Passive and Digital filters
Passive Filters
A filter is said to be passive when its composition is made up entirely of passive circuit elements, such as the inductors, capacitors, and resistors. However, the design of high frequency selective passive filters is based exclusively on reactive elements, like the inductors and capacitors. Resistive elements enter the design only as source resistance or load resistance.
The determination of the elements of the filter is known as network synthesis. It is true that passive filters played a major role in design and communications until digital filters were introduced in 1963.
Digital filters
The filtering action that is to be performed on a continuous-time signal is implemented using computation in digital filters. A / D or analog to digital converter is used to convert the continuous-time signal x(t) into a corresponding sequence number. The digital filter processes the sequence of numbers x[n] on a sample-by-sample basis to produce a new sequence of numbers, y[n] which is then converted into the corresponding continuous-time signal by the digital-to-analog (D / A) converter. Finally, the reconstruction or low-pass filter at the output of the system produces a continuous-time signal y(t), representing the filtered version of the original input signal x(t).
Two important points about digital filters that should be noted are:
1. The underlying design procedure is usually based on the use of an analog or infinite precision model for the samples of input data and all internal calculations, this is done in order to take the advantage of a discrete-time, but continuous-amplitude mathematics. The designers get a theoretical framework from the resulting discrete-time filter.
2. When the discrete-time filter is implemented in digital form for practical use, the input data and the internal calculations are all quantized to be of finite precision.
Analog filters, exemplified by the passive filters, are characterized by an impulse response of infinite duration.
On the other hand, the digital filters are classified into classes, depending on the duration of the impulse response.
The digital filters can be further divided into two other classes:
Finite-duration impulse (FIR) digital filters
They are operations that are governed by linear constant-coefficient difference equations of a nonrecursive nature. The transfer function of an FIR digital filter is a polynomial in z^-1, there are also certain properties of the finite-duration impulse response that are important to keep in mind.
Some points to be noted about them are:
- They have finite memory.
- They are BIBO stable.
- There is no phase distortion.
Infinite-duration impulse response (IIR) digital filters
They are filters whose input-output characteristics are governed by linear constant-coefficient difference equations of recursive nature.
The use of an IIR digital filter generally results in a shorter filter length than does the use of the corresponding FIR digital filter.
Though, this is possible only with phase distortion and a transient start-up that is not limited to a finite time interval.
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