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⛄ 内容介绍
许多信号包含多个具有时变瞬时频率 (IF) 的分量，这些分量具有共同的轨迹趋势，例如机械振动信号、语音信号和生物医学信号。为了分析此类信号并实现高时频分辨率，本文提出了一种称为参数化重采样时频变换（PRTF变换）的方法。采用一般参数化时频变换（GPTF变换）的思想，我们使用参数化核来表示重采样函数，并进一步构造时变和时不变重采样算子来消除中频变化并重新定位中频位置。这些算子可以同时提高时频表示（TFR）中多个分量的能量集中度。
⛄ 核心代码
% Numerical example for W-PRTF transformclcclearclose all%% InitializeSampFreq = 5000;t = 0:1/SampFreq:1;RTF = 200*(1.5+sin(10*t)+sin(30*t)/3+sin(50*t)/5+sin(70*t)/7);phase = 200*(1.5*t-cos(10*t)/10-cos(30*t)/9/10-cos(50*t)/25/10-cos(70*t)/49/10);R = [(1:-0.1:0)';zeros(11,1)];G = [(1:-0.1:0)';(0:0.1:1)'];B = [ones(11,1);(1:-0.05:0.5)'];map = [R G B];%% Generate the signalSig = 0;for i = 1:6 Sig = Sig + cos(2*pi*(0.6+i*0.4*phase));end%% Waveformfigureset(gcf,'Position',[20 100 320 250]); set(gcf,'Color','w'); plot(t,Sig,'linewidth',0.5,'color','b');xlabel('Time (Sec)','FontSize',12,'FontName','Times New Roman');ylabel('Amplitude','FontSize',12,'FontName','Times New Roman');set(gca,'FontSize',12)set(gca,'linewidth',1);axis([0 1 -8 8])%% Short-time frequency transformfigure[Spec,f] = STFT(Sig',SampFreq,1024,1024);imagesc(t,f,Spec); colormap(map)axis([0 t(end) 0 1500]);set(gcf,'Position',[20 100 320 250]); xlabel('Time (Sec)','FontSize',12,'FontName','Times New Roman');ylabel('Frequency (Hz)','FontSize',12,'FontName','Times New Roman');set(gca,'YDir','normal')set(gca,'FontSize',12);set(gcf,'Color','w');%% Parameterized resampling time-frequency transform with Fourier Series kernelfigurecoef = [10 1.5 0 0 0 0 0 0 0 1 0 1/3 0 1/5 0 1/7];[Spec,f] = W_PRTFtransform(Sig',SampFreq,coef,1024);%[Spec,f] = W_PRTFtransform2(Sig',SampFreq,coef,1024,0.99);imagesc(t,f,abs(Spec)); colormap(map)axis([0 1 0 1500]);set(gcf,'Position',[20 100 320 250]); xlabel('Time (Sec)','FontSize',12,'FontName','Times New Roman');ylabel('Frequency (Hz)','FontSize',12,'FontName','Times New Roman');set(gca,'YDir','normal')set(gca,'FontSize',12);set(gcf,'Color','w');
⛄ 运行结果
⛄ 参考文献
T. Li, Z. Peng, H. Xu and Q. He, "Parameterized domain mapping for order tracking of rotating machinery," in IEEE Transactions on Industrial Electronics, 2022, doi: 10.1109/TIE.2022.3201311
