Any band-limited linear time-invariant system can be implemented as a digital filter

Evidence

Most commonly, filters are implemented as digital filters using DSP structures, or as analogue filters using electronic circuits. … Digital filtering (Haykin, 1989; Jackson, 1989; Parks and Burrus, 1987) is a fundamental technique in digital signal processing. The input–output relationship of any band-limited LTI system (Figure 3.2) can be represented and implemented using a digital filter. Since algorithms for computing digital filters can be well optimized, this approach is useful when simulating or solving LTI engineering problems. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 417

Categorization

• QUESTION: This claims total representability of LTI systems as digital filters under band-limiting — worth chasing the exact conditions and limits on sampling rate.
• corroborated: 2 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 417