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Concept
Filter design
Summary
Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful.
The filter design process can be described as an optimization problem where each requirement contributes to an error function that should be minimized. Certain parts of the design process can be automated, but normally an experienced electrical engineer is needed to get a good result.
The design of digital filters is a deceptively complex topic. Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of advanced research.
Typical requirements which are considered in the design process are:
The filter should have a specific frequency response
The filter should have a specific phase shift or group delay
The filter should have a specific impulse response
The filter should be causal
The filter should be stable
The filter should be localized (pulse or step inputs should result in finite time outputs)
The computational complexity of the filter should be low
The filter should be implemented in particular hardware or software
An important parameter is the required frequency response.
In particular, the steepness and complexity of the response curve is a deciding factor for the filter order and feasibility.
A first-order recursive filter will only have a single frequency-dependent component. This means that the slope of the frequency response is limited to 6 dB per octave. For many purposes, this is not sufficient. To achieve steeper slopes, higher-order filters are required.
In relation to the desired frequency function, there may also be an accompanying weighting function, which describes, for each frequency, how important it is that the resulting frequency function approximates the desired one. The larger weight, the more important is a close approximation.
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Related units (6)
Related concepts (18)
Filter (signal processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist.
Infinite impulse response
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response which does not become exactly zero past a certain point, but continues indefinitely. This is in contrast to a finite impulse response (FIR) system in which the impulse response does become exactly zero at times for some finite , thus being of finite duration. Common examples of linear time-invariant systems are most electronic and digital filters.
Analogue filter
Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, mid-range, and tweeter loudspeakers; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen radio station in a radio receiver and rejection of others.