Analog Filters

For our purposes, an *analog filter* is any filter which operates
on *continuous-time* signals. In other respects, they are just
like digital filters. In particular, LTI analog filters can be
characterized by their (continuous) impulse response , where
is time in seconds. Instead of a difference equation, analog filters
may be described by a *differential equation*. Instead of using
the *z* transform to compute the transfer function, we use the *Laplace
transform*. Every aspect of the theory of digital filters has its
counterpart in that of analog filters. In fact, one can think of
analog filters as simply the limiting case of digital filters as the
sampling-rate is allowed to go to infinity.

In the real world, analog filters are usually electrical models, or
``analogues'', of mechanical systems working in continuous time. If
the physical system is linear and time-invariant (LTI) (*e.g.*,
consisting of elastic springs and masses which are constant over
time), an LTI analog filter can be used to model it. Before the
widespread use of digital computers, physical systems were simulated
on so-called ``analog computers.'' An analog computer was much like
an analog synthesizer providing modular building-blocks
(``integrators'') that could be patched together to build models of
dynamic systems.

- Example Analog Filter
- Capacitors

- Inductors

- RC Filter Analysis
- Driving Point Impedance
- Transfer Function
- Impulse Response
- The Continuous-Time Impulse
- Poles and Zeros

- RLC Filter Analysis

- Relating Pole Radius to Bandwidth
- Quality Factor (Q)

- Analog Allpass Filters

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