In: Electrical Engineering

x(n)=(1/4)^{|n|}, find x(ω)

By using DTFT analysis equation and infinite geometric series we get the solution. The Question is (1/4)^|n| , but in question power symbol is missing. With this correction below is the answer.

Note: If the question is (1/4)|n| the DTFT doesn't exist because convergence condition fails.

f(x) = xln(x+1)
Find the Taylor polynomal to n=4 at the point c =1

find zero state response y[n+4]-y[n]=x[n], if x[n]= e^-n
u[n]

Find the radius and interval of convergence of the series X∞ n=1
3^n (x − 5)^n/(n + 1)2^n

use simpsons rule to find the integral from 0 to 1, n
=4
sqrt(1+x^3)

Prove or disprove each of the
followings.
If f(n) = ω(g(n)), then
log2(f(n)) =
ω(log2g(n)), where
f(n) and g(n) are positive
functions.
ω(n) + ω(n2) =
theta(n).
f(n)g(n) =
ω(f(n)), where f(n) and
g(n) are positive functions.
If f(n) = theta(g(n)), then
f(n) = theta(20 g(n)), where
f(n) and g(n) are positive
functions.
If there are only finite number of points for which
f(n) > g(n), then
f(n) = O(g(n)), where
f(n) and g(n) are positive
functions.

A 5th filter is described by the difference equation: 2y(n)=2
x(n)+7 x(n-1)+3 x(n-2)-8 x(n-3)+ x(n-4)-8 x(n-5)+7 y(n-1)-3
y(n-2)+5y(n-3)- y(n-4) Determine the frequency response. Plot the
magnitude and the phase response of this filter. Consider the plot
-π≤w≤π for 501 points. Describe the magnitude response (Low pass
filter, High Pass filter, etc.) Determine the system stability.
Determine the impulse response h(n). You may set the period to
-100≤n≤100 Determine the unit step response for -100≤n≤100 .
(Matlab)

Given a sequence x(n) for 0 ≤ n ≤ 3, where x(0)=4, x(1)=3,
x(2)=2, and x(3)=1, evaluate your DFT X(k)

Let
f(x)=x • 3^x
a) Find formula for f^(n) •(x) for natural n (the n order
derivative).
b) Write the Taylor series generated by f(x) in 0.

Find the pointwise limit f(x) of the sequence of functions fn(x)
= x^n/(n+x^n) on [0, ∞). Explain why this sequence does not
converge to f uniformly on [0,∞). Given a > 1, show that this
sequence converges uniformly on the intervals [0, 1] and [a,∞) for
any a > 1.

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is
concave up, and the intervals where f(x) is concave down, and the
inflection points of f(x) by the following steps:
i. Compute f 0 (x) and f 00(x).
ii. Show that f 00(x) is equal to 0 only at x = −2 and x =
2.
iii. Observe that f 00(x) is a continuous since it is a
polynomial. Conclude that f 00(x)...

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