signals 8. Consider the rectangular function & comide to resto de la me m orialin ....
Consider the function f(x) with period 4 which has f(x) = 1, -2<< -1, 0, -1<x< 1, -1, 1<x< 2. a) Sketch the function f(x) in the interval (-2,2] b) Calculate the Fourier Series for f(x). Circle your answer. c) What values does the series converge at the points x=-1 and x=1. Circle your answer.
Consider the 2-periodic function given on the interval [0,27) by if 0 <<< 2 (x - 72 if <<< 27. 1. Sketch the graph of this function. 2. Find its Fourier series.
Define the rectangular window as follows: wlnl otherwise (a) Show that its DTFT has the following expression: W(eju)-e-jaa, sin Me Find out what the constant α is. sin(?) (b) Make a sketch of IW(ejoj as a function of ω for the case of M-4, and show where the zero crossings are. (c) Now, consider the Hann window defined as follows, πη 2M 0, otherwise. Make a sketch of wH[n] Define the rectangular window as follows: wlnl otherwise (a) Show that...
QUESTION 26 Given the following function: int secret(int num, int m) inti, prod=1; if (m=0) return 1: - for (i=0; i<m; i++) { prod = prod * num; } return prod; What is the output for this function call? cout << secret(10,6);
4. Define the family of functions fe(1) DE -E<x<€ otherwise (a) Sketch a graph of fe for e = 1,3,5, D. Describe, in words, what happens to fe as € + 0. (b) Show La fer)dt = 1. (c) Calculate the Laplace transform of felt – to), for Io > 0. (d) Roughly speaking the limit lim fe() gives rise to the Dirac Delta function 8(). It has the properties that 8(x) = () for x = 0, and L...
Consider the IVP: x = √2, 2(0) = 0 A) Is the function S 0, 0<t < 5 X(t) = iſt - 5), t>5 a solution of the DE on I = 0,0), Justify your answer. (Hint: Verify the first two conditions for each interval (0,5) and (5,0).
Consider the probability density function 0 ifr <0 8.77 if 0 < x <1 0 if > 1 Find the median. Enter your answer to 3 decimal places. Answer:
Question-2 Consider the joint uniform density function C for 22 + y2 < 4, f(x,y) 0 otherwise. What is the value of c? 0 What is P(X<0)? What is P(X <0, Y <0)? What is f( x | y=1)?
2. Consider the function 3 I < (a) Find the Laplace transform of f by direetly using the integral definition of a Laplace transform. (b) Write f in es of step functions, and use the t-shiting theorem to find the Laplace transform of f. (c) Use MATLAB to find the Laplace transform of f
Consider the steady temperature T (2,y) in a rectangular plate that occupies 0 <<< 9 and 0 <y<5, which is heated at constant temperature 150 at 9 and 0 along its other three sides. (a) For separation solutions T(1,y) = F(x)G(y), you are given that admissible F(1) are the eigenfunctions Fn (1) = sinh(An I) for n=1,2,... and G(y) are the eigenfunctions Gn(y) = sin(Any) for n=1,2,... A for In = (b) The solution is the superposition T(z,y) = an...