FFT + filtering sound = triggering signal
I would suggest building some sort of bandpass filter followed by a peak detector and a comparator.  You can build an RLC bandpass filter or perhaps an active bandpass filter with a couple of op amps and some passive components.  How steep does the cutoff on the filter need to be?  If you need a very steep cutoff, then you probably need an active filter.  

Alternatively, you can run the signal through an RC low pass filter, sample it with the Arduino ADC, and the filter it with a DSP bandpass filter.  I know Matlab has a toolbox for building FIR and IIR filters; I would suggest using that to calculate the correct filter coefficients.  I don't think the Arduino will give you enough cycles to do an FFT in real time, and you'd still have to do the low pass filtering and sampling with an FFT.