A system has a difference equation: y[n] = {x[n] + x[n − 1] + ²x[n=2] a. Determine whether the system is linear.
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Determine whether the system is linear
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A system has a difference equation:
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y[n] = x[n] + x[n − 1] + x[n-2]
a. Determine whether the system is linear.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40fd1737-b499-4969-b8a1-2e8bce8ef321%2F66c5411e-df90-4b21-bd88-c41fb846d7d0%2F2tpxfxc_processed.png&w=3840&q=75)
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- B. Determine the stability of the following linear system y(n) = 0.5 x(n) + 200 x(n – 2) –- 200x (n – 10)REC O x .002 w to Determine If 2 Events Are Independent: Substitute in what you know in to P(An B) = P(A) • P(B) and check to see if left side equals right side. o If it's equal, then it's independent. o If it's not equal, then it's not independent (or dependent). Let event M = taking a math class. Let event S = taking a science class. Then. M and S = taking a math class and a science class. Suppose P(M) = 0.6. P(S) = 0.5. and P(M and S) = 0.3. Are M and S independent? PCM)- P(S) = P(Mand5) .3 .3 indep endent .3 9. In a class, 60% of the students are female. 50% of all students in the class have long hair, 45% of the students are female and have long hair. Of the female students, 75% have long hair. Let F be the event that the student is female. Let L be the event that the student has long hair. One student is picked randomly. Are the events of being female and having long hair independent? ELMOThe differential equation formed by eliminating the arbitrary constant A : y = A cos x + 1 is y cot x + y +1= 0 y' tan x + y –1 = 0 y cot x – y – 1 = 0 y cot x + y –1 = 0
- Compute the effective value of current. 9 TIP: Use your CASIO's INTEGRATE function. i(t) A ... a T/2 b a = 13 A b = -15 A T= 4 s4.Determine the discrete equation of the direct form-I structure shown in the below figure: w(n) x(n). y(n) y(n -1) 3 x(n -1) У(n -2) 4y(n-1)-8y(n-3)+x(n)+3x(n-1) 4y(n-1)-8y(n-2)+x(n)+3x(n-1) O 4y(n-1)-8y(n-2)+x(n)+3x(n-2)Homework 2 Determine the stability of the system having a characteristic equation given below q(s) = s + 2s + 25 + 4s2 + 11s + 10
- Dr. Mohamad Alhabbar Digital Signal Processing Ninevah University Communication Engineering Department College of Electronics Engineering Example Convert the fol lowing tracfer functions into its di fference equation. 2-1 H(2) = 7+13z+0.36 Solution: a. Dividing the numerator and denominator by z? toobtain the trasfer function whose numerator and denominator polynomi als have the negative power of z, it follows that (22-1)/2 (F-137+036)/ 1-72 H(2) = 1+13z +0.36z 2 Y(z) X(Z) 1-z 2 1-1 3z+0367 Y(2)(1+13z1+0.36z ) = X(z)(1-z 2) Y(2) + 13z Y(2) +0 36z 2Y(z) X(2)- z x(z) y(n) +13y(n- 1) +036yn- 2) = x(n) - x(n - 2) y(n) = x(n) – x(n- 2) - 13y(n - 1) -0.36y(n - 2) H.W1: Draw the system which is expressed in the above difference equation.The 3-pt DFT of the sequence is defined as X (k) for k = 0, 1, and 2 If X (1) = 1 + jv3 and the energy of the sequence is 3 sq unit Also, the DC value of the sequence is greater than zero. Determine the elements of the sequence defined as follows: x [n] = ao + a18 [n – 1] + azd [n - 2] ao = a = a2 =VR7NXRXIPNJHM Join a Meeting - Zo.O movies.awesomese.. ndll al O ispe v e 6 This option This option Question* 2s If F(s) then (s+1)2 f(t) = te* +et f(t) = 2et- 2tet This option O This option ft) = - sin (3t) f(t) = t sin (3t) O This option O This option
- 1- Linearize the nonlinear function f(x) = x3 + 2x around x = 3. If the linearized function is shown as finearizea (x) = ax + b find a and b and write in the box below. Show your work. a= b=Homework x1(n) = 8(n)+ 8(n–1)+8(n–2) x2(n) = 28(n)–8(n-1)+28(n– 2) | Find x1 O x2B- Discuss the stability of the system given by the characteristic equation: 255 +54 + 65³ + 3s² + s = -1