The Z-Transform of x (n) = e -3(n-4) cos(0.17 (n- 4))u (n- 4) Where u(n-4) = 1 for n 24 while u(n-4) = 0 for n < 4 z-3 (z – 0.0474) X (z) = z2 – 0.0948z + 0.0025 X (z) = z' - z (n – 4) О 22 – 0.1z - X (z) = %3D z3 – 2z2 + 0.0025
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Q: The Z-Transform of x (n) = e-3(n-4) cos(0.17 (n-4))u (n- 4) Where u(n-4) = 1 for n 24 while u(n-4) =…
A: We have to find the Z transform
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- Consider the Fourier expansion = (−1)²k+1 . 2 k ∞ f(x) = [ck · sin(kx), k=1 where Ck = Describe the periodic function f(x). Verify that the first Fourier coefficient satisfies C1 = CTT -π xsin (x) dx.* (30) 13 Find the Fourier transform of (x) = LIOBLEON 3x ifbxK1 O if | x | > 1 ={₁ II- Ž 2(1 − (−1)") sin( 21² ) In n=1 Sf(x) = f(x)=x on [-1,1] Sf(x) = + -4 (-1)" z²n² n=1 Match the Function with its Fourier Series Look here to see if you are correct. f(x) = x² on [−1,1] cos(xnx) - Σ - ²(-1)" An n=1 Sf(x) = f(x) = |x| on [-2,2] sin(xnx) Sf(x) = 1 + ((−1)ª −¹) cos( z** ) n=1 f(x) = 1 on [0,2] and f(x) = -1 on [-2,0)
- Find the Z-transform of: 1. (n + 1)2 2. sin? 4 () nn 3. sin3 6. пп 4. cos 2 5. (n + 1)(n + 2)Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.
- Consider f(t)=9+2t+6t², for -Let f(x)={0 for 0<x<1 f(x)={−(3−x) for 1<x<3. Compute the Fourier cosine coefficients for f(x) 1. A0= 2. An= Give values for the Fourier cosine series C(x)=A02+∑n=1∞Ancos(nπ3t)C(x)=A02+∑n=1∞Ancos(nπ3t). C(1) C(−2) C(4)2y + 2y = e y(0) = 0, y'(0) = 1, 2) Consider the function f: [-1. 1]> R defined by f() 1) Show that the Fourier series expansion of f is given by: 2². 1 4 Cos(na). {(*) = - + 2 X (-¹)^ 3 n² 7=1 ii) Show that Σ 12 x ii) Compute the value of -1)^-+-1 n² iv) Deduce the values of and 20 a odd n even- Find the Fourier series expansion of the given function, whose definition in one period as: (24) f(x)=cosx (25) f(x) = sinx | (26)f(x)=x| (27) f(x) = sin(tx) 三 (28) f(x)=x3 (29) f (t)= (30) f ( )= sint 一π n-tf(x) and g(x) is periodic and has a Fourier Series representation: f(x) = cos(6*pi*x) g(x)=sin(6*pi*x) z(x) = f(x)*g(x) Find a0, a1, a2, a3 for z(x). Simplify as much as possible!Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,