a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l
sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y)
+-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is
given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the
numeric value for the AM index of modulation, m, fors(f) ?
If u(t) = < sin(8t), cos(4t), t > and v(t) = < t,
cos(4t), sin(8t) >, use the formula below to find the given
derivative.
d/(dt)[u(t)* v(t)] =
u'(t)* v(t) +
u(t)* v'(t)
d/(dt)[u(t) x v(t)] =
<.______ , _________ , _______>
If u(t) = < sin(5t),
cos(5t), t > and
v(t) = < t, cos(5t),
sin(5t) >, use the formula below to find the given
derivative.
d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)
d/dt [ u(t) x v(t)] = ?
a) Calculate and plot the DTFT of ?[?] = sin( (?/ 4)?) / ?? *
cos ( ?/2 ?) by hand.
b) By using a 2x1 subplot, plot ?[?] signal defined in Question
1 in the first row. Take ? between -100 s and 100 s and limit
x-axis between -20 sand 20 s. Be careful about when ? = 0. What is
the value of ?[0]? While plotting ?[?] please write an if statement
for ? = 0. After...
Show
that in 2D, the general orthogonal transformation as matrix A given
by
{{cos, sin}, {-sin, cos}}. Verify that det[A] = 1 and that the
transpose of A equals its inverse. Let Tij be a tensor in this
space. Write down in full the transformation equations for all its
components and deduce that Tii is an invariant.
f (x) = -0.248226*cos (2 x) - 0.0184829*cos ((2+2)x) -
0.0594608*cos(x)*sin(x) + 0.123626*sin ((2+2)x).
The intervall is ]0, 3/2[
What is the local maximum and local minimum? Answer with 5
decimals