Matlab digital filter design (IIR and the FIR) (containing Matlab code)

Matlab digital filter design (IIR and the FIR) (containing Matlab code)

The advantages and disadvantages of the FIR filter
advantages: good phase linearity, fast processing speed, the stability of the feedback loop is not stronger than the IIR.
Disadvantages: the FIR amplitude-frequency characteristic IIR low precision compared to
the IIR filter
advantages: better IIR filtering order at the same
drawback: a high level of non-linear phase, bi-directional filtering needs to be corrected when the correction is not easy to control.
The key is that the FIR filter window function: Here are
Hamming window:
FIR - the Hamming window

1. The lower side-lobe amplitude, in particular the first side lobe;
2. Sidelobe amplitude to decrease faster, in order to facilitate increased stopband attenuation;
3. The width of the main lobe is narrower, so that the filter transition band is narrower.
   N = 40
   leakage factor of 0.04%, relative sidelobe suppression -42.1dB, 0.0625 main lobe width (the normalized frequency)
   
   N, the longer the calculation time is, the longer group delay. Take N = 40 (according to different situations, the filter order may take different values, here we filtered audio signal of a specific period, thus taking 40)
   N greater, the longer the calculation time is, the longer the group delay. Take N = 40

Filtering results show:

blue front filtered signal; the red is FIR filtered signal
using the IIR elliptic filter filtering the audio signal:

filtering result shows:
direct songs IIR_ Eliptic (oval) filter
FIR filtering (yellow), IIR filtered (purple)
for different audio signals, the original spectrum analysis, only changes to the design parameters of the filter, to implement a digital filter.
See the code below:

[x,fs]=audioread('C:\Users\a\Desktop\大三上\精密仪器\讨论课题目\新闻(加噪声).wav');
n=length(x);
  y=fft(x,n);       %做FFT变换
  f=fs*(0:n/2-1)/n;
  subplot(2,1,1);
  plot(x);
 axis([0 1400000 -1.5 1.5]);
  title('原始新闻信号采样后的时域波形'); 
xlabel('时间轴')
ylabel('幅值A')
subplot(2,1,2); 
plot(f,abs(y(1:n/2))); 
axis([0 1000 0 5000]);
title('原始新闻信号采样后的频谱图'); 
xlabel('频率Hz'); 
ylabel('频率幅值');
% n=0:N-1;
% w=2*n*pi/N;
FIRsignal=IIR_BANDPASSCheby;
outsignal=filter(FIRsignal,x);
%  IIRsignal=IIR_BANDPASSEliptic;
%  outsignal2=filter(IIRsignal,outsignal);
% set(gca,'fontsize',15,'tickdir','out')
% axis([0 5.0E-4 -2 2])
% xlabel('Time');ylabel('Amplitude')
% legend('FIR低通数字滤波器后的信号')  
 m=fft(outsignal,n);
 f=48000*(0:n/2-1)/n;
 figure
 subplot(211);
  plot(outsignal);
   axis([0 1400000 -1.5 1.5]);
  title('新闻滤波信号时域波形');
xlabel('时间轴')
ylabel('幅值A')
 subplot(212);
 plot(f,abs(m(1:n/2)))
 axis([200 2700 0 5000]);
  title('新闻滤波信号频谱图'); 
xlabel('频率Hz'); 
ylabel('频率幅值');
    sound(1.5*outsignal,44100);
%    audiowrite('C:\Users\a\Desktop\精密仪器\讨论课题目\新闻(IIR滤波后).wav',outsignal2,44100);
%    sound(x,44100);

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