Digital filter design, the basic structure of a digital filter

I'm sorry, I'm too professional to understand this.

features: Transforms the input sequence into an output sequence through a certain operation.

Essence: The filtering process of a digital filter is a computational process.

Implementing a digital filter requires: an adder, a multiplier, and a unit delay

For the same system function h(z), there are many kinds of algorithms that can be implemented, and each algorithm corresponds to a different arithmetic structure.

Be sureComputing speed, economy, precision and stability

The basic structure of the IIR filter:Direct Type I, Direct Type II, Cascade Type, Parallel Type

Therefore, for IIR filters above the third order, other forms of structure such as cascade type and parallel type are adopted.

Each system function needs to be in the form of a product of several second-order primitive sections.

System functions can be paralleled by n1 first-order elementary sections and n2 second-order elementary sections and the constant a0.

Basic structure: direct type (convolutional type, cross-sectional type), cascading type, fast convolutional type, linear phase.

When the zero point of the control system is required, the transfer function h(z) is decomposed into the form of a second-order real coefficient factor.

The most important feature of the FIR system is that it can form a filter with linear phase characteristics.

Digital filters can be classified as one-dimensional, two-dimensional, or multi-dimensional digital filters according to the number of dimensions of the signal being processed.

A one-dimensional digital filter processes a signal as a sequence of univariate functions, such as a sample value of a time function.

A two- or multi-dimensional digital filter processes a signal as a function sequence of two or more variables.

For example, a 2D image discrete signal is a sampled value on planar coordinates.

An algorithm or apparatus for processing one-dimensional digital signal sequences.

In the corresponding z-domain to empty Hu leakage shift function in Figure 2, ar, bk are the digital filter coefficients, and z[y(n)] and z[x(n)] are the z-transforms of the output and input signal sequences, respectively.

The inverse z-transform of the transfer function h(z) is called the unit impulse response of a one-dimensional digital filter, i.e., h(n)=z-1 [as a limb h(z)].

If the unit impulse response h(n) of a digital filter has only a finite number of non-zero values, it is called a finite impulse response digital filter.

If the unit impulse response has an infinite number of non-zero values, it is called an infinite impulse response digital filter.

The finite impulse response digital filter generally adopts a non-recursive algorithm structure, so it is also called a non-recursive digital filter.

The infinite impulse response digital filter can only adopt a recursive algorithm structure, so it is also called a recursive digital filter.

An algorithm or apparatus for processing two-dimensional digital signal sequences.

The corresponding transfer function is as follows: in Figure 5, where a b is the filter coefficient, and z[y(m,n)] and z[x(m,n)] are the two-dimensional z-transforms of the output and input signal sequences, respectively.

The two-dimensional inverse z-transform h(m,n)=z-1 of the transfer function h(z1,z2) is called the unit impulse response of the two-dimensional digital filter.

The output y(m,n) of a two-dimensional digital filter can also be expressed as a two-dimensional discrete convolution of the input signal sequence x(m,n) and the unit impulse response h(m,n) (Figure 6).

The response of two-dimensional digital filters to unit impulse is also divided into two types: finite impulse response and infinite impulse response.

The two-dimensional finite impulse response digital filter is a non-recursive algorithm structure, so it is also called a two-dimensional non-recursive digital filter.

The two-dimensional infinite impulse response digital filter is a recursive algorithm structure, so it is also called the two-dimensional recursive digital filter rotten waver.

Dear --- how the digital filter is filtered1The main difference between a digital reed filter-oscillator and an analog filter is that one is numerically calculated by software (program) (digital filter-waver), and the other is obtained by hardware circuit (analog filter-waver). 2.

There are many principles of digital filters, and averaging is one of them. Averaging is the process of filtering out any signal that has a variable component of frequency. The digital filter can also be programmed according to different principles to perform special calculations on the acquired signal to filter out the signal at a specific frequency.

3.The principle of analog filter is mainly to use the low impedance of the capacitor to the high-frequency signal, the high impedance of the low-frequency signal of the Shenliang and the inductance to the low impedance of the low-frequency signal and the high-impedance of the high-frequency signal to filter out the signal of a specific frequency. 4.

