SSB signal
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