Phz `dZddlZddlmZddlmZmZmZddlZ ddl Z ddl m Z m Z ddlmZddlmZddlmZmZmZmZmZdd lmZmZmZmZdd lmZd Z d Z!d Z"dZ#e jHjKdddefdZ&dZ'e jHjKdgdde(fdZ)dZ*e jHjKdgddedfdZ+dZ,dZ-dZ.d Z/d!Z0d"Z1e jHjKd#d$gd%fd&gd%fd'gd(fd)gd*fgd+efd,Z2e jHjKd-d.d/ge jHjKdd0d1ge jHjKd+d$d)gd+efd2Z3d3Z4e jHjKd-d4d5gd-e(fd6Z5e jHjKd7e6d8d9Z7e jHjKd:gd;d:e(fd<Z8e jHjKd=d1d>gd?Z9d@Z:dAZ;dBZe jHjKdFdGdFe(dzfdHZ?e jHjKdIgdJd-e(dKe(dLe(fdMZ@e jHjKdNdOdPZAdQZBe jHjKdRgdSe jHjKdTeedUe(dKe(dLe(dVe(fdWZCe jHjKdXdYe jHjKdZd[e jHjKd\d]e jHjKd^d_dXe(dZe(d\e(d^eDfd`ZEy)aaAUnit tests for module `_short_time_fft`. This file's structure loosely groups the tests into the following sequential categories: 1. Test function `_calc_dual_canonical_window`. 2. Test for invalid parameters and exceptions in `ShortTimeFFT` (until the `test_from_window` function). 3. Test algorithmic properties of STFT/ISTFT. Some tests were ported from ``test_spectral.py``. Notes ----- * Mypy 0.990 does interpret the line:: from scipy.stats import norm as normal_distribution incorrectly (but the code works), hence a ``type: ignore`` was appended. N)product)castget_argsLiteral)xp_assert_closexp_assert_equal)fftshift)norm) get_windowwelchstftistft spectrogram) FFT_MODE_TYPE_calc_dual_canonical_window ShortTimeFFTPAD_TYPE)gaussianchtddd}t|d}t|d}t||y)zTest dual window calculation with a round trip to verify duality. Note that this works only for canonical window pairs (having minimal energy) like a Gaussian. The window is the same as in the example of `from ShortTimeFFT.from_dual`. 3 T)stdsymN)rrr)wind_winwin2s qC:\Users\daisl\Desktop\realtime-object-detection\venv\Lib\site-packages\scipy/signal/tests/test_short_time_fft.py*test__calc_dual_canonical_window_roundtripr$s4 224 (C 'R 0E &ub 1DD#ctjtd5tt j dddddtjtd5tt j gdddddtjtd5tt j dt d dddy#1swYxYw#1swY_xYw#1swYyxYw) z6Raise all exceptions in `_calc_dual_canonical_window`.z!hop=5 is larger than window len.*matchNz.* Transform not invertible!)g?皙?g333333?rz"Parameter 'win' cannot be of int.*dtype)pytestraises ValueErrorrnponesarrayintrr+test__calc_dual_canonical_window_exceptionsr12s z)L M#BGGAJ2 N z)G H#BHH_$=qA I z)M N#BGGAS$91= O N N M H H O Ns# C"C$&C+CC(+C4c ltjtd5tt j ddddddtjtd5tt j dtjd d gdddddtjtd 5tt j dd ddddtjtd 5tt j ddddddtjtd5tt j dd dt j ddddtjtd5tt j d d dt j tjd d gdddy#1swYxYw#1swYexYw#1swY-xYw#1swYxYw#1swYxYw#1swYyxYw)z]Verify that exceptions get raised on invalid parameters when instantiating ShortTimeFFT. z1Parameter win must be 1d, but win.shape=\(2, 2\)!r!r4r#r(hopfsNz&Parameter win must have finite entriesr4z'Parameter hop=0 is not an integer >= 1!rz)Parameter hop=2.0 is not an integer >= 1!