represent a solution as integral by using Fourier transform
R" + 2x' + 3x O(otherwise) g(t)such _ that, g(t) lif(-1 < t < 1),g(t) = =
4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by (a) Use pr(t) and properties of the Fourier transform to find the Fourier transform, D(w), of d(t) shown below, in terms of P(. First state the approach that you are using to find D(), then show all of the details. d(t)
Suppose, we let g(t) of problem 1 be periodic (i.e., g(t) is 9T (t) according to the notation using). To be precise let A 4Volts, let the pulse width T-0.1 seconds and let the 0.2 seconds. Find its continuous Fourier transform. Hint: gr. (t) is now that we are fundamental period To periodic and hence you can first find the Fourier series coefficients (C,) and relate those coefficients to the continuous Fourier transform of a periodic signal. Accurately sketch the...
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =
5. Find the Fourier Transform of g(t) = {o. (1-x?, x<1, 1</z/.
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods)
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
I really appreciate it. please explain in detail. Thank you.
a) f(t) = r|t| -1<t<1 t = 1 Compute the Fourier integral representations of f(t). It > 1 NI b) g(t (t, ostsi t = 1 Compute the Fourier cosine integral representation of g. t> 0 c) Compute the Fourier sine integral representation
Please show all steps to solution.
7. Use a suitable Fourier Transform to find the solution of the IVP 2t-r-1 ,2-1 t 〉 0, , u(x, t), uz (x, t) 0asx→00, t〉0, →
7. Use a suitable Fourier Transform to find the solution of the IVP 2t-r-1 ,2-1 t 〉 0, , u(x, t), uz (x, t) 0asx→00, t〉0, →
Engineering Mathematics (2) Homework #2 Due date: 23:59 9 Apr. 2020 1. Find the eigenvalue and eigenfunction a. y' + 2y = 0, y(0) = 0, y(10) = 0 b. y' + 8y' + 1 + 16)y = 0, 0) = 0, y(TT) = 0 2. Fourier integral (sin x, if 0<x<T a. f(x) = { 0, if x > represent f (x) as a Fourier Cosine Integral j1, if 0<x<1 10, if x >1 represent f(x) as a Fourier...
Given that f (t) e-au(t to), where a 0, determine the Fourier transform F() of f(t). 7.1 (b) Given that where a > 0, determine the Fourier transform G (w) of g(0) by using the symmetry property and the result of part (a). Confirm the result of part (b) by calculating g) from G(w), using the inverse Fourier transform integral
(a) Let the correlation be defined as r (t) x(T) y (tT) dT T Express R jw= F{r (t)} in terms of X (jw) and Y (jw), the Fourier transform of x (t) and y (t) respectively. (b) Suppose (t) = y (t) = e-H. Find R (jw) using frequency domain properties and the relationship derived in (a) extra Find R (jw) by evaluating the convolution integral in the time domain to get r (t) and then doing the FT.