I need to chart 3 sine waves of differing amplitudes and frequencies. Then I need to place each of the sine waves seperately on a positively sloped line. The sine wave has to treat the line as if it’s a zero line, so I can’t just add the sine values to an incrementing series because it doesn’t maintain a sinusoidal shape.
After that, I need to show all three waves combined; I figure that’s just adding them.
I suppose I could figure this out if I wasn’t low on sleep. Someone please come to the rescue. Thanks.
KidC, I am not quite understanding what you want in terms of the plotting.
First, you have to remember that excel assumes that the angle is in radians.
You could do it this way:
column 1 has a line of increasing integers, say 1 to 1000
columns 2, forward would have the sine values
for example b2=constant1sin(constant2a2/100)
constant1 would change the amplitude and constant2 would change the period.
if you wanted to plot b,c,d, and the sum versus degrees, you would have to scale the radians, viz. e2=a2*180/pi()
hope this helps. BTW plotting in excel sucks. For that matter, anything more than keeping your bank balances in excel sucks.
Well what I wanted to do was have the graph of each individual sine wave look as if I took Y=sin(x) and just tilted the graph 45 degrees, rather than adding those values to the increasing integers which makes the sine wave look…ummm…funny?
What you’ve got now is the result of a “shear” transformation of the original axes. What you want instead is a rotation. To do this you need to transform both the x and y coordinates. Rotation by 45° is easy: If your data is in column 1 (x) and 2 (y, your waveform) then create two new columns, u and v, with the data calculated by u=(x-y)/sqrt(2) and v=(x+y)/sqrt(2). Do a scatter plot of columns 3 and 4.
This is driving me nuts trying to get this stuff to line up right. I’m trying to superimpose 3 sine waves so that they look similar to the pattern on this page (it’s about the fifth chart down and is called “Compound Elliot Waves with 5 subwaves.”
That should be able to mimicked with the superimposition of three cycles, at least I think, but I can’t get them to line up correctly. I’m playing with cycles with frequencies related to each other by phi, but I can’t get it to work. I’m crying uncle. I’m sure this is easy for someone who knows this stuff. Any of you out there? Thanks for the help so far. I’ve dumped the idea of rotating the axis, I’d be happy just to add it too a trendline at this point.
Whoops. Here is the site:
Are you trying to come up with a sine curve that fits a set of data or are you trying to graph equations?
I’m trying to recreate that chart with 3 sine waves. In the OP I was just trying to figure out how to graph the 3 sine waves that would ultimately create the graph I linked to. I figured that I could create that chart with 3 sine waves of increasing amplitude and frequency, probably if each were incremented by a factor of 3.
I can’t tell how exact a fit you’re looking for here. Of course, the graph you provide is piecewise linear, while a finite sum of sinusoids is smooth. If you want a good match, you can Fourier decompose the actual graph into an infinite sum of sinusoids, but it sounds like this is not what you want. It looks from the description to the left that the actual graph is supposed to display “self-similarity” (e.g., the overall structure of the graph, when suitably rescaled, looks much like the first section, with (1) and 1 corresponding, (2) and 2, etc.). You’re not going to see any fractal structure like this, or any other of the high-frequency structure you expect to see in a stochastic process (at any frequencies higher than you explicitly indicate) with a Fourier series, either.
But if you just want a smooth fit that somewhat matches the peaks shown, and are willing to squint as hard as the practitioners of Elliot Wave Theory, then you might try something like
x(t) = 0.15t - cos(t/4-pi/10) - 0.8cos(t) - 0.4cos(4t)
(angles in radians).
I don’t need it to match those hard angles at all, just whatever 3 waves can approximate. I’m gonna try that formula in Excel. I’m assuming that each of the cosines is one of the three waves. Thanks a tons!
Omphaloskeptic: Perfect! You even mentioned to capture one higher degree fractal. I can’t thank you enough.