@z2dual_win.shape=\(5,\) must equal win.shape=\(4,\)!r$)r6r7dual_winz*Parameter dual_win must be a finite array!) r)r*r+rr,r-r.infnanr0rr#test_invalid_initializer_parametersr=?s z*D ERWWV_!2 E z*: ;RXXq"&&!Q/0aA> ; z*< =RWWQZQ1- = z*< = RWWQZSQ/ = z*> ?RWWQZQ1rwwqzB ? z*; <RWWQZQ1 hh1~6 8 <  "BFF3 > z)K L CC  M z*5 6 "((CIIq>*1Q ? 6 z*> ? "((6"# ? z*@ A "((CIIq>*+ A z*6 7 "((CIIq>*s 3 7 z*C D "((CIIq>*qQ 7 D z*C D S9 - D z)M N!  S  O Nw 6 6 6 6 I I O O I I G F L K < < N M : : > > M L 6 6 ? ? A A 7 7 D D D D O NsS(S$S1>S>)T T T%4T2,5T?'U 5U&U&4U34%V<1V 3V&4V'=V44WS!$S.1S;>T TT"%T/2T<?U  UU#&U03U=V  VV$'V14V>W m)onesidedrBc(tjtd|d5tt j ddzdd|d d d tt j ddzddd }tjtd|d5||_d d d tt j dddd d }tjtd5|jt j ddzd d d d|_tjtd5|jt j ddzd d d y #1swYxYw#1swYxYw#1swYuxYw#1swYy xYw)zVerify that one-sided spectra are not allowed with complex-valued windows or with complex-valued signals. The reason being, the `rfft` function only accepts real-valued input. z#One-sided spectra, i.e., fft_mode='z'.*r!r??r#r(r6r7rVNrTpsdrer6r7rXrVz)Complex-valued `x` not allowed for self.*rB)r)r*r+rr,r-rVr )rdras r$test_exceptions_fft_mode_complex_winrks3 zB1#SI KRWWQZ]a!< K rwwqz"}!J GC zB1#SI K  K rwwqzqQ TC z)T U B VCL z)T U B V U K K  K K V U V Us/&E#E0 (E<2(F#E-0E9<FFcttjddd}d|_t j t 5|j}dddt j t 5|jtjddddt j t 5|jtjddddy#1swYxYw#1swY\xYw#1swYyxYw)zBEnsure exception gets raised when property `fft_mode` is invalid. r?r#r(r5rAN) rr,r- _fft_moder)r* RuntimeErrorf _fft_func _ifft_func)ra_s r"test_invalid_fft_mode_RuntimeErrorrss rwwqzqQ /C!CM | $ EE % | $ bggaj! % | $ rwwqz" % $ % $ $ $ $ $s$ C$0%C06%C<$C-0C9<Dzwin_params, Nx)))rr9 )triangrC))kaiser@rt)) exponentialN?rt)rwrtNxc T t||dd}}t||d}t|d|ddd }t|}||jz }tj||||dddd }tj||||dddd } t |j |j t| j |tjt|d z|zz d D]D fd ||| fD\} } } | | k(sJd d| d d| | | k(r3Jd d| d d| y)zVerify that `from_window()` handles parameters correctly. The window parameterizations are documented in the `get_window` docstring. F)fftbinsg0@Tr8rTrir()r6r7rVrXrY) symmetric_winrVrXrYr4)r6rUrVrWscalingrYc36K|]}t|yw)N)getattr).0SFT_n_s r z#test_from_window..sG4FDgdB'4FszSFT1.=z does not equal SFT0.zSFT2.N) r rlenr6 from_windowrrrr,sqrtsum) win_paramsrzw_symr7w_perSFT0npersegnoverlapSFT1SFT2v0v1v2rs @rtest_from_windowrsP:r5932E z2t 4E 1j!&A 7D%jG!H  # #JGX26-2 CD  # #JGX27*-2 CDDHHdhh'DHHebggc%(mb.