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Class #12 - Aliasing of Digital Signals

Engineering Applications of Correlation and Spectral Analysis, 2nd Edition

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(LEM) Cl“ Wlszu b15t.ov6r<‘-“{ bpwaLsW LAM; 1,03” 1942,) -: ‘ ;Xké:¢ x,6 I E E F E M “— LlfirK/M- t 5% Acceleration (mlsls) 10 E Centro Earthquake (1940 ~ NS) 15 2O 25 Time (sec) 30 35 40 Magnitude ‘EO Frequency Spectra of El Centro Earthquake (1940 - NS) 15 20 25 30 35 Frequency (Hz) mm- initial — Smoothed 40 45 50 Acceleration (mlsfs) Acceieration (mlsls) AND) 40 1O 10 El Centro Earthquake (1940 - NS) 15 20 25 Time (sec) El Centro Earthquake (1940 — NS) 15 2O 25 Time (sec) — EICentro I ~~~ Hanning Window 30 35 40 30 35 40 C:\matlale2\work\Class8.m Page 1 October 21, 2004 11:56:39 AM % Jerome Peter Lynch % University of Michigan, Ann Arbor % CEE619 — Advanced Dynamics and Smart Structures clear; % Load El Centro Earthquake {ECQ, Tecq, DTecq] = equake2('elcentroNS.eqf‘,9.81); % N is size of record size(ECQ,l); Z n % Plot Earthquake figure; plot(Tecq,ECQ); xlabe1('Time (sec)') ylabei('Acceleration (m/s/s)') titie('E1 Centro Earthquake (1940 — NS)‘) % Perform Fourier Transform (Discrete) w use “fft” [Hecq] = fft(ECQ); [Fecq] = [OzlzN—l]' * (l/(DTecq*N)); 5 Plot Discrete Fourier Spectra figure; semilogy(Fecq,abs(Hecq)); axis([0 (N/2)*(1/(DTecq*N)) 0 250]),- xlabe1('Frequency (Hz)') ylabe1('Magnitude') title('Frequency Spectra of El Centro Earthquake (1940 — NS)') % Averaging DFT of El Centro for j = 1:20 [Hech(:,j)] fft(ECQ(1+j*50:3000+j*SO),4000); end for k = l:N [Hech(k,l}] II mean(abs(Hech(k,:))); end 0 5 Plot Discrete Fourier Spectra hold on; semilogy(Fecq,abs(Hech),‘r‘); legend('Initial',‘Smoothed‘); % Perform Window on El Centro w = hanning(N); for i=l:N ' O C:\matlabR12\wor}c\ClassB.m Page 2 October 21, 2004 ll:56:39 AM WECQ(i,l) 'end w{i)*ECQ(i,l); O 5 Plot Earthquake figure; subplot{2,l,l) plot(Tecq,ECQ); xlabel('Time (sec)') ylabel('Acceleration (m/s/s)') title('El Centro Earthquake (1940 — NS)') hold on; plot(Tecq,w,'r-—‘}; legend('El Centro‘,‘Hanning Window') subplot(2,l,2} plot(Tecq,wECQ); xlabel(‘Time (seCJ') ylabel(‘Acceleration (m/s/s)') title(‘El Centre Earthquake (1940 w NS}‘) D 6 Perform DFT on Windowed El Centro [wHecq] = fft(wECQ); [ercq] = [OzlzNwl]E * (l/(DTecq*N)); 6 Plot Discrete Fourier Spectra figure; semilogy(Fecq,abS(Hecq)); hold on; semilogy(eroq,abs(wHecq),'g'); axis([0 (N/2}*(l/(DTecq*N)) O 250]); xlabel(‘Frequency (Hz)’) ylabel(‘Magnitude‘) title(‘Frequency Spectra of El Centro Earthquake (1940 — NS)‘) legend(‘No Window‘,’Hanning Window'}; § CDN$1%6fi. 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