Can a Fourier series be adjusted to model a decreasing period function?

[flatmaster]

I have a function I want to model. It is periodic, but the period keeps decreasing. Basically, it'll be a periodic function "squished" for larger values of x.

The typical Fourier series is...
y = SUM{aSin(nx)} + SUM{bCos(nx)}

I think I will attempt

y = SUM{aSin(nx^2)} + SUM{bCos(nx^2)}

replacing x -->x^2 should give me the "smushing" that I want.

The application is bladder level as a function of beers consumed. The basic function is an increasing (quadratic, exponential) function followed by a linear, steeply sloped drop to zero.

 

[fresh_42]

I guess you should worry the amplitude as well. Your general function is $f(t) = A(t)\sin(p(t)+p_0)$. Now you can try some functions for $A(t)$ and $p(t)$. I would let WolframAlpha do the graphics until I'm satisfied.

 

[Dr Transport]

sounds like you need a wavelet transform, not a Fourier transform