Basically x= randn(100,15)
x_centered=(eye(100)-(1/100)*ones(100,100))*x to subtract the mean to center the data
[s,d,v]=svd(x_centered);
I need to find the principal components
which just the eigenvalues but according to my professor {divi}for i = 1 to 15.
Then I am asked what is the pca...
If I am trying to find the steady state coefficients of a filter, when do I know the coefficients went into the steady state? In another words, steady state means it converged to a single value or that it is bounded between values? If say it is bounded between values how would I go about...
There is really no details on the problem as it was not really homework.But I assumed n=1 to N and each were equally likely.
I do not understand your approach.
I am not having trouble getting a function for auto-correlation, I am just not sure how to code u(n) in a way to input it into xcorr, also how would I represent v(n) in a way so it remains uncorrelated with s(n).
Homework Statement
u(n) = .4s(n)+.7s(n) -.1s(n-2)+v(n) where v(n) is zero mean and has variance 0.003 and uncorrelated with s(n)
I want the autocorrelation is E[u(n-k)u(n)] I can solve it easily by hand which is the follow
so r(k) = 0.663 for k =0, 0.21 for k=1 , -0.04 for k=2 and the rest...
Homework Statement
I have a signal where w(n) is white noise
u(n) = .4s(n) +.7s(n-1)-.1s(n-1) +w(n) and where variance of w(n) = .003
I want to find the cross correlation matrix against the optimal delay which I found to be 6.
Homework Equations
The Attempt at a Solution...
Using a MVDR method for a uniformly spaced linear array of sensors, I calculated the optimal weights. The procesing gain is (SIR)out / (SIR)in . The value turned out complex. Is this possible/makes sense?
Homework Statement
RC parallel circuit with the resistor first and the capacitor next.
find the transfer function H(jw)
resistor first then capacitor
transfer function of a circuit with resister serial then capacitor and resister parallel
I have absolutely no background in...
I have a linear question A*F =R where R is the diagonal 11 x 11 matrix A is 9X11 and F is 9X1. This system is over determined. I am confused on how to get the values of F .
I get that F =[(A'A)^-1 ]A' R which gives me a 9 x 11 matrix which does not make sense .
Find the mean square error using the pseudo inverse approach.
I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix
so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?
Homework Statement
x(t) = 5cos(2*pi*1000*t) and g(t) = ∑ from n=-infinity to infinity delta(t-n/10000)
find fourier transform of x(t) and g(t) and the product of the two
The Attempt at a Solution
x(w) = 5*sqrt(pi/2) [delta(w-2000pi)+delta(w+2000pi)]
g(w) = 1
so would the...
Homework Statement
V(t) = 4 for 0<t< 1 and 0 for 1<t<3 and repeats itself for all t (negative and positive)
Find the first 5 harmonics of the fourier series in cosine form and find the power if this is the voltage over 100 ohm resistor
The Attempt at a Solution
power = d_dc ^2 / R +...
I am confused. Originally I wanted to take the characteristic equation, but the inverse fourier transformation to avoid cases. Do I have to assume each case when e,f,g,h, <0 and e,f,g < 0 and h> 0 .... etc all combination of events and maybe = 0 ? There seems to be way too much work for...
Homework Statement
X is uniform [e,f] and Y is uniform [g,h]
find the pdf of Z=X+Y
Homework Equations
f_z (t) = f_x (x) f_y (t-x) ie convolution
The Attempt at a Solution
Obviously the lower pound is e+g and the upper bound is f+h
so it is a triangle from e+g to f+h...
Homework Statement
x(t) = 4 for 0 <x<1 and 0 otherwise and this process repeats for all values including negative.
find X_0 and X_n
and find the first 6th harmonics of the fourier series in cosine form
Homework Equations
The Attempt at a Solution
x_0 = 4/3
x_n =...
Homework Statement
Proposition: If C(0)>0 and C(h)->0 as h-> infinity, then the covariance matrix gamma_n =[c(i-j)] for i,j- 1,2,....n of (x_!,....x_x)' is non singular for every n.
I want to convince myself that the converse is not true. (ie I want a counter example of a stationary...
The probability space of the event might not be infinite (ie discrete), then the argument above fails. In the continuous (infinite) case, we consider the probability over a region since the probability of any single exact event is zero. Think of it this way, the probability of two events...
Homework Statement
f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0
Find E[Y|X]
Homework Equations
E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy
The Attempt at a Solution
f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x))
When taking the integral of y[(4/5)(x+3y)exp(-x-2y)]...
X = # of clubs in a 13 card hand drawn at random without replacement from 52 card deck
Y= # of queens in the same 13 card hand
the pdf of x is f_x (x) = (13 choose x)( 39 choose 13-x) / (52 choose 13) for x=< x =< 13
and o otherwise
the joint distribution of x and y = (13 choose x)...
Oh yeah! Using the marginals would lose information.
So E[Z]=integral 0 to 2 integral 0 to x (3x+4y)/(x+2y) (3/16)(x+2y) dy dx = integral 0 to 2 (3/16)(3x+4y) dx = 5/2 Am I using the Unconscious Statistician theorem correctly? Thanks for all the help! <3