Linear Systems (3) Write an expression for the following functions using shifted and scaled versions of...
3. Write the following signal as a combination (sums or products) of scaled and shifted unit rectangles rect(t) and unit triangles Alt). a X(t) 1 ta b) x(t)
1 Direct discretization Derive the transfer functions of the discretized versions of the following systems, using i) 8-Ac-1), ii) 8-AU-z-1), and iii) 11) S I-z ), and ii s+1 2. H(s)
need solution and code for this signal and system problem 1) Linearity: In order for a system to be linear it must satisfy the following equation: In other words, the response of a linear system to an input that is a linear combination of two signals is the linear combination of the responses of the system to each one of these signals. Let xi)- u(t) -u(t-1) and x2t) u- u(t-2) be input signals to the systems described by the i/o...
Are the Resulting Functions Linear? At this point you should wonder whether these combinations of functions are linear or not Problem I Show that if S and T are linear functions from V to V and c is a real number, then the functions S+T and c.T defined above are indeed linear functions from V ta V Because of Problem 1 we know that the set Linear(V, W) (all linear functions from V to W.) has rules for addition and...
Write the equation that results in the desired translation, The cubing function, shifted 3 units downward. y= (Type an expression using x as the variable.) i instructor Tip Write the problem number and the problem completely, including the directions. Use the letter y for the translation function. Write the basic function using the proper notation. Goose Enter your answer in the answer box.
3. Write the expressions for the shape functions for a linear truss element. Explain the following properties (what they are and what they mean): delta function property, partitions of unity property, and property of linear field reproduction. Does the shape function for the linear truss element satisfy these three properties? Why or why not? 3. Write the expressions for the shape functions for a linear truss element. Explain the following properties (what they are and what they mean): delta function...
Sketch the functions shown below for the intervals indicated. Make sure values for maximums and minimums are clearly indicated. 0sts4 a). b), c). q(t) 2tu(t)- 2(t-1)u(t-1)-2(t-2)u(t-2)+ 2(t-3)u(t-3) g(t) = 2coszt u(t)-2 cost(t-2) u(t-2) q,(t) = 2δ(t-1)-8(t-2) 0sts4 0sts3 Write the expression for the following functions using the unit step notation y(t) 니 7 z(t)
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10 t - CC Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = (3-2)u(t-2)+(-3t+4)u(t-4) OB. g(t) = (3-6)112,3(t)+(-3t+12)813,4(t) OC. g(t) = (3-6)112,4(t)+(-3t+12)u(t - 3) D. g(t) = u(t-2)+(3-6)/12,3(t)+(-3t+ 12)813,4(t) + ut - 4) Compute the Laplace transform of g(t). ${g}= (Type an expression using s as the variable.)
Write the function in terms of unit step functions. Find the Laplace transform of the given function. Įt, f(t) t, ost<3 10, t23
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1