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Let x[n] and h[n] be two real finite-length sequences such that
We wish to compute the sequence y[n] = x[n]∗h[n], where ∗ denotes ordinary convolution.
(a) What is the length of the sequence y[n]?
(b) For direct evaluation of the convolution sum, how many real multiplications are required to compute all of the nonzero samples of y[n]? The following identity may be usefuL
(c) State a procedure for using the DFT to compute all of the nonzero samples of y[n]. Determine the minimum size of the DFTs and inverse DFTs in terms of L and P.
(d) Assume that L = P = N/2, where N = 2ν is the size of the DFT. Determine a formula for the number of real multiplications required to compute all the nonzero values of y[n] using the method of part
(c) if the DFTs are computed using a radix- 2 FFT algorithm. Use this formula to determine the minimum value of N for which the FFT method requires fewer real multiplications than the direct evaluation of the convolution sum
A three-phase, four-wire system operating with a 208-V line voltage is shown in Fig. 12.64. The source voltages are balanced. The power absorbed by the resistive wye-connected load is measured by the three-wattmeter method.
Assume the motor is connected in wyne and that each branch can be represented by a resistance R in series with an inductive reactance X. (a) Calculate the value of R and X. (b) What is the phase angle between the line current
The Power Consumption of a single-phase electric load fed from a 120 V source is represented by: P(t) = 100(1- e -t/10 ) KW where t is the unit of time in hours. Compute the energy consumed by the load over the period of 24 hours.
Use MATLAB to compute the inverse Laplace transform of X(s)=(s^2+2s+1)/(s(s+1)(s^2+10s+50)) and determine the value of x(t) in the steady state. How would you be able to obtain this value without computing the inverse? Explain.
1)A passive high-pass filter is built from a 100 kohm resistor and a 100 nF capacitor. what is its cutoff frequency 2)For the filter in the above question what is its numeric gain at its cutoff frequency
For either the original system or its transpose, determine the difference equation relating the input x[n] to the output y[n]. (Note: The difference equations will be the same for both structures.)
A circuit is needed to divide a 10 Hz signal down to 1 Hz using only a 7493 4-bit counter. Produce a logic diagram for the design.
A power supply, when connected to a radio, provides 5V to the radio. When connected to a lamp, it provides 4V to the lamp. Assume the radio can be modeled as 6ohm resistor and the lamp can be modeled as a 0.7ohm resistor.
placing the compensator or zero such that it will cancel the open-loop pole at -1. For both compensators you design, show the corresponding closed-loop transfer functions and compare the transient responses (P.O. and Ts).
Given x1(t)=cos(t), x2(t)=sign(pt) and x3(t)=x1(t)+x2(t). (a) Determine the fundamentals periods T1and T2 of signals x1(t) and x2(t). (b) Show that x3(t) is not periodic, which requires T3=k1T1=k2T2 for some integer k1 and k2.
Cellular membranes create voltage potentials by seperating thecharged ions. A membrane with 70 mV potential has 1 x 10^4 Na+ ionsflowing through it. Assuming the potential is constant, what is thechange of electrical potential energy experienced b..
Determine the service overcurrent protection device rating and undergrounded and grounded service conductor size. Use XHHW copper conductor and 75oC device terminal ratings and allow for 25% load growth. Do not use larger than 600 kcmil conductor ..
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