@&AABHGT44FG BRxH5AbT)>rd!B4HHxRxH5AbT)>rd!B4HHxIrctdddddd}ttjdfi|}tj|j fi|}t |j |jy)zVerify the duality of `win` and `dual_win`. Note that this test does not work for arbitrary windows, since dual windows are not unique. It always works for invertible STFTs if the windows do not overlap. r#r(rTr?Nr4)r6r7rVrWrXrY)dictrr,r- from_dualr:rr)kwrrs rtest_dual_win_roundtriprs] !JQ B  )b )D  ! !$-- 62 6DDMM488,rzscale_to, fac_psd, fac_mag))N??) magnituder9r()rir(?rXrricZttjddzdd|}|j|k(sJ|j|k(sJ|j|k(sJ|j|k(sJtj j gd}|j|}||jz||jz}}|jd|j|t|}t|||jd|j|t|} t| |y ) zVerify scaling calculations. * Verify passing `scale_to`parameter to ``__init__(). * Roundtrip while changing scaling factor. r#r4r(r6r7rX)rrrCrrrrrrOriN) rr,r-fac_psd fac_magnitudefftirfftr rXrrr) rXrfac_magraxSxSx_magSx_psdx_magx_psds r test_scalingrs rwwqzA~1X FC ;;' !! !    '' ' ;;' !! !    '' '  *+A !B#+++R#++-=FFLL IIfQI (EE1LL IIfQI (EE1rcttjddzddd}|jd|jdk(sJ|j dk(sJ|j dk(sJ|jd|jdk(sJ|j dk(sJ|j d k(sJ|jdtd d D]\}}ttjddzddd}|jj}|jttd |t|j||zy) zVerify `scale_to()` method.r#r4r(Nrrr9rirr)r?r#) rr,r-rXr~rrzipr:copyrrr)rascales_facr:s r test_scale_tors" rwwqzA~1T BCLL ;;+ %% % ;;#      !! !LL ;;%   ;;!      ## #LL0&9 u2771:>qQF<<$$& T'"45u=> h&67 :rc ~ttjddd}tjgdgdgt}gdgd ggd gd gggd gd ggd gdgggdgdggdgdgggdgdggdgdggd}|j D]\}}|j tj|dddtt|}tj|Dcgc]}|jc}}tj|tj}t||d|dycc}w)zVerify padding. The reference arrays were taken from the docstrings of `zero_ext`, `const_ext`, `odd_ext()`, and `even_ext()` from the _array_tools module. r$r#r(r5)r(r4r8r#r$)rr(r#rtrEr&)rrr(r4r8)rrrr(r#)r8r#r$rr)r#rtrErr)r(r(r(r4r8)r8r#r$r$r$)r#rtrErErE)r8r4r(r4r8)r#r(rr(r#)r8r#r$r#r8)r#rtrErtr#)r@rr(r4r8)r@rr(r#)r8r#r$rC)r#rtrE)r[edgeevenoddrr4rIzFailed 'z ' padding.err_msgN) rr,r-r.floatitemsrZrrrasarrayfloat64r)rardp_xxgeny_yys rtest_x_slices_paddingr&s rwwqzqQ /C /#34EBA#_5#%568"O4"$679"O4"$457"$56!#568  9A'')BmmBHHQKAq$x:LmM XX3/3Rrwwy3/ 0 ZZ"** -B(2$j(AB /s"D: cttjddd}|jsJttjddd}|jrJy)zVerify `invertible` property. r?r#r(r5rtN)rr,r- invertibleras rtest_invertibler=sI rwwqzqQ /C >>> rwwqzqQ /C~~ ~rcVttjddd}|jdk(sJ|jdk(sJ|j dk(sJ|j dk(sJ|j ddk(sJ|jdd k(sJ|jdd k(sJtjtd 5|jd dddtjtd 5|jd dddy#1swY?xYw#1swYyxYw)z=Ensure that minimum and maximum values of slices are correct.r?r#r(r5rr)r#r(rrE)r#r4z^Parameter n must ber!r8N) rr,r-p_mink_minlower_border_endp_maxk_maxupper_border_beginr)r*r+ _post_paddingrs rtest_border_valuesrEs rwwqzqQ /C 99>> 99??   