Determine stability from open-loop frequency response.

A system maps an input ( x ) to output ( y ).

This is the bridge to digital processing. Key concepts include:

Continuous Signal ──> [ Sampler (Fs) ] ──> Aliased / Perfect Digital Signal The Nyquist-Shannon Theorem

. For a signal with 10 minutes of audio at 44.1 kHz, a standard DFT would take roughly to compute on a standard laptop.

Insufficient sampling causes high frequencies to mimic lower ones. Irreversibly distorts the digitized signal representation.

Ideal reconstruction: LPF with cutoff ( \omega_s/2 ) [ x_r(t) = \sum_n=-\infty^\infty x[n] ,\textsinc\left(\fract-nT_sT_s\right) ]