Introduction to Digital Filtering

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Introduction to Digital Filtering [Copy link]

	Let the filter factor of the first convolution filter be r = 0, 1, ..., m-1, and the filter factor of the second convolution filter be s = 1, 2, ... , then
	From this we get:
	This means that to calculate the current value, not only the current value and past value are used, but also the past value. Using the past value to calculate the current value is called a recursive relationship in mathematics, so this kind of filtering is called recursive filtering.
	If the above formula is written in the form of , it will be an infinitely long impulse response sequence. The filter with an infinitely long impulse response sequence is called an infinite impulse response (IIR) digital filter.
	Advantages and disadvantages : A steep transition band can be obtained with less computational effort, but it is difficult to ensure a linear phase shift.
2. Several issues in calling digital filtering subroutines
	1. Parameters during calling
	Commonly used digital filters in engineering are Butterworth, Chebyshev, Bessel, etc. They are all designed with the help of mature analog filters of the same name, so they have similar characteristic parameters.
	(1) Filter type Generally, the same subroutine can be used as a low-pass, high-pass, band-pass or band-stop filter by selecting different type parameters.
	(2) For low-pass filtering, only the upper cutoff frequency should be selected; for high-pass filtering, only the lower cutoff frequency should be selected; for band-pass and band-stop filtering, both the upper and lower cutoff frequencies should be selected.
	(3) Sampling frequency For all types of filtering, the sampling frequency of the filter timing should be input.
	(4) Filter order The higher the filter order, the faster the attenuation of the transition band of its amplitude-frequency characteristic curve. When the order n is 1, 2, 4, and 8, the amplitude-frequency characteristic curve of the low-pass Butterworth filter is shown in the figure.
	(5) Ripple Amplitude The amplitude-frequency characteristic of the Chebyshev digital filter in the passband is ripple-shaped, so this parameter is needed to control the ripple amplitude, which is generally 0.1 dB. The amplitude-frequency characteristic curve of the Butterworth and Bessel filters in the passband is relatively flat, so this parameter is not needed.
	2. Online filtering and offline filtering
	a. Offline filtering
	Definition : Filter an existing finite length time series
	Note : Since enough past values are needed to determine the current value, the first short segment obtained by filtering is incorrect. In other words, it must be long enough to get a normal filtering output.
	b. Online filtering
	Online filtering is a continuous input, which is mostly used for real-time sampling digital signal filtering. Obviously, after a short period at the beginning, normal filtering output will be obtained.
	3. Frequency mixing phenomenon
	When A/D conversion is obtained , if the sampling theorem is not satisfied, frequency mixing will occur, and the high-frequency components greater than n have been mixed into the low-frequency band of n. Digital filters cannot separate these mixed frequency components, so digital filtering cannot completely replace analog pre-processing filtering.
	4. Using FFT method to realize digital filtering
	The FFT method is used to find ( K=0, 1, ..., N-1). For the frequency band to be filtered out, let = 0, and then perform an inverse FFT transform on the obtained discrete time series to separate the frequency components within the frequency band. As shown in the figure.
	At this time, it should be noted that the symmetry is symmetrical.

yang_xian521

It's really an introduction. Anyway, give it a thumbs up.