Simple Differential eq. question

[itsjuly13]

Hi. I need help getting started with the following problem. The second part I think would be easy but I'm a little confused on the first part.

Part 1.
Define f1(t):Low Frequency signal.
f2(t) High Frequency signal.
h(t) Filter transfer Function.

Part 2.
Then, I would use mathematica to graph f1, f2,h.
Find the Laplace Transforms F1, F1, H.
outputs: F1-F1*H, G1=F1*H.
Inverse Laplace Transforms g1, g2 of G1, G2.
Then Discuss the filter Effects.

My question is. How would I define a Low/High frequency signal? and the filter transfer function? Any help/Guidance would be appreciated.
Thanks.

 

[Bill Simpson]

This might help introduce you to writing functions in Mathematica

http://reference.wolfram.com/mathematica/tutorial/DefiningFunctions.html

This is a tiny example that might help you get started.

In[1]:= f1[t_] := Sin[2 Pi t];

In[2]:= Plot[f1[t], {t, -2, 2}]

Out[2]= ...PlotSnipped...

In[3]:= LaplaceTransform[f1[t], t, s]

Out[3]= (2 Pi)/(4 Pi^2 + s^2)

In[4]:= InverseLaplaceTransform[2 Pi/(4 Pi^2 + s^2), s, t]

Out[4]= Sin[2 Pi t]

Mathematica is FANATIC about correct capitalization and correct use of () versus [] versus {} and = versus := versus == and there is even an === and they are all completely different. Make any tiny mistake with anyone of those and you will get error messages you don't know what to do with or incorrect results or even nothing at all.

 

[itsjuly13]

This might help introduce you to writing functions in Mathematica

http://reference.wolfram.com/mathematica/tutorial/DefiningFunctions.html

This is a tiny example that might help you get started.

In[1]:= f1[t_] := Sin[2 Pi t];

In[2]:= Plot[f1[t], {t, -2, 2}]

Out[2]= ...PlotSnipped...

In[3]:= LaplaceTransform[f1[t], t, s]

Out[3]= (2 Pi)/(4 Pi^2 + s^2)

In[4]:= InverseLaplaceTransform[2 Pi/(4 Pi^2 + s^2), s, t]

Out[4]= Sin[2 Pi t]

Mathematica is FANATIC about correct capitalization and correct use of () versus [] versus {} and = versus := versus == and there is even an === and they are all completely different. Make any tiny mistake with anyone of those and you will get error messages you don't know what to do with or incorrect results or even nothing at all.

Thank you Bill.

How would I go about defining a transfer function?