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Define a Fourier Transform. What are its properties and application areas ? Describe its application in signal processing.
Find the Fourier coefficients of sums of sinusoids by inspection. This involves first finding the fundmental period p of the sum.
Give expressions for kn and An. Given that f(x) = 1 for 0 < x < L/2, obtain an expression for An. Hence, or otherwise, show that.
Using the Fourier transform integral, find Fourier transforms of the following signals.
Do this for the third function, e-3t. That is, chooses C and D such that f3(t) - CF2(t) - DF1(t) is orthogonal to both F1(t) and F2(t).
Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1]
What is the Fourier Transform for the convolution of sin(2t)*cos(2t) .
What is the ratio of the energies contained in the fundamental and third normal modes?
For 0 less than or equal to x less than or equal to 1 with boundary conditions u(0,t)=u(1,t)=0 and initial conditions u(x,0)=u (t)(x,0)=0
A general form of Parseval's Theorem says that if two functions are expanded in a Fourier Series
Let f(x) be a 2pi- periodic function such that f(x) = x^2 -x for x ? [-pi,pi]. Find the Fourier series for f(x).
Find the region in the xy - plane in which the equation is hyperbolic.
Consider a bar insulated on both sides with the ends held at some constant temperature (other than 0) my analysis gives, that as times goes to infinity.
Assume a(t) = a0,b(t) = b0 are constant. Determine the steady state solution uE. How does this ?solution depend on the initial value f(x)?
Verify, from the expression of the solution, that limt?8 u(x, t) = uE (x) for all x, 0 < x < 4.
Solve using separation of variables andD'Alembert. Show solutions in detail. Graph both solution u(x, t) for t = 0, 1, 2, 4.
Consider the displacement of ,u(r,T,t) , a "pie-shaped" membrane of radius a and angle p/3that satisfies:
Solve: Left and Right sides are kept at zero temp. top and bottom are insulated.
Consider the heat equation for a rectangular region, 0 0 .
Subject to the following boundary conditions. Find an expression for the solution if the initial conditions are.
Compute the arithmetic mean for the following data: 8, 2.2, 25, 7, -9, 10, 2, and 5.9.
4 different math books, 2 different Chemistry books, and 6 different physics books are arranged on a shelf. How many different arrangements are possible if:
Assume you have ten (10) very expensive, leather bound books (all different authors) and you want to display these books on your fireplace mantle
A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats
In an experiment, a pair of dice is rolled and the total number of points observed.