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A. Irreversibility and Generalized Noise // Phys.Rev. 1951. Vol. 83. P. 34–40.105. CoyneD.,WillemsP.ThermalNoiseIncreasedueGold Coated Barrel // LIGO Technical Note T080003.toa2008.DCC: https://dcc.ligo.org/T080003/public.106. Harry G., Bodiya T. P., DeSalvo R. Optical Coatings and Thermal Noisein Precision Measurement. 1 edition. Cambridge: Cambridge UniversityPress, 2012. P. 75. ISBN: 9781107003385.113Приложение АИсходный код цифровой обработки сигналаА.1. Реализация метода Уэлча на языке С++ сиспользованием библиотеки fftw12// e r r o r and i n c o r r e c t p a r a m e t e r s c h e c k s a r e omitted f o r s i m p l i c i t y3b o o l Q f f t w H e l p e r : : p r e p a r e S i m p l e ( i n t FS , i n t N, Window win )4{clear () ;567m_FS = FS ;8data_step = d a t a _ s i z e = d a t a _ s t a r t = c_data_size = 0 ;9window_size = N;10r e t u r n p r e p a r e C o r e ( win ) ;1112}13b o o l Q f f t w H e l p e r : : p r e p a r e C o r e (Window win )141516{i n t f f t _ o u t _ s i z e = window_size /2 + 1 ;1718m_in_array = ( double * ) f f t w _ m a l l o c ( s i z e o f ( double ) * window_size ) ;19m_out_array = ( fftw_complex * ) f f t w _ m a l l o c ( s i z e o f ( fftw_complex ) *fft_out_size ) ;2021m_freqs = new double [ f f t _ o u t _ s i z e ] ;22m_psd = new double [ f f t _ o u t _ s i z e ] ;2324f o r ( i n t i =0; i <f f t _ o u t _ s i z e ;++ i )25{26m_freqs [ i ] = i *m_FS/ double ( window_size ) ;114m_psd [ i ] = 0 .
;27}2829m_window = new double [ window_size ] ;303132wS1 = wS2 = 0 ;33d ouble tmp ;34f o r ( i n t i =0; i <window_size;++ i )35{36tmp = window ( win , window_size , i ) ;37wS1+=tmp ;38wS2+=tmp*tmp ;39m_window [ i ] = tmp ;}4041wENBW = m_FS*wS2 / ( wS1*wS1 ) ;4243m_plan = fftw_plan_dft_r2c_1d ( window_size , m_in_array , m_out_array44, FFTW_ESTIMATE) ;return true ;4546}4748v o i d Q f f t w H e l p e r : : simpleFFT ( c o n s t double * i n p u t )49{50i n t i =0;51i n t f f t s = window_size /2 + 1 ;52d ouble f f t _ c o e f f = 2 . / (m_FS*wS2 ) ;53f o r ( i =0; i <window_size;++ i )54{m_in_array [ i ] = ( * ( i n p u t++)) * m_window [ i ] ;5556}57f f t w _ e x e c u t e ( m_plan ) ;58f o r ( i =0; i < f f t s ;++ i )59{60m_psd [ i ] = f f t _ c o e f f * fftw_complex_abs2 ( m_out_array [ i ] ) ;115}6162}6364b o o l MainThreadWorker : : rawPRMsubblockFFT ( c o n s t QString& f i l e P a t e r n ,i n t block , i n t s u b b l o c k )6566{QList<QPointD > m o n i t o r _ f r e q s = getFreqRange ( prm_params .
f f t _ f r e q s );67QfftwHelper f f t _ h e l p e r ;68i n t FS ;69i n t sampleCount , stepCount ;70uint32_t samplesRead ;71c o n s t double * f r e q s ;72c o n s t double * psd ;73int fft_size , fft_count ;74RawFileReader : : SubblockReadInfo r e a d I n f o ;75PRMConverter c o n v e r t e r = MainWindow : : makeConverter ( s e t ) ;7677c o n s t PRMRawFile : : ChannelMapping& chmap = rawPrmReader .channelMapping ( ) ;78QList<i n t > normdInds = QList<i n t >()<<chmap . a m p l i f 1 <<chmap . a m p l i f 2<<chmap . phd1<<chmap .
