Consider the following time series: {5, 13, 6, 7, 8, 13, 11, 11, 3, 18} (a) Define the “2 × 2 moving average” smoother. (b) Apply the 2 × 2-MA smoother to the series to produce a new smoothed series. (c) Assuming an additive decomposition model with a seasonality of order 2, estimate the seasonal coefficients of the time series.
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Consider the following time series: {5, 13, 6, 7, 8, 13, 11, 11, 3, 18}
(a) Define the “2 × 2 moving average” smoother.
(b) Apply the 2 × 2-MA smoother to the series to produce a new smoothed series.
(c) Assuming an additive decomposition model with a seasonality of order 2, estimate the seasonal coefficients of the time series.
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- Generate the Simulink models for the constitutive equations of stress and strain for Kelvin-Voigt and Maxwell viscoelastic models with the following constraints: Your source should always be a step function with a step of 10 - regardless of whether it's stress or strain For all models, use the following values: E-3 n-5 You should have a total of 4 models: 1. Kelvin Voigt– input is strain, output (scope) is stress 2. Kelvin Voigt – input is stress, output (scope) is strain 3. Maxwell – input is strain, output (scope) is stress 4. Maxwell – input is stress, output (scope) is strain2. A discrete time system has the system function H(z) = z8-3' (a) If the system is stable. What is the region of Convergence of H(2)? (b) For the stable system of part (a), determine h(n), the unit sample response for this system, using any method you choose.Boolean function is represented by its truth table as follows: хуz f(x,y,z) 000 1 001 1 010 011 100 101 1 110 111 1 (a) Write corresponding minterm expansion. (b) Write corresponding maxterm expansion. (c) Minimize (Simplify) and Represent f(x,y,z) using Karnaugh map (K-map). (d) Minimize (Simplify) f(x,y,z) using Boolean identities. (e) Represent the simplified function using logic diagram.
- 1. Suppose that we have four observations and compute a dissimilarity matrix given by 0.3 0.3 0.4 0.7 0.5 0.8 0.4 0.5 0.45 0.7 0.8 0.45 For instance, the dissimilarity between the first and second observations is 0.3, and the dissim- ilarity between the second and fourth observations is 0.8. (a) On the basis of this dissimilarity matrix, sketch the dendrogram that results from hierar- chically clustering these four observations using complete linkage. Be sure to indicate on the plot the height at which each fusion occurs, as well as the observations corresponding to each leaf in the dendrogram. (b) Repeat (a), this time using single linkage clustering. (c) Suppose that we cut the dendrogram obtained in (a) such that two clusters result. Which observations are in each cluster? (d) Suppose that we cut the dendrogram obtained in (b) such that two clusters result. Which observations are in each cluster?We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, X2, ..., Xn,..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: N-2 Li f(x)dx = * f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even N-1 f(x,) + f(xn)] . Now complete the Python function InterageSimpson(N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f (x) = 2x³ (Already defined, don't change it). In [ ]: # Complete the function given the variables N,a,b and return the value as "TotalArea". # Don't change the predefined content, only fill your code in the region "YOUR CODE" from math import * def InterageSimpson (N, a, b): # n is…We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, x2,.. Xn,..., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x) dx N-1 Ax [ƒ(x0) + 4 (Σ1,n odd f(xn)) ƒ(x₂)) + f(xx)]. N-2 + 2 (n=2,n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is ƒ(x) = 2x³ (Already defined in the function, no need to change).
- We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1,x2,..., X., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x)dx ≈ [ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)]. Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change). *Complete the function given the variables N, a,b and return the value as "TotalArea"." "Don't change the predefined content' only fill your code in the region *YOUR CODE"" from math import * def InterageSimpson (N, a,…Simplify the following Boolean functions, using K-maps: F (w, x, y, z)=Σ(11, 12, 13, 14, 15)In Sammon mapping, if the mapping is linear, namely, g(x|W) = WTx, how can W that minimizes the Sammon stress be calculated?
- F(w, x, y, z)=Σ m(0,1,2,8,9,10) + X(4,6,12,14) Karnaugh Map and give the simplified logical expression derived from Karnaugh Map with indicating every simplification step below.Please explain, as simplistically (but thoroughly) as possible, how to develop a k-map from a truth table to be used to simplify an equation.Examples: xz + (xy + ~z) ~xyz + yz + x~ySimplify the following Boolean functions, using Karnaugh maps: a. F(w, x, y, z) = E(0,2,3,8,10,11) b. F(A, B,C, D) = E(1,5,9,12,13,15) %3D