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### Periodic Signals in Excel

Periodic Signals, What does periodic mean? Repeating, right? Yes, but what about the phase and applications of periodic analysis.

Consider a signal : y=A*cos(ω*t) Where A is a scaling multiplier(Literally, scales the vertical(up/down) axis(points ), ω is the frequency in radians(radians are used because the format actually makes for friendlier math) and t is time, but could be any index(independent(x) axis variable).

Whenever a text says “consider a signal” the author typically wants you to picture the signal in your head or actually plot it. Reading math is pointless if you aren't visualizing the functions response.

cos(ω*t) keep in mind that ω has units of radians/sec. t, in seconds, can take on any value from -infinity to +infinity relative to any other position. Why is it allowed to? because mathematics says so. Is t practically allowed to be anything? This is where understanding the bigger picture (system) view sets the limits and appropriate scale. "y" is the dependant variable. The value of y depends on the value of t in this case. If we are talking about a mechanical wave then ω will typically be less than 1000radians/sec and it probably would not be useful to increment (move forward) t by 0.000000001 seconds. However, if talking about a radio frequency (rf) signal at 15.072e9 rad/s, the 1e-9 time step would step right over cycles.

Mmmkay, don’t just consider the signal, put the signal into Excel (or the Open Office free version) by:

1. Make a column(A,B,C…) with numbers, representing phase in degrees, from 0-360 ( radians)

a.       Start by filling out the first 3 rows: 0,1,2

b.      Highlight the 3 rows and drag down to fill in values to 360

2. Convert the values to radians by multiplying by π/180 (The astute reader knows that there is a radians() command in excel that does the same thing. You should always know (or at least try to) what a function/command is doing.)

a.       Type into the first column of row B: =(pi()/180)*

i.      Left arrow to grab column A, Row 1

ii.      Hit Enter to finish

3)      Now in Column C

a.       Type =cos(

i.      Left arrow to grab column B, Row 1

ii.      Hit Enter to finish

b.      Highlight Columns A,B and C and drag fill down to row 361

You should have 3 populated columns

4)      Select column C by clicking on “C”

a.       Insert a line graph by selecting the “insert tab” then selecting the line graph

If everything went right you should get a Cosine wave from 0degrees to 360 degrees

Now, the Cosine signal doesn’t really look like a traditional wave response… How can we improve this? Periodic Examples