Working with the Fourier Transform Derivation.
An electrical signal comprises a single triangular pulse, as shown in Figure A4 as a function f(t) against time t. Derive the Fourier transform of the pulse. Sketch F(w) giving the positions of the points at which F(w)=0 and the magnitude of F(0).
(a) Explain the relationship between the spectral components indicated above and the corresponding graph showing the motion of the surface of the motor plotted as a function of time. What do they represent? (b) Given the amplitudes indicated in the above diagram, copy and complete the table below for the amplitude of the vib ...continues
Find the Fourier series, sketch the graph of the function for 3 periods.
Please see the attached file for the fully formatted function. Find the Fourier series, sketch the graph of the function for 3 periods. Is this a discontinuous graph? Is it an even or odd function, I know there are Fourier series rules for them.
Fourier Transform of a Normal Gaussian curve - 3 PARTS!!!
1) if f(x) is a Gaussian with unit area - show that the scaled and stretched function 1/a * f(x/a) also has unit area - that's the hardest part. The other parts (along with a detailed explanation of this one) are in an attachment as both mathcad v.11 and in an html file - they're the same thing - but if you don't have mathca ...continues
Please see the attached file for the fully formatted problem. Let Y: R --> R be the periodic function whose restriction to [0,1] is X (0,1/2) - X(1/2,1) Y is an odd function. S 1--> 0 Y(x) cos 2pi kx dx = S 1/2-->-1/2 Y(x) cos 2pi kx dx Vk Conclude the the complex Fourier Series...can be expressed in the form... ...continues
Fundamental Theorem of Fourier Series to Express Pi-squared
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Continuously Differentiable Fourier series : Derivatives and Vanishing Conditions
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Fourier Series - Fourier Transform Problem
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Find the Fourier transform of:
3 when 1
Fourier Transform of a Partial Differential Equation
Please see the attached file for the fully formatted problems. Consider the partial differential equation: d3y/dx3 =d2y/dt2 Using Fourier Transforms, reduce this to solving an ODE.
Fourier Series - Uniform and Pointwise Convergence Problem
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