Filter construction: Nonperiodic frequency response
A filter has its own frequency response, defined by the magnitude and the phase plot.

A filter works for both periodic and non-periodic signals:
the reason is that while periodic signals can be represented as a superposition of infinite oscillations at frequencies multiples of the fundamental one (Fourier Series), non-periodic signals as well can be represented as a superposition of an infinite number of oscillations very close each other in frequency. In the limit, the series becomes a continuous sum, i.e., an integral (Fourier Integral). 

Mathematically, this could be explained by the fact that non-periodic signals
can be viewed as 'periodic' functions with 'infinite period' (which means infinitesimally small fundamental frequency, i.e.,  infinitesimally small frequency spacing between the spectral components).

Therefore, it is correct to say that human ear 'captures frequency components approximately between 20Hz and 20kHz', even if the sounds we hear are non-periodic signals.



What about filter implementation? 

If you want to limit the frequency components of a signal with some filter, you just need to design it keeping in mind the periodic sinusoidal components! 
If you want to achieve a sinc() filter impulse response (i.e., a sharp rectangular-shaped magnitude response) you should better accept that only approximations are possible in the real world; 
your bandwidth will never have such sharp edges and flat in-band response : instead, there is a well-known tradeoff between edge sharpness (related to the filter's selectivity together with the bandwidth) and the in-band flatness. 

For this reason, the bandwidth of filters is generally evaluated in terms of the -3dB frequency (i.e., the frequency corresponding to a gain reduction of 3dB with respect to the peak value).

Filter implementations in electronics design can be either passive (using just capacitors, inductors, resistors) and active (using active components like operational amplifiers). A popular example of active lowpass or highpass filter is the Sallen-Key topology.

Beyond these physical implementations, however, in most cases you start from some design specifications relating the bandwith, cut-off frequency, flatness, time-domain overshoot , center frequency and, according to them, a 'filter approximation' is chosen (this is true in particular for OpAmp-based active filters): these are just mathematical models which allow you to locate the poles of your filter starting from the desired frequency response. Popular examples are the Bessel, Čebyšëv and Butterworth filters; for the same model, different approximate implementations are possible.

There are online interactive tools which help in this design process (since sometimes there is a lot of nasty algebra behind it); these services are offered by famous analog IC technology companies; I don't know if I can link here, but just google 'filter design analog online' or something like that and you will find it.
I hope this helps and... enjoy!!!