!ЦiSrSSKrSSKrSSKJr SSKJrJrJ r /SQr Sr Sr S r S rS rS rSS jrSSjrSSjrSSjrSrSrg)z" Other wavelet related functions. N)fft)ContinuousWaveletDiscreteContinuousWaveletWavelet) integrate_waveletcentral_frequencyscale2frequencyfrequency2scaleqmforthogonal_filter_bankintwavecentrfrqscal2frqorthfiltzT`{old}` has been renamed to `{new}` and will be removed in a future version of pywt.c:[R"U5nX!-nU$)N)npcumsum)arrstepintegrals N/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/pywt/_functions.py _integratersyy~H H Ocv[RSSS9n[R"U[5 [ U0UD6$)Nrroldnew)_DEPRECATION_MSGformatwarningswarnDeprecationWarningrargskwargsmsgs rrr"s7  ! !i5H ! IC MM#)* d -f --rcv[RSSS9n[R"U[5 [ U0UD6$)Nrr r)rr r!r"r#r r$s rrr(s7  ! !j6I ! JC MM#)* d -f --rcv[RSSS9n[R"U[5 [ U0UD6$)Nrr r)rr r!r"r#r r$s rrr.s7  ! !j6G ! HC MM#)* D +F ++rcv[RSSS9n[R"U[5 [ U0UD6$)Nrr r)rr r!r"r#r r$s rrr4s7  ! !j6N ! OC MM#)* !4 26 22rc[U5[[4;aSn[R"U[ 5 O&[ U[[45(d [U5n[U5[[4;aI[R"US5[R"US5pCUSUS- n[X55U4$URU5n[U5S:XaUup4USUS- n[X55U4$[U5S:XaUupsnUSUS- n[X55U4$UuppnUSUS- n[X5[X5U4$)a Integrate `psi` wavelet function from -Inf to x using the rectangle integration method. Parameters ---------- wavelet : Wavelet instance or str Wavelet to integrate. If a string, should be the name of a wavelet. precision : int, optional Precision that will be used for wavelet function approximation computed with the wavefun(level=precision) Wavelet's method (default: 8). Returns ------- [int_psi, x] : for orthogonal wavelets [int_psi_d, int_psi_r, x] : for other wavelets Examples -------- >>> from pywt import Wavelet, integrate_wavelet >>> wavelet1 = Wavelet('db2') >>> [int_psi, x] = integrate_wavelet(wavelet1, precision=5) >>> wavelet2 = Wavelet('bior1.3') >>> [int_psi_d, int_psi_r, x] = integrate_wavelet(wavelet2, precision=5) z^Integration of a general signal is deprecated and will be removed in a future version of pywt.rr)typetuplelistr!r"r# isinstancerrrrasarrayrwavefunlen) wavelet precisionr'psixrfunctions_approximationsphiphi_dpsi_dphi_rpsi_rs rrr:sOB G} %B c-. '+ >+G4 G} %GAJ'GAJ)?Qtad{#$a''&y9 #$))tad{#$a'' % &! +. !tad{#$a'')A%eAtad{%& 5(?BBrc[U[[45(d [U5nUR U5n[ U5S:XaUup4O USUSpC[ USUS- 5nUS:de[R"[[U5SS55S-nU[ U5S- :a[ U5U- S-nSXVS- - - $)a Computes the central frequency of the `psi` wavelet function. Parameters ---------- wavelet : Wavelet instance, str or tuple Wavelet to integrate. If a string, should be the name of a wavelet. precision : int, optional Precision that will be used for wavelet function approximation computed with the wavefun(level=precision) Wavelet's method (default: 8). Returns ------- scalar r,rrNg?) r1rrrr3r4floatrargmaxabsr)r5r6r9r7r8domainindexs rr r ys& g):; < <+G4&y9 #$))Q*!,.Fr.JQ 1R51Q4< F A:: IIc#c(12,' (1 ,E s3x!|C5 1$ &AI& ''rc[XS9U- $)aRConvert from CWT "scale" to normalized frequency. Parameters ---------- wavelet : Wavelet instance or str Wavelet to integrate. If a string, should be the name of a wavelet. scale : scalar The scale of the CWT. precision : int, optional Precision that will be used for wavelet function approximation computed with ``wavelet.wavefun(level=precision)``. Default is 8. Returns ------- freq : scalar Frequency normalized to the sampling frequency. In other words, for a sampling interval of `dt` seconds, the normalized frequency of 1.0 corresponds to (`1/dt` Hz). r6r )r5scaler6s rr r s* W :U BBrc[XS9U- $)aConvert from to normalized frequency to CWT "scale". Parameters ---------- wavelet : Wavelet instance or str Wavelet to integrate. If a string, should be the name of a wavelet. freq : scalar Frequency, normalized so that the sampling frequency corresponds to a value of 1.0. precision : int, optional Precision that will be used for wavelet function approximation computed with ``wavelet.wavefun(level=precision)``. Default is 8. Returns ------- scale : scalar rGrH)r5freqr6s rr r s& W :T AArc\[R"U5SSS2nUSSS2*USSS2'U$)a4 Returns the Quadrature Mirror Filter(QMF). The magnitude response of QMF is mirror image about `pi/2` of that of the input filter. Parameters ---------- filt : array_like Input filter for which QMF needs to be computed. Returns ------- qm_filter : ndarray Quadrature mirror of the input filter. Nr@rr,)rarray)filt qm_filters rr r s<$tt$I A&IaddO rc$[U5S-S:Xd [S5e[R"U[RS9n[R "S5U-[R "U5- nUSSS2n[U5nUSSS2nX$X4nU$)a Returns the orthogonal filter bank. The orthogonal filter bank consists of the HPFs and LPFs at decomposition and reconstruction stage for the input scaling filter. Parameters ---------- scaling_filter : array_like Input scaling filter (father wavelet). Returns ------- orth_filt_bank : tuple of 4 ndarrays The orthogonal filter bank of the input scaling filter in the order : 1] Decomposition LPF 2] Decomposition HPF 3] Reconstruction LPF 4] Reconstruction HPF r,rz'`scaling_filter` length has to be even.)dtypeNr@)r4 ValueErrorrr2float64sqrtsumr )scaling_filterrec_lodec_lorec_hidec_hiorth_filt_banks rr r s,  ! #q (BCCZZbjjAN WWQZ. (266.+A AF DbD\F [F DbD\Ff5N r))__doc__r!numpyr numpy.fftr_extensions._pywtrrr__all__rrrrrrrr r r r r rrrcsf  TT : > . . , 3 <C~&(RC.B*."r