phd2 ;79FS = rawPrmReader . getSamplingFrequency ( b l o c k ) ;80sampleCount = prm_params . fft_sample_time *FS ;81stepCount = Q f f t w H e l p e r : : windowStep ( Q f f t w H e l p e r : : HFT248D ,sampleCount ) ;8283rawPrmReader . prepareReadData ( block , subblock , RawFileReader : :Output_NormDiff , normdInds , - 1 ,readInfo )848586f f t _ h e l p e r . p r e p a r e S i m p l e ( FS , sampleCount , Q f f t w H e l p e r : : HFT248D) ;8788freqs = fft_helper .
frequencies () ;89psd = f f t _ h e l p e r . psd ( ) ;11690fft_size = fft_helper . f f t S i z e () ;91f o r ( i n t k=0;k<f f t _ h e l p e r . f f t S i z e ( ) ;++k )92{93i f ( f r e q s [ k]>=prm_params . fft_max_freq )94{95fft_size = k;96break ;}9798}99100// ///101SmartArray<double> normd_data ( sampleCount ) , b u f f e r ( sampleCount *readInfo . channels ) ;102SmartNumberArray<double> o u t _ f f t ( f f t _ s i z e ) ;103104d ouble fmain = 0 ;105106QFile m f f t _ f i l e ( QString ( f i l e P a t e r n+s b F i l e P a t ( block , s u b b l o c k )+" normd - s t %1- Mfft .
praw" ). a r g ( qRound ( prm_params . fft_sample_time ) ) ) ;107108m f f t _ f i l e . open ( QFile : : WriteOnly ) ;109QTextStream ostm ;110111samplesRead = sampleCount ;112rawPrmReader . doReadSubblock ( r e a d I n f o , samplesRead , b u f f e r . p o i n t e r ( ) ,normd_data . p o i n t e r ( ) ) ;113a p p l y L u mi n o s it y ( normd_data . p o i n t e r ( ) , samplesRead , prm_params .lumin_val ) ;114115f f t _ h e l p e r .
simpleFFT ( normd_data . p o i n t e r ( ) ) ;116o u t _ f f t . cp ( psd ) ;117fft_count = 1;118119fmain = f r e q s [ maxIndex ( psd+f m a i n _ o f f s e t , fmain_last - f m a i n _ o f f s e t )+fmain_offset ] ;117120121w h i l e ( r e a d I n f o . samplesRead < r e a d I n f o .
dataCount )122{memmove( normd_data . p o i n t e r ( ) , normd_data . p o i n t e r ( )+stepCount ,123( sampleCount - stepCount ) * s i z e o f ( double ) ) ;124125samplesRead = stepCount ;126rawPrmReader . doReadSubblock ( r e a d I n f o , samplesRead , b u f f e r .pointer () ,normd_data . p o i n t e r ( )+sampleCount -127stepCount ) ;128i f ( samplesRead != stepCount )129{break ;130131}132a p pl y L u mi n o s it y ( normd_data . p o i n t e r ( )+sampleCount - stepCount ,samplesRead , prm_params .
lumin_val ) ;133134f f t _ h e l p e r . simpleFFT ( normd_data . p o i n t e r ( ) ) ;135o u t _ f f t . add ( psd ) ;136fmain += f r e q s [ maxIndex ( psd+f m a i n _ o f f s e t , fmain_last f m a i n _ o f f s e t )+f m a i n _ o f f s e t ] ;++f f t _ c o u n t ;137138}139fmain /= f f t _ c o u n t ;140141ostm . s e t D e v i c e (& m f f t _ f i l e ) ;142ostm<<"#F␣ S_theta ␣S_M\n#Hz␣ rad ^2/Hz␣Nm^2/Hz\n#FS : "<<FS143<<"␣ENBW: ␣"<<f f t _ h e l p e r . enbw ( )<<"␣F0 : "<<fmain144<<"␣Uhv : "<<rawPrmReader . getSubblockUhv ( block , s u b b l o c k )<<"␣Q: "<<c o n v e r t e r .
c o e f f _ q145<<"␣Nwin : "<<sampleCount146<<"\n#S t a r t e d : ␣"<<QMat : : toMatlabDateTime ( rawPrmReader .getBlockTime ( b l o c k ) . addMSecs ( r e a d I n f o . s t a r t T i m e *1000) ) ;147148ostm . setRealNumberNotation ( QTextStream : : S c i e n t i f i c N o t a t i o n ) ;118149ostm . s e t R e a l N u m b e r P r e c i s i o n ( 8 ) ;150f o r ( i n t k=1;k<f f t _ s i z e ;++k )151{152ostm<<"\n"<<f r e q s [ k]<<"␣" ;153o u t _ f f t [ k]*= PRMSetupConstants : : kNormdToTheta *PRMSetupConstants : : kNormdToTheta /fft_count ;154ostm<<o u t _ f f t .
