(The integral of a Gaussian/Bell curve) Let Exercise 34: e~t2(1+z2) -dz 12 da f(t) and g(t) = e and h(t) f(t2 g(t) 1 Pr...
please help me with these, thank you. Exercise 34: (The integral of a Gaussian/Bell curve) Let et(1+x2) dr 12 f(t) dr g(t) and and h(t) f(t)2 + g(t) Problem sheet 9 Homework 29. Mai 2019 a) Compute h(0) b) Compute h'(t) for all t 0 Remark: You have to argue why you can interchange differentiation and integration c) Compute lim h(t) d) Use a)- c to show that edr 1 da and _ Exercise 34: (The integral of a Gaussian/Bell...
1. Auto- and Cross-Correlation. For each of the following, compute the cross correlation T/2 Rry(,) = E[drpd, + n-linx t-Tax(ry(, + rdr . Hint: Use trigonometric identities (see HW 1), 27T such as sin a sin b-2 [cos(a-b)-cos(a + b)] . Also use the fact that j cos(ont-б unless co-0 x(t) = sin(2n/r), y(t)-sin(2nft) (here x and y are the same, so Rry-Rrr is the a. autocorrelation of x). x(t) = sin(2nft), y(t) = sin(2nf(t-to)) c. x(t)-n(), y()2x(t) +n2(t) where...
1. Auto- and Cross-Correlation. For each of the following, compute the cross correlation T/2 Rry(,) = E[drpd, + n-linx t-Tax(ry(, + rdr . Hint: Use trigonometric identities (see HW 1), 27T such as sin a sin b-2 [cos(a-b)-cos(a + b)] . Also use the fact that j cos(ont-б unless co-0 x(t) = sin(2n/r), y(t)-sin(2nft) (here x and y are the same, so Rry-Rrr is the a. autocorrelation of x). x(t) = sin(2nft), y(t) = sin(2nf(t-to)) c. x(t)-n(), y()2x(t) +n2(t) where...
3. Let z,-34J4 and z2-10e'. Find the results of: zit 22,21 * 22,21/22, ะ?, and å . Find the Laplace transforms of the following functions: note that t2 0 1). f(t) =e®.4tcos 12t. f) sin(t 3), f(t) =cos2wtcos3wt. Hint: You may want to use the following identities: cos(o + β)-cosoosß-sino sind, sin θ = , 2 2j 3. Let z,-34J4 and z2-10e'. Find the results of: zit 22,21 * 22,21/22, ะ?, and å . Find the Laplace transforms of the...