You are an audio engineer working on the latest Moog synthesizer filter and living in Asheville, NC
Filter Specifications: The filter should amplify sounds in the human vocal range, from 100 to 1000 Hz, at a constant gain of 20 dB. Below and above that range, it should aggressively attenuate input sound at a rate of 40 dB/decade.
Problems:
(a) (1 point) What are the input and output signals of this filter?
(b) (2 points) Sketch a gain plot for this synthesizer that fulfills the specifications above.
(c) (2 points) Propose a transfer function that could have the gain plot you sketched.
(d) (2 points) Sketch the corresponding phase plot for your transfer function.
(e) (2 points) Use MATLAB to check if your transfer function actually has the same gain and phase plots as your sketch. What differences do you notice?
Hint:
\% create a symbolic TF
syms s;
G\_sym = 1/(s+1);
\% convert to TF object
[n,d] = numden(G\_sym);
nc = double(sym2poly(n));
dc = double(sym2poly(d));
G\_TF = tf(nc,dc);
\% make Bode plot
bode(G\_TF)
(f) (1 point) If you implement this filter in real life, would it create cool, distorted, weird sounds? Why or why not?