ignore if you hate math

-- and help me if you can.

say i have a function that is composed of (a) a sinusoidal component, (b) an increasing linear trend, and (c) gaussian noise. i don't want to make any assumptions about the phase of the sine wave, but i do have a definite value of its frequency.

i) how do i remove (a) from the function so that i can plot some sort of regression line through the residuals (and thus estimate (b) and find the variance of (c)).
ii) what's the easiest program in which i can do this calculation in large batches (say 120 datasets)?
iii) if i want now to say that the function is composed of a small number (n; say 1< n <4) of sin/cos waves + (b) + (c); is there an inverse fourier decomposition that works sort of like principal component analysis (in that it removes only the n waves of lowest frequency) while leaving the linear trend (and whatever other noise) intact?

(i'm not sure i expect to get any answer for this, but there can be miracles.)

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