What is a filter and its application and selection

A filter, as the name suggests, is a device that filters waves. "Wave" is a very broad physical concept. In the field of electronic technology, "wave" is narrowly limited to describe the process of changing the value of various physical quantities over time. Through the action of various sensors, this process is converted into a time function of voltage or current, which is called the time waveform of various physical quantities, or a signal. Because the independent variable time' is a continuous value, it is called a continuous time signal, and it is also habitually called an analog signal (Analog Signal).
With the emergence and rapid development of digital electronic computer (generally referred to as computer) technology, in order to facilitate computer processing of signals, a complete theory and method of transforming continuous time signals into discrete time signals under the guidance of the sampling theorem has been developed. That is to say, the original signal can be expressed only by the sample values ​​of the original analog signal at a series of discrete time coordinate points without losing any information. Since the concepts of wave, waveform and signal express the changes of various physical quantities in the objective world, Nature is the carrier of all kinds of information that modern society depends on. Information needs to be spread, relying on the transmission of waveform signals. The signal may be distorted due to the existence of the environment and interference in every link of its generation, conversion and transmission, and even in quite a few cases, the distortion is so serious that the signal and the information it carries are distorted. buried deep in the noise.
Several low-pass prototype filters are the basis for designing filters by modern network synthesis methods. Most of the low-pass, high-pass, band-pass and band-stop filters are derived based on this characteristic. Because of this, the design of the filter is simplified and the accuracy is improved.
An ideal low-pass filter should allow all signals below the cut-off frequency to pass without loss, and all signals above the cut-off frequency should be attenuated infinitely, thus showing a rectangle on the amplitude-frequency characteristic curve, so it is also called a rectangular filter. filter (brick-wallfilter). Unfortunately, such ideal characteristics cannot be achieved, and all designs are simply trying to approximate the characteristics of a rectangular filter. Depending on the selected approximation function, different responses can be obtained. Although there are various approximation functions, the "Butterworth response" or the "Chebyshev response" is usually chosen considering the use requirements of the actual circuit.
"Butterworth response" bandpass filters have flat response characteristics, while "Chebyshev response" bandpass filters have steeper decay characteristics. Therefore, the specific characteristics to be selected need to be determined according to the specific requirements of the circuit or system. However, the "Chebyshev response" filter is the least sensitive to component changes, and has both good selectivity and good standing wave characteristics (located in the middle of the passband), so in general applications, it is recommended to use "Chebyshev Response" filter.
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