# Simple Differential eq. question

1. Apr 16, 2014

### 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.

2. Apr 17, 2014

### Bill Simpson

This might help introduce you to writing functions in Mathematica

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

Code (Text):
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 any one of those and you will get error messages you don't know what to do with or incorrect results or even nothing at all.

3. Apr 18, 2014

### itsjuly13

Thank you Bill.

How would I go about defining a transfer function?