Recall that the following Taylor series is used to approximate
Cosine: cos(x) = ∑ (−1) nx 2n (2n)! ∞ n=0 You have been tasked with
developing an m-file that allows other engineers to quickly
determine the minimum n needed to reduce the truncation error below
an error threshold. The truncation error is the absolute error
between the approximation and MATLAB’s cos() function. You may want
to Google the Taylor series to better your understanding of it.
Your code should perform...
Use induction to prove
Let f(x) be a polynomial of degree n in Pn(R). Prove that for
any g(x)∈Pn(R) there exist scalars c0, c1, ...., cn such that
g(x)=c0f(x)+c1f′(x)+c2f′′(x)+⋯+cnf(n)(x), where f(n)(x)denotes the
nth derivative of f(x).
Use simulation to prove that when X ∼ N(0, 1), Z ∼ N(0, 1), Y =
X3 + 10X +Z, we have V ar(X +Y ) = V ar(X) +V ar(Y ) + 2Cov(X, Y )
and V ar(X −Y ) = V ar(X) + V ar(Y ) − 2Cov(X, Y ).
Use and provide Matlab for the following: Generate the
discrete-time signal x[n] = 4 cos (2pi. 10. nT5) + 2cos(2pi. 100.
nT5) + 3cos(2pi 200. nT's), with Ts0.001 sec. Display the signal in
both time and frequency-domain. Assume that the 100 Hz component of
x [n] is your desired signal while the other two components are
noise. Design a suitable filter to extract the desired (i.e. 100
Hz) signal. Display the filter's response. Display the output
signal in the frequency-domain....
given the sequences
x1 = cos (0.5*pi*n) + cos (0.25*pi*n) + cos (0.125*pi*n); for n = 0
to 7;
x2 = sin (0.5*pi*n) - cos (o.25*pi*n) + sin (0.125*pi*n); for n = 0
to 7;
plot the sequences and comment on the results. increasing the
number of samples to n = 0 to 99, compute the DFT of the two
sequences in MATLAB and plot the magnitude and phase of the
computed DFTs. comment on the results
Let x[n] = cos(17?n 64 ) + 2sin(23?n 32 ) for 0 ? n ? 255, and 0
otherwise. The signal x[n] is passed through an LTI system with
transfer function H(z) = (1? 1 2z?1)(1? 1 3z?1). Denote the signal
at the output of the system by y[n]. We want to recover x[n] by
passing y[n] through an inverse system.
(a) Find (analytically) an impulse response g[n] of the inverse
system, G(z) = 1 H(z). (Note: the inverse system...
Prove combinatorially: {{n \ choose x)= {{k+1 \ choose n-1)
This question is asking to prove combinatorially
whether n multi-choose k is equal to k+1 multi-choose
n-1
Thank you