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1. Consider the sinusoidal signal
x(t) = 8 sin(6Πt + φ0).
Assume φ0 = Π/4 for this question and φ0 = 0 for the following two questions. Compute analytically the spectrum. Sketch the magnitude and phase spectrum.
What is the meaning of "Nyquist rate", and what is the Nyquist rate for this signal? (Consider the signal to be a low-pass signal.)
2. The sampling function
Ts = 1/4, is used to obtain the sampled signal y(t) = x(t) • s(t).
Sketch y(t) alongside x(t) (at least 3 periods). Sketch the magnitude spectrum of y(t). Hint: Explicit computation of the spectrum Y(f) is not required.
3. Assume now Ts = 1/16. The signal x(t) is reconstructed from the sampled signal y(t) using flat-top sampling, giving the reconstructed signal z(t).
Sketch z(t) alongside x(t) (at least three periods). Discuss if the original signal x(t) can be perfectly reconstructed from z(t).
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Behaviour of the functions at their end and midpoints points to suggest features that increase the convergence and those that are bad for convergence.
How much money will Dave and Jane raise for charity
Every convergent sequence contains either an increasing, or a decreasing subsequence.
Solve differential equation of d 2 h /dx 2 =0 using the Galerkin method and considering 0 ≤ x ≤ 3 given that: h = 0 cm when x = 0 m and h = 10 cm when x = 3 m .
Suppose that in the four player game, the person who rolls the smallest number pays $5.00 to the person who rolls the largest number. Calculate each player's expected gain after one round.
Use the Crank-Nicolson procedure to solve the following partial differential equation
State the multiple regression equation
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A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds ranging from 10 miles per hour to 75 miles per hour. The results ar..
Find the probability density function.
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