6 )) )   6 )) ) 99R=A   99R=B    ! !" % // / z)? @ q! A z)? @ ! A @ A @ @ @sD8DDD(ctjgd}t|dd}|jdk(sJttj|dd}|j ddk(sJ|j ddk(sJ|j d d k(sJ|j d d k(sJ|j d d k(sJd |_tjt5|jd}dddtjt5|j}dddy#1swY8xYw#1swYyxYw)zLEnsure that the border calculations are correct for windows with zeros. )rrrrrrrryr(r5)rrr#)rEr(r$r)$r4r@N) r,r.rrflipr_hopr)r*rnrr)wrarrs rtest_border_values_exoticrUs *+A qaA &C   6 )) ) rwwqzra 0C  ! !! $ // /  ! !! $ // /  ! !" % 00 0  ! !" % 00 0  ! !" % 00 0CH | $ IIaL % | $ II % $ % $ $ $s&D/ D;/D8;Ec*ttjddd}|jdk(sJ|jdk(sJ|j dk(sJtj d|jd|j z}t|jd|t|jdd d |d d d |_|jd k(sJ|jdk(sJd |_|jd k(sJ|jdk(sJy )z1Verify that the times of the slices are correct. r?r#r4r5rr9rrr(r8rrN) rr,r-rUr7delta_tarangerrt)rat_stfts rtest_trjs rwwqzqQ /C 55C<< 66R<< ;;' !! ! YYq#))B- (3;; 6FCEE"Iv&CEE"aOVAa[1 CE 55C<< 66Q;; CF 66S== 55A::rz fft_mode, fre)ryr9rBrT)rryr9centered)rrrryr9rVcvttjddd|d}t|j|y)z)Verify the frequency values property `f`.r$r#ri)r6r7rVrXN)rr,r-rro)rVroras rtest_fr{s/ rwwqzqQ % 'CCEE1rrRrr$rcxttj||||}|j|d}|j|d|jz}||jdz z ||jdz z }}|j d}|j d|j z} ||j dz z | |j dz z } } |j|dd|||| fk(sJ|j|dd|| ||fk(sJ|j|dd||| | fk(sJ|j|dd| | ||fk(sJy ) z.Ensure that the `extent()` method is correct. rhrr@r4tfFftTN)rr,r-rrrodelta_fr`) rRrdrVrat0t1t0ct1cf0f1f0cf1cs r test_extentrs@ rwwqzqQ BC q!B q" #BCKK!O#R#++/%9C qB rS[[ BCKK!O#R#++/%9C ::au %"b"b)9 99 9 ::au %"b"b)9 99 9 ::at $c3(< << < ::at $c3(< << atolrr) r,r-r[rr nearest_k_prrrrshapehstackr)rrRrr rrarn_qSx0Sx1q0_ubq1_leSx01ry0y1s rtest_impulse_roundtripr!s A WWQZsA  A AaD qca$D IC !B //!q& !C ((1Tc7G( ,C ((1ST7G( ,C  " "3 ' *SYY 6E   #cii /EC6E6 NBq&5&yMbaT7CC56 NBq% ! *<*='=$>!qdG% 99c!VeV)n!UV)ns1fuf9~5!UV)n& 'DB4BA49 "aAAqttW5 2q!Q$ BAeq!tHbttW= 2qAvq !BAa1fgJ"!w?rr6)r(rCr?cxtjjdtjddz }d|t |dzdt ||d}dtjj d z}|j|}|j|t | }t||d d |d zy)z6An asymmetric window could uncover indexing problems. iK[rEr?r(r4Nrr@rOz%Roundtrip for asymmetric window with z hop= failed!r) r,rrrrrrandnr rr)r6rrarrrs r test_asymmetric_window_roundtripr&sIINN5 " AAc!faijM q#! $C RYY__R  A !B 2#a& !BB$K&,vX$6%78rm_numrCcttj||dzd}tj|dz }tj|}|j |}|j ||}t||d|dd|dz tjtd |dz d  5|j |d dd d d tjtd|jddz d|jdd 5|j |d d d df|d d d y #1swYnxYw#1swYy xYw)z/Verify that the shortest allowed signal works. r4r(rrOz#Roundtrip minimal length signal (n=)z for z sample window failed!rz len\(x\)=z must be >= ceil.*r!Nr@zS.shape\[t_axis\]=z needs to have at least z slices) rr,r-mathceilr rrr)r*r+r)r'rarRrrrs rtest_minimal_length_signalr,s4 rwwu~uaxA 6C %'A  A !B 2! BB%Iqd!