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, linear, time-invariant (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* (introduced in Appendix D). 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 often electrical models, or
``analogues'', of mechanical systems working in continuous time. If
the physical system is 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 (such as
``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)
- Q of a Complex Resonator
- Q of a Real Second-Order Resonator
- Decay Time is Q Periods
- Q as Energy Stored over Energy Dissipated

- Analog Allpass Filters

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University