Filter (signal processing)
Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, computer graphics, and structural dynamics.
The modern design methodology for linear continuous-time filters is called network synthesis.
On the other hand, analog audio systems using analog transmission can tolerate much larger ripples in phase delay, and so designers of such systems often deliberately sacrifice linear phase to get filters that are better in other ways—better stop-band rejection, lower passband amplitude ripple, lower cost, etc.
Often the components in different technologies are directly analogous to each other and fulfill the same role in their respective filters.
For instance, the resistors, inductors and capacitors of electronics correspond respectively to dampers, masses and springs in mechanics.
Due to the sampling involved, the input signal must be of limited frequency content or aliasing will occur.
This means that quartz resonators can directly convert their own mechanical motion into electrical signals.
In this scheme, a "tapped delay line" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal.
The tapped delay line has become a general scheme of making high-Q filters in many different ways.
SAW (surface acoustic wave) filters are electromechanical devices commonly used in radio frequency applications.
The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response filter.
The garnet sits on a strip of metal driven by a transistor, and a small loop antenna touches the top of the sphere.
The advantage of this method is that the garnet can be tuned over a very wide frequency by varying the strength of the magnetic field.
Atomic clocks use caesium masers as ultra-high Q filters to stabilize their primary oscillators.
Another method, used at high, fixed frequencies with very weak radio signals, is to use a ruby maser tapped delay line.
The construction of a transfer function involves the Laplace transform, and therefore it is needed to assume null initial conditions, because And when f(0) = 0 we can get rid of the constants and use the usual expression An alternative to transfer functions is to give the behavior of the filter as a convolution of the time-domain input with the filter's impulse response.
The convolution theorem, which holds for Laplace transforms, guarantees equivalence with transfer functions.
Impedance matching structures invariably take on the form of a filter, that is, a network of non-dissipative elements.
For instance, in a passive electronics implementation, it would likely take the form of a ladder topology of inductors and capacitors.
Although the prime purpose of a matching network is not to filter, it is often the case that both functions are combined in the same circuit.
