Data analysis using FFT

[Odee]

Help!
I have a ton of time series data on which I have performed the FFT. Looking at the power spectrum, I have selected a threshold power, below which I set my transformed data equal to zero. When I perform the inverse transform I get this nice curve, unencumbered by noise. If I want a trigonometric expression of that curve, is there a way of calculating it?
Thanks in advance.
Odee

 

[shg]

If you have a set of Fourier coefficients, you can express the function directly in terms of those coefficients, either in sine/cosine form, or cosine /phase form.

So, what have you got?

 

[Odee]

Here are the positive data of the xform. The rest are zeros until the folding.

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BACKGROUND-COLOR: transparent" height=17>-12.1576371710311+1.06251825827259i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right height=17 x:num>0</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>11.1677553671005+2.9078061293012i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right height=17 x:num>0</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>-11.5546793763536+12.6644664617742i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>11.9389302913783+1.68091821064519i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>15.5528578488784-1.25996461308535i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right height=17 x:num>0</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2.34429764705162-9.29734390180133i</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; 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[shg]

The first term is the DC component, and the following terms are coefficients of cosine and sine. The reconstruction is

f(t)=a<SUB>0</SUB>/2
+ a<SUB>1</SUB>Cos(Ωt) + b<SUB>1</SUB>Sin(Ωt)
+ a<SUB>2</SUB>Cos(2Ωt) + b<SUB>2</SUB>Sin(2Ωt)
+ a<SUB>3</SUB>Cos(3Ωt) + b<SUB>3</SUB>Sin(3Ωt)
+ …

Where
Ω = 2pi/T
a<SUB>0</SUB> = the DC term
a<SUB>i</SUB> = IMREAL(your complex numbers)
b<SUB>i</SUB> = IMAGINARY(your complex numbers)

 

[Odee]

Great!
Thank you very much.
Odee