Comments on: ACCELERATION, VELOCITY & DISPLACEMENT SPECTRA – OMEGA ARITHMETIC http://blog.prosig.com/2006/12/07/acceleration-velocity-displacement-spectra-%e2%80%93-omega-arithmetic/ Notes, tutorials, news and articles on digital signal capture, processing, techniques and applications Fri, 21 Nov 2008 19:36:05 +0000 http://wordpress.org/?v=2.5 By: Sun Xioachang http://blog.prosig.com/2006/12/07/acceleration-velocity-displacement-spectra-%e2%80%93-omega-arithmetic/#comment-462 Sun Xioachang Mon, 15 Sep 2008 07:31:11 +0000 http://blog.prosig.com/2006/12/07/acceleration-velocity-displacement-spectra-%e2%80%93-omega-arithmetic/#comment-462 must do the complex calculation, use both parts. u can only use the multiplicaion and addition, basic calculation rules are: (a+jb)*(c+jd) = a*c-b*d + j(a*d+b*c); (a+jb) + (c+jd) = (a+c) + j(b+d); if use c, u can use two arrays to hold the real part and imaginary part separately, input spectrum vactors are acc_real[N], acc_imagine[N], N is the number of vectors. in yr programm what u only need to calculate are: omega_disp_real[N], omega_disp_imagine[N]. Omega_disp_factor_real = -1.0/w^2; Omega_disp_factor_imagine = 0; for each n omega_disp_real[n] = acc_real[n]*Omega_disp_factor_real - acc_imagine[n]*Omega_disp_factor_imagine + acc_real[n]*Omega_disp_factor_imagine + acc_imagine[n]*Omega_disp_factor_real ; omega_disp_imagine[n] = acc_real[n]*Omega_disp_factor_real - acc_imagine[n]*Omega_disp_factor_imagine; omega_disp_real[n] = acc_real[n]*Omega_disp_factor_imagine + acc_imagine[n]*Omega_disp_factor_real ; time squence magitude value use: magitude_disp[n] = sqrtf(omega_disp_real[n]^2 + omega_disp_imagine[n]^2); phase[n]=... if use matlab, the vectors can be directly devided by -w^2, Omega_disp = acc_fft_vector./(-w^2). matlab takes care of the complex calculation automatically. time squence magitude value use magitude_disp = |Omega_disp|; phase value: ... must do the complex calculation, use both parts. u can only use the multiplicaion and addition, basic calculation rules are:

(a+jb)*(c+jd) = a*c-b*d + j(a*d+b*c); (a+jb) + (c+jd) = (a+c) + j(b+d);

if use c, u can use two arrays to hold the real part and imaginary part separately, input spectrum vactors are acc_real[N], acc_imagine[N], N is the number of vectors.

in yr programm what u only need to calculate are: omega_disp_real[N], omega_disp_imagine[N].

Omega_disp_factor_real = -1.0/w^2; Omega_disp_factor_imagine = 0;

for each n

omega_disp_real[n] = acc_real[n]*Omega_disp_factor_real - acc_imagine[n]*Omega_disp_factor_imagine + acc_real[n]*Omega_disp_factor_imagine + acc_imagine[n]*Omega_disp_factor_real ;

omega_disp_imagine[n] = acc_real[n]*Omega_disp_factor_real - acc_imagine[n]*Omega_disp_factor_imagine;

omega_disp_real[n] = acc_real[n]*Omega_disp_factor_imagine + acc_imagine[n]*Omega_disp_factor_real ;

time squence magitude value use: magitude_disp[n] = sqrtf(omega_disp_real[n]^2 + omega_disp_imagine[n]^2); phase[n]=…

if use matlab, the vectors can be directly devided by -w^2, Omega_disp = acc_fft_vector./(-w^2).

matlab takes care of the complex calculation automatically.

time squence magitude value use magitude_disp = |Omega_disp|; phase value: …

]]> By: Linus Lin http://blog.prosig.com/2006/12/07/acceleration-velocity-displacement-spectra-%e2%80%93-omega-arithmetic/#comment-442 Linus Lin Tue, 26 Aug 2008 11:25:42 +0000 http://blog.prosig.com/2006/12/07/acceleration-velocity-displacement-spectra-%e2%80%93-omega-arithmetic/#comment-442 Dear Dr Mercer: I read your article about Omega Arithmatic and try to apply it on my experiment results, and met some problems really need your help!! I use accelerometer to collect data. Following the article, I do the Fourier transform and divided by -w^2 to get the displacement spectrum. After that when i do the inverse Fourier transform to get displacement time sequence, the result is a "complex vector". So my question is how can I convert this "complex vector" to a displacement time sequence?? Is it correct to get the magnitude of each complex number, or just keep the real part and leave the imaginary part?? I really appreciate your kindly help!! Dear Dr Mercer:
I read your article about Omega Arithmatic and try to apply it on my experiment results, and met some problems really need your help!! I use accelerometer to collect data. Following the article, I do the Fourier transform and divided by -w^2 to get the displacement spectrum. After that when i do the inverse Fourier transform to get displacement time sequence, the result is a “complex vector”. So my question is how can I convert this “complex vector” to a displacement time sequence?? Is it correct to get the magnitude of each complex number, or just keep the real part and leave the imaginary part?? I really appreciate your kindly help!!

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