Please help me in solving this problem. Please see attached file for full problem description. Using Mathematica and computer facilities express the function f(x) in terms of Fourier series expansion and show that the series converges as the number of terms increases: f(x) = x e-x/4 sin(x/3) -π < x < π
Please see attachment. 1. What is the Fourier Transform for the convolution of sin(2t)*cos(2t). 2. Compute the inverse Fourier transform for X(w)= sin^2*3w 3. A continuous time signal x(t) has the Fourier transform X(w) = 1/jw+b where b is a constant. Determine the Fourier transform for v(t) = x*(5t-4)
On attachment 111 do problems 14, 16, 20, 24 On attachment 22 do problems 2, 7, 8, 11, 12 Show steps as needed.
Find the Fourier series expansion of the functions: f(t) = 1 if Pi/3<|t|<2Pi/3 0 everywhere else f(t) = 1 Pi/3 < t < 2Pi/3 -1 -2Pi/3 < t < Pi/3 0 everywhere else In the interval [-Pi , Pi]
Please see the attached file for the fully formatted problems.
The question is the example on page 2 of the attachment (entitled 'Uniform Transducer'). it states that the centre of the finger is at z'=L/4. I assume this is an arbitrary position. For Eq (2.4.6), the contribution from the left-hand finger is added. I'm not entirely sure how this equation is arrived at. It does not look like a
Please see the attached file for the fully formatted problems. You don't have to worry about (iii).
Suppose f(x) has the Fourier transform F(ω). If a ≠ 0 show that f(ax) has the Fourier Transform 1/|a| F (ω/a). Please see the attached file for the fully formatted problems.
I am having difficulty computing u(x,t), also interpretation when e -> 0 See attached file for full problem description.
Solving Partial Differential Equations : Laplace Transforms, Fourier Transforms and Separation of Variables
Please use: 1.) LaPlace Transform and 2.) Fourier Transforms methods and 3.) our old friend separation of variables with eigenvalues expansion to solve each problem. It is not necessary to evaluate an inverse transform. Where convenient, show any solution as a convolution of two functions and indicate how these functions are det
See attached file for full problem description. Question 5 is also a proof, but requires a further matlab plot.
Let f (x) = |x| for x greater or equal to -1, less than or equal to +1 a) Write the Fourier series for f (x) on [-1,1]. b) Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1] c) Determine f'(x) and write it's Fourier series on [-1,1] d) Compare b and c. key
We use the Fourier expansions of certain poynomial functions to compute the sum of some useful numerical series. The formulas are quite general and give, at the end, the Fourier expansion of every polynomial function. By the way, these formulas can be also used for a numerical approximation of pi=3.14....
Functions, Interval. See attached file for full problem description. Given the set of functions f1(t) = A1*exp(-t) f2(t) = A2*e^(-2t) Defined on the interval (0, infinity). (a) Find A1 such that f1(t) is normalized to unity on (0, infinity). Call this function PHI_1(t). (b) Find B such that PHI(t) and f2
Using the Fourier transform integral, find Fourier transforms of the following signals. xa(t) = t *exp(-αt) * u(t), α > 0; xb(t) = t2 * u(t) * u(1 – t) xc(t) = exp(-αt) * u(t) * u(1 – t), α > 0;
Please see the attached file for the fully formatted problems. ODE: 1. Solve ()'sinyxy=+. 2. Find the complete solution of the ODE ()()42212cosyyyx−−=. 3. Find the complete solution of the ODE ()46sinyy−=. 4. Find a second order ODE whose solution is a family of circle with arbitrary radius and center on t
The sum of the infinite series, 1/2^2 - 2/3^2 + 3/4^2 - 4/5^2 + ... is given as pi^2/12 - log 2 on pages 64-65 in the book "Summation of Series" by L. B. W. Jolley, 2nd ed., 1961, Dover Pubs. Inc. (the ^ symbol denotes exponentiation in the above series and sum). For most of the series in his book, he lists a source (referen
From equation 6 of the attached, derive equation 7. In the expression for s(v), the natural log does not apply to the term [(v-vo)/(dv/2)]^2 , should just be ln(2). Yes, the limits from minus infinity to plus inifinity are adequate. Thanks for the help!
Fourier coefficients / b1, b2, b3, b4, b5... b11. -------------------------------------------------------------------------------- I have an output of an electronic device (full wave rectifier) that gives a sine wave with the negative part transposed symmetric to xx so that the function is always positive. I have to find the f
(See attached file for full problem description) For sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, so N=8 Using above x[n]: a) stem(x); b) Use the shift theorm to plot x delayed by 1, 4, 5, 6, and 8 samples, and plot the result for each. Remember the shift theorem says a delay by t0 seconds is equal to multiplying the spe
Please see the attached file for full description. Calculate by hand the X(omega), DTFT of the sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, zero else. Using Matlab, plot the real and imaginary components of your result for X(omega) for omega=0:0.01:2*pi, one plot for the real, one part for the imaginary. On the same plot
Using Fourier transforms where possible, derive the Fourier transforms of the following functions using the relationship: a.) f(x) = exp[i2po(x/lamda)sin(theta)] b.) f(x) = exp(- /ax/ ) See the attached file for full description.
Find the inverse Fourier transform of each of the following Fourier transforms: X(x) = jw The answer I have is x[n] = (-1)^n / n (for n not equal to zero) 0 (for n = 0) I don't know how to get there.
Define a Fourier Transform. What are its properties and application areas ? Describe its application in signal processing.
Find the fourier transform of x^k, where k is a positive integer and x is a single real variable.
Use tables and the scaling and time-shift property to find the Fourier transform of the signal below (which is zero for all other values of t than those shown, that is, it's not periodic) Plot the magnitude of the spectrum of this signal. Hint: Find the transform of the pulse centered around t=0, then use the time-shift p
Find the Fourier series in trigonometric form for f(t) = |sin(pi*t)|. Graph its power spectrum.
(See attached file for full problem description)
8. The first three Legendre polynomials are P0(x) = 1, P1(x) = x, and P2(x) = 1/2(3x2- 1). If x = cosθ , then P0( cosθ ) = 1 and P1( cosθ ) = cos θ . Show that P2( cosθ ) = 1/4( 3cos2θ + 1 ). 9. Use the results of problem 8, to find a Fourier-Legendre expansion ( F (θ) = )of F(
Number 18. Please don't do the CAS nor the plot. Please see the attached file for the fully formatted problems.