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2. The input-output relationship of a system is given by yk]-ylk-11- 2 cos (x[kl) For a...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
(Convolution DT) consider the following LTI system with input x[n] and output y[n]: (a) sketchbthe input signal x[n] = (1/2)^n(u[n])
2. (a)Classify the system with input-output relationship yoxio)dt as (i) Linear or Nonlinear(ii) Time-Invariant or Time-Varying. (b) Use Parseval's Theorem to evaluate the following integrals (c) Find the Fourier transform of the signal 1 + cos otherwise
Consider the system given by the input/output relationship 1.14. 32 1 2] n31+ 1 63 4 16 [Is- ]x+ [- u]x (a) When xn] is equal n5 (b) Write a MATLAB M-file to compute the output response y[n] resulting from the in- put x[n] = 5 sin(mn/10 +m/4) , for 0 s ns 69. Express your answer by giving the M-file and the MATLAB plot. to a constant c for all n 0, show that v[n] is equal to c...
A system has an input, x(t) and an impulse response, h(t). Using
the convolution integral,
find and plot the system output, y(t), for the combination given
below.
x(t) is P3.2(e) and h(t) is P3.2(f).
1/2 cycle of 2 cos at -2. (e)
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
2. In the following system, x(t) is the input and y(t) is the output. yt) fix(t)] for some f For each of the system, determine if they are linear. Justify your answers (providing counter- examples could be useful if the system is not linear) A. y(t) 4x(t) B. y(t) t2x(t) C. y(t) 2x(t) +3 D. y(t) 4x2(t) Fx) dt
Suppose we fit the points XK 0 | Yk 2 /6 -0.5 /4 -1 / 3 -1.2 31/4 3 2/3 2 5/6 1.5 by the curve f(x) = a + b cos x+csin 2x using least squares approach. Find the system of three linear equations that can be used to solve for a, b, c. (You may present your answer with 3 decimal digits and you are not required to solve the system).