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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.
How do you use the Cayley-Hamilton technique to find the state transition matrix and the state equation output y.
Design the simplest circuit that has three inputs, X1,X2, and X3, which produces an output value of 1 whenever exactly one or two of the input variables have the value 1; otherwise, the output has to be 0.
Calculate: Critical frequency for the input low pass network, and the output low pass network, estimate the values for Cbe, Cjc, Cbc, and Cje. Concider the resistance of the signal sourceRs to be equal to the 1 ohm resister in series with the source.
A beam of X-rays with a wavelength l of 0.15 nm is directed at a crystal whose planes have a spacing of 0.25 nm. How many diffraction peaks (each arising from a different order n) are possible
n the conduction band of a semiconductor, it has a lower valley at the center of the Bril- louin zone, and six upper valleys at the zone boundary along [100]. If the effective mass for the lower valley is 0.1m0 and that for the upper valleys
Design a counter that will execute the numerical sequence 0, 2, 4, 6,repetitively. Unwanted states should be directed into wanted states that give the simplest logic functions. - Identify the number of required JK D-FLIP FLOP;
A solar pond consists of a thin layer of fresh water floating on top of a denser layer of salt water. When the salty layer absorbs sunlight it warms up and much of that heat is held there by the insulating effect of the fresh water above it
A number stored in IEEE single precision floating point format has S=0, E=0111 1101, and F=0.1000 0000 0000 0000 0000 000. What is this number in decimal
Design an inverting singe stage low pass filter with gain = 40 dB, Rin = 10 kΩ , corner frequency of 50 Hz. Determine the max and min gain and the corne frequency for the component tolerances of 5%/ Plot gain vs frequency (Hz) with frequency on a ..
A certain signal is modeled by a continuous Gaussian random process X(t) with mean E {X(i)} = 2 and autocorrelation function R(t, r) = 4 + e-0.5|r|. Compute the covariance function C(t, r). Compute the variance of X(t). Write the PDF for a single ..
A windmill park produces energy at a tension level of 11kV. The park is going to be coupled up with a 11kV net not far from the park. To reduce the loss in transer the tension is tranfomred p at the parka nd down again right before coupling to the..
A polar binary pulse are required with peak amplitude Ap= 1mV, the channel noise is rms 192.3 μV theshold detection not used. 1 & 0 are equally likely. Find the detection error probability. Also find the error probability for a)ON, OF.
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