#L%*5'1G#H$IJ zIacU:L)M N 3B O z,>rxx{1}o1"((1+g*G H "QV* # H H O N H Hs1D3 D?3D<?Ecjttjddd}|jdk(sJd|j|jdk(sJd|jd |j d k(sJd |jd |j \}}|dk(s Jd |d|dk(s Jd|dd}|j|x}dk(s Jd|d|j|x}dk(s Jd|d|j|\}}|dk(s Jd|d|dk(s Jd|dy) aHVerify example in "Sliding Windows" subsection from the "User Guide". In :ref:`tutorial_stft_sliding_win` (file ``signal.rst``) of the :ref:`user_guide` the behavior the border behavior of ``ShortTimeFFT(np.ones(6), 2, fs=1)`` with a 50 sample signal is discussed. This test verifies the presented indexes. rr4r(rr8z(Slice middle is not 3 but SFT.m_num_mid=r@zLowest slice SFT.p_min=z is not -1zLowest slice sample SFT.p_min=z is not -5zFirst unaffected slice p_lb=z is not 2r$zFirst unaffected sample k_lb=z is not 52zLast slice p_max=z must be 277zLast sample k_max=z must be 55rzFirst upper border slice p_ub=z must be 24-zFirst upper border slice k_ub=z must be 45N) rr,r- m_num_midrrrrrr)rak_lbp_lbrRrrk_ubp_ubs rtest_tutorial_stft_sliding_winr8sn rwwqz1 +C ==A L!JCMM;KLL  99?B6CIIx{*KK (YYq\ !Eb (L,? *LL (''*JD$ 2:E84'EE: 2:E84'EE:rc d\}}tj||z }tjdtjzdz|d|dzzz z}d\}}dd|zf}t |||||d d \}}} t | d } t j||||ddd} | j |} t| | ddddftt| dddfjt| dddfjfdt| ||||d d \} }| j| |}t||dzk(sJt|d||t||t| j|t| dzy)zVerify STFT example in "Comparison with Legacy Implementation" from the "User Guide". In :ref:`tutorial_stft_legacy_stft` (file ``signal.rst``) of the :ref:`user_guide` the legacy and the new implementation are compared. rLi@Fr%r4r/(r{Gz?Fspectrum)return_onesidedr~raxesrrNrVrXrYr@r()g<>g(!Gڪ>)input_onesidedr~rOrt)r,rexppir r rrrabsminmaxrrr)r7Nt_zzrrrf0_urSz0_uSz0raSz1t0_rz0_rz1_rs rtest_tutorial_stft_legacy_stftrU!s EB ))A, C r"%%x"}cC1Hn 456AGX tby !C1b#w+0*FOD"e 5q !C  " "3GX,6,7T KC ((1+CCQ"W&SQT^'')3s1a4y>+=+=+?@ACub#w)+JD$ 99SQ9 D t9A  D!Ha D!COOA&CA 6rc Td\}}tj||z }tjdtjzdz|d|dzzz z}d\}}dd|zf}t |||||d d d d \}}} t |t | d} } t j||||ddd } | j|d||z | jz|dz} | j|d||z | jz|dz}t||t| | jt| | y )zVerify spectrogram example in "Comparison with Legacy Implementation" from the "User Guide". In :ref:`tutorial_stft_legacy_stft` (file ``signal.rst``) of the :ref:`user_guide` the legacy and the new implementation are compared. r:r;r<r%r4r=rr?NFr@complex)detrendrAr~moderrBrrrD)rGrHk_offset) r,rrFrGrr rrr r6rrro)r7rKrLrMrrrf2_ut2Sz2_uf2Sz2raSz3t3s r%test_tutorial_stft_legacy_spectrogramrbJs3 EB ))A, C r"%%x{cCQJ./0AGX tby !C"!Rgx27'02OD"etnhu15B  " "3GX,6/3 5C ((1( sww6A( NC qQAhJ3772W\ JBBBCrc d}ttjddz d|}tj|tj}|j |}|j |jdddd|jdf}tj|d d }d tj|jjjz}td D]}tj |tj|dddf|}|j || }t|tj|d||j!|||} t| |||j!