a t ( k )<<"␣"<<c o n v e r t e r . psdThetaToM ( o u t _ f f t . a t ( k ) ,155f r e q s [ k ] , fmain ) ;}156157return true ;158159}А.2. Библиотека для связи сред С++ и Matlab черезбинарный файл в формате Matlab12s t r u c t QMATWRITESHARED_EXPORT ArrayFlags3{4ArrayFlags ( ) : d a t a _ c l a s s (mxDOUBLE_CLASS) , f l a g s ( 0 ) {}5e x p l i c i t ArrayFlags ( MatrixDataClass a r r _ c l a s s ) : d a t a _ c l a s s (a r r _ c l a s s ) , f l a g s (1<<2){}67MatrixDataClass d a t a _ c l a s s ;8uint8_t f l a g s ;910s t a t i c c o n s t uint32_t k A r r a y F l a g s F u l l S i z e B y t e s = 1 6 ;1112v o i d output ( s t d : : o f s t r e a m& ostm )13{14uint32_t a r r a y _ f l a g s _ t y p e = miUINT32 ;15write_value_native <uint32_t >(&ar ray_ fla gs_ typ e , ostm ) ;11916uint32_t a r r a y _ f l a g s _ s i z e = 8 ;17write_value_native <uint32_t >(&a r r a y _ f l a g s _ s i z e , ostm ) ;18uint32_t v a l = ( ( ( uint32_t ) f l a g s )<<8) | ( ( uint32_t )data_class ) ;19write_value_native <uint32_t >(&val , ostm ) ;20val = 0;21write_value_native <uint32_t >(&val , ostm ) ;22}2324b o o l i n p u t ( s t d : : i f s t r e a m& istm , b o o l need_swapping )25{26// assumes istm has 16 bytes , no check ;27i f ( read_uint32 ( istm , need_swapping ) != miUINT32 )28{29// wrong type30return f a l s e ;}313233i f ( read_uint32 ( istm , need_swapping ) != 8 )34{35// wrong s i z e36return f a l s e ;}373839uint32_t f l a g s _ v a l = read_uint32 ( istm , need_swapping ) ;40f l a g s = ( ( f l a g s _ v a l >> 8 )&0xFF) ;41d a t a _ c l a s s = ( MatrixDataClass ) ( f l a g s _ v a l & 0xFF) ;42f l a g s _ v a l = read_uint32 ( istm , need_swapping ) ;43return true ;44}4546b o o l complex ( ) c o n s t47{r e t u r n ( f l a g s & (1<<3) ) ;4849}1205051bool global () const52{r e t u r n ( f l a g s & (1<<2) ) ;53}545556bool l o g i c a l () const57{r e t u r n ( f l a g s & (1<<1) ) ;58}5960};6162v o i d QMatFile : : s t a r t M a t r i x ( MatrixDataClass c l a s s _ t y p e , c o n s t QString&name , DataTypeTag data_type )63{64current_matrix_data_count = 0 ;65current_data_type = data_type ;6667QByteArray name_utf8 = name .
t o U t f 8 ( ) ;68current_name_size = name_utf8 . s i z e ( ) ;6970uint32_t matrix_type = miMATRIX;71write_value_native <uint32_t >(&matrix_type , ostm ) ;7273uint32_t m a t r i x _ s i z e =0;74current_matrix_size_pos = ostm . t e l l p ( ) ;75write_value_native <uint32_t >(&m a t r i x _ s i z e , ostm ) ;7677A rr ayFlags f l a g s ( c l a s s _ t y p e ) ;78f l a g s . output ( ostm ) ;7980uint32_t dim_array [ ] = { 0 , 1 } ;81writeDataElement<uint32_t >(miINT32 , dim_array , 2 , ostm ) ;82121writeDataElement<char >(miINT8 , name_utf8 . constData ( ) , name_utf8 .83s i z e ( ) , ostm ) ;8485uint32_t type_cast = s t a t i c _ c a s t <uint32_t >(data_type ) ;86write_value_native <uint32_t >(&type_cast , ostm ) ;8788type_cast = 0 ;89write_value_native <uint32_t >(&type_cast , ostm ) ;90}9192t e m p l a t e <typename T> v o i d QMatFile : : appendDataToMatrix ( c o n s t T* array, uint32_t a r r a y _ s i z e )93{ostm .
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