(b) Consider the difference equation for trapezoidal integration a(k)=11 (k-1)+-- e(n)+e(n-1 Draw...
b) Consider a simple difference equation ln)- x(n)+ax(n-D), where n7 is the input, y(n) is the output and D is a delay. Draw a block diagram of this filter and give a physical interpretation. Find its impulse response and transfer function. Calculate the zeros of the transfer function in terms of z Find the corresponding frequency response as well as the minimum and maximum values of the magnitude of the frequency response function. b) Consider a simple difference equation ln)-...
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
4. Consider the position control of a rigid body, Figure, where u(t) is the control force. An analog PID control law is described as de u)kpe)k kije0)dt; e({)= x4C)x) dt 0 kp. ky only a position sensor is available. are controller gains. Also, xq (t) is the desired position of the mass. It is assumed that kJ where and Derive a difference equation for the implementation of this PID control law on a digital computer. Use backward difference and trapezoidal...
Q1(b). Given the following difference equation: y(n) + y(n-1) + 0.25y(n-2) = x(n)-0.4x(n-1). (1) Determine the transfer function representing the LTID system. (2) Determine the output of the LTID system for the input x (n) (0.4)nu(n).
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Digital processing signals For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2) a) Draw its block diagram b) b.1 - Obtain its transfer function H(z) b.2-Calculate and PLOT | H(e*)l, for θ 0, π/4. π/2. 3π/4, and π. Obtain and plot its poles and zeros, in the z-plane c)
follows (3) Consider the difference equation given as у(п) %3 0.75у(п — 2) + z(п) — 2(n — 1) — z(п — 2). (a) Draw the block diagram of the above difference equation in terms of adders, multi pliers and delay blocks (b) How many multiplications and additions do we need per sample? (c) Find the output y(n) for an input x(n) = S(n). What is this response called? Is the system stable? unit-step input. (d) Find the response due...
Problem 3: Consider an IIR filter described by the difference equation (a) What is the system function H(a) of this fiter? [5 points) (b) Determine the zeros and poles of the system and sketch the zero-pole plot in z-plane. 5 points (c) Plot the block diagram of this IIR filter. [10 points (d) Given the input zfn-cos(mn/3) + 2δ[n] + 5in-11, determine the output yln. 15 points
A causal LTI system is described by the following difference equation: y(n) – Ay(n-1) - 2A2y(n − 2) = x(n) – 2x(n-1) + x(n–2), where A is a real constant. Determine the z-domain transfer function, H(z), of the system in terms of A.
Question 1: A filter is described by the difference equation y(n) = y(n-1)+3x(n) - 4x(n-4). (a) What is its transfer function? (b) Draw the signal-flow diagram of a realization of the filter.