Analog and digital filters

Digital filters are used in discrete systems; analog filters are used in continuous-time systems and can also be used in discrete-time systems, such as SC (switched capacitor) filters.

A digital filter is an algorithm or device composed of a digital multiplier, an adder, and a delay unit. The function of a digital filter is to process the digital code of the input discrete signal to achieve the purpose of changing the signal spectrum. Digital filters can be implemented by computer software or large-scale integrated digital hardware.

Analog filters are divided into active and passive. Active filters are mainly composed of op amps, or cross-op amps, resistors, and capacitors. Passive filters are mainly composed of R, L, and C. Analog filters have problems such as voltage drift, temperature drift, and noise, while digital filters do not have these problems, so they can achieve high stability and accuracy.

From the perspective of implementation, analog filters are generally built with analog devices such as capacitors and inductors, while digital filters can be implemented through software or digital chips. When analog filter parameters change, it is very troublesome to replace capacitors and inductors. When digital filter parameters change, sometimes you only need to modify the coefficients to achieve this (such as when implementing software).

From the perspective of technical indicators, for example, it is very difficult for an analog filter to reach -60dB, while a digital filter can achieve this indicator relatively easily.

I think the bridge between analog and digital filters is the sampling theorem. Generally, the analog signal x(t) is sampled (such as A/D conversion) to obtain the digital signal x(n), and then these digital signals are passed through the digital filter. At this time, the filter outputs the digital signal y(n), and y(n) is converted to y(t) through a D/A converter. From x(t) to y(t) can be understood as analog filtering.

1. Digital filters are less sensitive to the external environment and have higher reliability. 2. Digital filters can achieve functions that analog filters cannot achieve, such as precise linear phase and multi-rate processing. 3. Digital filters can achieve signal processing of arbitrary precision as long as the word length is increased. 4. Digital filters are more flexible and can store signals at the same time. 5. Of course, the frequency domain width of digitally processed signals is limited by the sampling rate.

The biggest difference between analog filters and digital filters is that digital filters are flipped about the Fs/2 frequency, that is, symmetrical; while analog filters are not.

Therefore, a large number of interpolation filters are selected in the DAC to put the image frequency at a far frequency point, and then use analog filters such as SAW to filter out the image frequency in the RF band. Therefore, both digital and analog filters are indispensable.

1. The expressions of analog filters and digital filters are different:

Analog filtering is represented by H(S), while digital filtering is represented by H(Z). Analog filtering is mainly based on the approximation of amplitude-frequency characteristics, while digital filters can achieve phase matching;

2. There are two types of digital filters: IIR and FIR. IIR mainly has two methods: impulse response invariance method and bilinear transformation method, while FIR can achieve linear phase, window method, frequency sampling method, and optimization method. It can be achieved by FFT.