Weird results out of fourier transform of unknown signal, what am I doing wrong? It has been a long time since I studied engineering, please forgive my mistakes.

I got data sampled from a digital accelerometer. It is sampled at 20 hz, then collapsed into 1 second epochs. The data is then filtered to remove noise.  The system outputs 0 at rest, a lot more during activity.

I'm looking at the fourier transform of the signal, 1024 samples, sampled once per second. I'm  seeing this: 

Here's a real-imaginary plot of the real-imaginary results of the Fourier transform.


The signal appears to be a helix in frequency domain.The system appears to oscillate around some limit cycle within frequency domain.

Is this possible? 
Is Fourier transform completely wrong for the digital signal?
 Should using only the DFT for this kind of analysis? 
Is my window size wrong ?
 Am I seeing aliasing due to incorrect window size? 

It has been a few years since my last engineering class, and I'd really appreciate any help on the subject. I got 3 books on engineering, signal analysis and transforms, but it takes time for this kind of knowledge to come back to me.
My guess: nothing to see here. Move along.

You mention that "the signal appears to be a helix in [the] frequency domain". I assert that what this helix really is, is a complex exponential. And there is nothing wrong with that, because complex exponentials are what you get when you time-delay a signal: $f(x-a)\Leftrightarrow \hat{f}(\xi)e^{-2\pi i a \xi}$. The helix pattern simply reflects that most of the power in the signal you are acquiring isn't located at $T=0$. (And it shouldn't be there anyway!)

Eyeballing, the period of oscillation in your frequency plot appears to be ~28 samples. At a sampling rate of 20hz, if what I'm saying is true, then most of the energy in your time-domain signal should be centered roughly around $t\approx\frac{28}{20}=1.4$ seconds. Was I close?

The real problem here is likely to be your plots. It seems like you're plotting raw real/imag DFT outputs. Don't do that. Instead, compute magnitude/phase from real/imag values, and plot that.