Design a filter that has infinite DC gain, a gain of one from 1Hz to 100 Hz and filters (1storder) any signals above 100 Hz. a) Sketch the bode plotb) Sketch the s-planec) write the transfer function of the filterd) write the differential equatione) write out the unforced transient responsef) write out the frequency response

Attached below are the  sketches

answer :

c) G(s) = 100 / ( s + 100 )

d) y'(t)  + 100Y(s) = 100 X(s)

e) g(t) = e^-100t  u(t)

Explanation:

a) Sketch the bode plot

The filter here is a low pass filter

b) Sketch the s-plane

attached below.     pole ( s ) is at 100

c) write the transfer function of the filter

Transfer function ; G(s) = 100 / ( s + 100 )

d) write the differential equation

Y(s) / X(s) = 100 / s + 100

Y(s) [ s + 100 ] = 100 X(s)

= sY(s) + 100Y = 100 X(s)

∴ differential equation = y'(t)  + 100Y(s) = 100 X(s)

e) write out the unforced transient response

g(t) = e^-100t  u(t)

f) write out the frequency response

attached below

x+2 because it just doubles hon so the pattern can actually tell you the expression.

so for example,

if x=2 then 2+2 is 4

if x=4 then 4+4 is 8

and so on and so forth.

i really hope that this makes sense and you out in a way hon: )

answer: hi

explanation: