1 Introduction
Filters are one of the commonly used test instruments in dynamic test signal processing. A filter is a device used to eliminate interfering noise. The input or output is filtered to obtain pure DC power. A circuit that effectively filters out frequencies at a particular frequency or frequencies outside of that frequency is a filter whose function is to obtain a particular frequency or to eliminate a particular frequency. Filters, as the name implies, are devices that filter waves. "Wave" is a very broad physical concept. In the field of electronic technology, "wave" is narrowly limited to the process of describing the fluctuations of various physical quantities over time. This process is converted into a time function of voltage or current by the action of various types of sensors, which is called a time waveform of various physical quantities, or a signal. Since the independent variable time 'is continuous value, it is called continuous time signal, which is often used for anti-aliasing filtering to avoid aliasing in the frequency domain during Fourier transform, or complex signals with multiple frequency components. In the process, the frequency components of interest are extracted, and the frequency components that are not of interest are attenuated. In traditional test instruments, the function of the filter usually depends on the hardware system.
With the continuous improvement of digital signal processing technology, the rapid development of computer hardware technology and the rapid development of software technology, the design idea of ​​test instrument system has undergone major changes. Some traditional dedicated test equipment will gradually be replaced by virtual instruments with computer and application software as the core [1]. The emergence of virtual instruments marks the arrival of the era of "The soft is the instrument." In the Computer Aided Test (CAT), the functions of the analog filter (AF, Analog Filter) can be divided into passive and active filters. Passive Filters: Two types of circuits mainly consist of passive components R, L and C. Active filter: integrated op amp and R, C components, with no inductance, small size, light weight and so on. The open-loop voltage gain and input impedance of the integrated op amp are high, and the output resistance is small. After the active filter circuit is formed, it also has a certain voltage amplification and buffering effect. However, the bandwidth of the integrated op amp is limited, so the operating frequency of the current active filter circuit is difficult to do very high. A digital filter can be used instead. The implementation of digital filters is not only much easier than analog filters, but also achieves better filter performance.
2 Time domain description and classification of digital filters
For a linear shift invariant (LSI, Linear Shift Invariant) discrete time system, as shown in Figure 1, the following difference equation can be used: y(n) + ∑Nk = 1a(k)y(nk) = ∑Mr = 0b (r)x(nr)(1) where a(k) and b(r) are equation coefficients
Figure 1 LSI system
If a(k), k=1, 2, Λ, N are not all zero, the system is an infinite impulse response (IIR) system. If a(k) is zero and b(0)=1, then y(n)=∑Nr=1b(r)x(nr)+x(n)(2) The system has a finite impulse response ( FIR) system.
Thus, the digital filter is divided into an IIR filter and an FIR filter in terms of implementation. These two types of filters are very different in terms of performance and design methods. A digital filter consists of an algorithm or device consisting of a digital multiplier, an adder, and a delay unit. The function of the digital filter is to perform arithmetic processing on the digital code of the input discrete signal to achieve the purpose of changing the spectrum of the signal. A digital filter is a discrete-time system (a specific functional device that converts an input discrete-time signal into a desired output discrete-time signal according to a predetermined algorithm). When applying analog filters to analog signals, the input analog signals must first be band limited, sampled, and analog-to-digital converted. The sampling rate of the digital filter input signal should be greater than twice the bandwidth of the processed signal. The frequency response has a periodic repetition characteristic at intervals of the sampling frequency, and is mirror-symmetrical at the folding frequency, that is, the 1/2 sampling frequency point. In order to obtain an analog signal, the output digital signal processed by the digital filter is subjected to digital-to-analog conversion and smoothing. The digital filter has the advantages of high precision, high reliability, programmable change characteristics or multiplexing, and easy integration. Compared with the FIR filter, the IIR digital filter retains the advantages of the analog filter, and the amplitude-frequency characteristics are better, but there is phase distortion. The latter has better phase-frequency characteristics and can achieve linear phase, but it is much higher than the former in the same index.
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