Application of Matlab in FIR digital filter

The design scheme of FIR digital filter is proposed , and the filter simulation is realized based on Matlab. By using the functions provided by Matlab signal processing toolbox, the appropriate window function is selected to write the program, in which the window function is selected according to the processing requirements of the actual signal and the parameters are compromised. The experiment obtains relatively ideal filter characteristics and can achieve better filtering effect. Moreover, in practical applications, only the filter parameters need to be modified according to the requirements, and combined with the corresponding changes in the program, filters with different functions can be realized. In addition, the method of designing filters using FDATool is introduced, and a variety of filters can be realized by simply modifying the parameters.

1 Digital filter and design scheme

When applying digital filters to process analog signals, the input analog signals must first be band-limited, sampled, and converted to analog/digital. The sampling rate of the digital filter input signal should be greater than twice the bandwidth of the processed signal. Its frequency response has a periodic repetition characteristic with the sampling frequency as the interval, and is mirror-symmetric at the folding frequency, i.e., 1/2 sampling frequency. The output signal of the filter must be converted to digital/analog and smoothed.

The relationship between the output value u(Kt) of the FIR digital filter and the past value u(Kt-kt) of the output is as follows:

This is a process of continuous multiplication and accumulation, which solves the problem of the filter coefficient α. The filter design can be realized by adding multiplication and addition calculations. Since the unit impulse response h(n) of the FIR filter is a finite length sequence, the filter has no instability problem. The FIR filter is generally a non-recursive structure. Therefore, when using Matlab to design, finite precision calculation is used to avoid unstable phenomena such as polarity oscillation in the recursive structure. The two common FIR filter design methods are the window function method and the frequency sampling method. Although the frequency sampling method can accurately control the frequency response of the sampling point, the transition point must be inserted in the design to improve the ripple, and the cutoff frequency is not easy to control. The transition point also needs further optimization. In contrast, the window function rule is a basic design concept and the design method is relatively mature. In addition, the functions provided in Matlab can easily realize the design of windowed linear phase FIR filters, including the more common low-pass, band-pass, high-pass and band-stop digital filters. This paper adopts the design method of combining window function with programming.

The basic idea of ​​the window function method is to first give the ideal filter frequency response as

,

Where: ωc is the cut-off frequency; α is the sampling delay.

The required frequency response is

, the next task is to make

Approach

The windowed w(n) is truncated to the unit sampling response hd(n) (see equation (3)) of the ideal filter to obtain the h(n) to be designed.

For the FDATool design method, this paper uses Matlab to complete it by selecting appropriate parameters.

2 FIR digital filter design

2.1 Window function method to design FIR filter solution

In Matlab, window functions can be directly generated: Rectangle Window, Triangular Window, Hanging Window, Kaiser Window, etc. The window can be loaded by calling the system function. The specific calling method is as follows: calling format: w=function name (n), a rectangular window w is generated according to the length n. Generally, the normal ECG signal frequency range is within 0.05~100 Hz, which is itself a relatively weak electrical signal. When it is interfered by other organs of the body, the ECG signal will be seriously distorted. In addition, the existence of electronic device noise and 50 Hz power frequency signal must be considered. This requires to eliminate the influence of noise and interference as much as possible. The design indicators of the low-pass filter selected here are: passband cutoff frequency ωp=0.2π, stopband cutoff frequency ωs=0.3π, and minimum stopband attenuation As≥50 dB. Therefore, the transition bandwidth tr_width=ωs-ωp and the column length N=10 π/tr_width are obtained. When selecting a window function, it is generally recommended to choose a wider main lobe, which can increase the attenuation of the stopband and ensure the stability of the passband. In addition, while ensuring the minimum attenuation index of the stopband, the column length N value is appropriately increased to narrow the transition band. According to the characteristics of the minimum stopband attenuation of the window function. Only the Hamming window and the Kaiser window can provide an attenuation greater than 50 dB. In practical applications, the selection of window functions is mostly a compromise between them. The Kaiser window can compromise the main lobe width and sidelobe attenuation by changing the parameter value. The filter based on this has strong adaptability and is relatively flexible. This article adopts the Kaiser window programming design. The window function design method is to use a certain width window function to intercept an infinite pulse response sequence to obtain a finite length pulse response sequence. The design steps are:

(1) The unit impulse response hd(n) of the ideal filter is obtained by inverse Fourier transform.

(2) Determine the window function W(n) and window length N based on performance indicators.

(3) Obtain the unit impulse response h(n) of the actual filter, where h(n) is the designed FIR filter coefficient vector a(n).