An ideal digital differentiator is described by the system 1 yn=(xn+1-xn-1)-— — (xn+2] − x n − 2]) + 1 = (x[n + 3] − x[n − 3]) + ... (a) Is the system LTI? (b) Is it causal? (c) Prove it is not BIBO stable. (d) Provide a bounded input a[n] that produces an unbounded output y[n].

Write python program to plot the zeros and poles if a user provides the coefficients for the numerator and denominator of the transfer function. Since the zeros and poles can be complex, this plot is essentially and argand diagram, where the x axis is the real component and the y axis the imaginary component of a given zero or pole. Create a method called plot-poles zeros(num, den) which takes two lists containing the coefficients. Here is an example and the resulting plot. num [1, 3, 7] # yields zeros at -1.5 +/- 2.17945j den = [1, 4, 5, 3] # yields poles at -2.46557, -0.7672143 +/- 0.7925519j plot_poles_zeros(num, den) Imaginary Page 2 Pole-Zero Plot 3 Zeros × Poles 2 1 -2 1 * Real When you write your code you are only allowed to use the packages numpy and matplotlib. Make sure you label the axes, provide a legend and give a title to your plot (See the example plot). Hint: numpy has a method called roots. When given a list of numbers corresponding to the coefficients of a polynomial,…

Ex. 810. A PID controller has a derivative gain of 48. What is the integral gain and proportional gain if the zeros are placed at s=-21 and s=-29? Where is the pole? ans:3

Derive an equation for linear signal conditioning that will convert a sensor output voltage in spanning the range -1V to 3V into a -5V to 5V span. Also, design a circuit to do the corresponding transformation.