I hope to help you kiss it.

Hello dear, according to your problem description: Digital filter filtering operation is as follows: Commonly used digital filtering methods.

1. Average FilteringAverage filtering is the average algorithm for multiple sampled values, which is the most commonly used method to eliminate random errors. It can be divided into the following types. 1.

Arithmetic mean filteringThe arithmetic mean filtering is to sample the measured signal y m times within the sampling period t, and the arithmetic mean value after adding m sampling values is taken as the effective value of this sampling. The number of filter samples m determines the smoothness and sensitivity of the signal. Increasing the value of m can improve the smoothness, but the sensitivity of the system decreases, and the value of the number of samples m varies with the control object.

Under normal circumstances, the flow signal can be about 10, the pressure signal can be about 4, and the slow-varying signal such as temperature and composition can be taken 2 or even without arithmetic averaging. When compiling the algorithm, m is generally taken as an integer power equal to 2, so that the average value can be obtained by using the shift instead of division. This algorithm is suitable for signal filtering and filtering where there is periodic interference2

The arithmetic averaging filter of the depolarization does not eliminate the obvious accidental pulse interference, but only averages it into the sampling results, thus reducing the measurement accuracy. The depolarization averaging filter compares m data sampled continuously, removes the maximum and minimum values, and then calculates the arithmetic mean of the remaining m-2 data. When compiling the algorithm program, in order to facilitate the use of shift instead of division to obtain the average value, m-2 should be taken as equal, so m is taken as equal.

This algorithm is suitable for signal filtering of sharp pulse interference commonly encountered in industrial scenarios through nuclear front shooting. 3.There is a contradiction between smoothness and sensitivity in weighted average filtering, arithmetic mean filtering and depolarization average filtering.

If the number of sampling is too small, the smoothing effect is poor, and if the number of samples is too much, the sensitivity will decrease, and the change trend of the measurement parameters will not be sensitive. In order to coordinate the relationship between the two, a weighted average filter can be used.

Summary. It cannot be said that there is an obvious relationship between the zero pole and the high and low pass, but generally we derive the frequency response of the system in an appropriate way, and then according to the requirements of the stability of the system (this is related to the zero pole), and finally deduce the high and low pass characteristics of the system.

And the normalized frequency:

For a low-pass filter with a cut-off frequency of a certain Wc, let s wc replace S in the normalized prototype filter system, i.e., .

s-->s/wc）

For the high-pass filter, the band transformation method can be used, and the normalized prototype filter is obtained by frequency band transformation.

Digital Signal Processing + Filter Calculations.

Hello, it's an honor for me to answer your questions, it will take a little time to sort out the answers, please be patient

Hello! It depends on the condition that the fir filter has a strict linear phase, and the condition for it to have a linear phase is dual-symmetry: h(n) = h(n-1-n) odd symmetry:

h(n) = h(n-1-n) and h(n) is a real number.

It cannot be said that there is an obvious relationship between the zero pole of yx and the high and low pass, but generally we get the frequency response of the system in an appropriate way, and then according to the stability of the system (this is related to the zero pole), and finally launch the high hail and low pass characteristics of the system. And the normalized frequency: For the low-pass filter with a cut-off frequency of a certain wc, let s wc replace the s in the normalized prototype filter system, i.e., s-->s wc) For the high-pass filter, the frequency band conversion method can be used, and the normalized prototype filter is obtained by frequency band transformation.

Summary. Digital filtering, also known as software filtering, is actually an algorithm that can weaken or eliminate the effects of interference and noise through the processing of digital filtering programs.

Digital filtering, also known as software filtering, is actually an algorithm that can weaken or eliminate the effects of interference and noise through the processing of digital filtering programs.

In addition to taking anti-interference measures for the signal in the hardware, it is also necessary to carry out the digital filtering in the software to further eliminate all kinds of interference attached to the data, so that the collected data can truly reflect the actual process situation on site.