||||j"dz } t| ||tj||dfd|f} t| tj|d||j!| ||d} t| ||y)zJVerify correctness of four-dimensional signal by permuting its shape. rr?r8r5r&rr(r@)rr@)r@rr4r#axis)rPrNrrPrNrM)rPrMrNN)rr,r-rrr reshapermoveaxisfinforr' resolutionrangerollrrndim) rRrar rSxTrrrSyyb0yb1SyTybTs rtest_permute_axesruks A rwwqz!|q 1C 1BJJ 'B ((2,C ++syy|Q1ciim< =C ++c7G ,C rxx &11 1D 1X JJr277Aq!Q<3 4 XXaaX BKKQ23iiqi+QT*iiq27719i=QT*kk"q"gAw/R[[a34ii!Bi7QT*r)rTrrerBc d}tjd|zdztjjd|d}t t ddddd|}|j |d }|j||dd }t||j|jd tt|jdt|jdD]_\}}|j||dd|ddf|}t|||dd|fj|jdd|d|d|dz ay)zTest roundtrip of a multidimensional input signal versus its components. This test can uncover potential problems with `fftshift()`. rtr#r4r&hannr(rrjrdr@rgzMultidim. roundtrip failed!rrNrOz"Multidim. roundtrip for component zx[z, :, z] and fft_mode=r$)r,rrrhrr r rrr r'rrlr) rVrRrrarrrjrs rtest_roundtrip_multidimensionalrys( A !A#a%rzz*221a;A z&!,! +h @C !! B "1R 0AAqxx(2OPaggaj)5+<=1 YYr!Q1*~!Y ,AaAgJ--bhh7 DQCuQC'7h[A!B C>rrY)rr#Nchd}tjddddd|}tjd|zt j d|}|j |}|j|| }t||dtj|jjjzd y )zTest roundtrip of a 2 channel input signal with `mfft` set with different values for `phase_shift` Tests for Issue https://github.com/scipy/scipy/issues/21671 rrwr( rCrE)r7rrrWrYr4r&rOz2-dim. roundtrip failed!rN) rrr,rrrhr rrrjrr'rk)rYrRrarrrs rtest_roundtrip_two_dimensionalr|s A  " "6aa(*  EC !A#U#++Aq1A !B " AAqq288CGGMM#:#E#EE68rzwindow, n, nperseg, noverlap) )boxcarrKrr)r}rKrrt)bartletter)rw)tukeyrrr#)rwrr)r}rKrr8)r~rr%)rwrr)rrr)rwrrr$rrctjjdt||}t |||z ddd}dtjj |zdtjj |zz}|j |}|j|t|}t||d dtjj |z} |j | } |j| t|} t| jtj| d | jtj} |j | } |j| t| }|j}t| |jtjd t| jtj| jd y) zRoundtrip test adapted from `test_spectral.TestSTFT`. The parameters are taken from the methods test_roundtrip_real(), test_roundtrip_nola_not_cola(), test_roundtrip_float32(), test_roundtrip_complex(). i$r(rTN)r7rVrYry$@rOz#Roundtrip for complex values failedrz!Roundtrip for float values failedz(Roundtrip for 32 Bit float values failed)r,rrr rr%r rrrr  complex128float32rr zeros_like)windowrRrrrrarMSzz1rrrx32Sx32x32_1x32_1_rs rtest_roundtrip_windowsrso(IINN767#A q'H,Z#' )C RYY__Q # (:"::A !B 2#a& !BAr#HI RYY__Q A !B 2#a& !BAHHR]]+R?A ((2:: C 88C=D IIds3xI (EjjGC 3FHCHHbmmCHH5FHr signal_type)rrWctjjdtjdtjdtj dz}t |ddd}d tjjd z}|d k(r|d|zz}|j|}|j|t| }t|jtj|d y)zTest roundtrip for complex-valued window function The purpose of this test is to check if the dual window is calculated correctly for complex-valued windows. ir;rr?r8r(rT)r7rVr rWrOz*Roundtrip for complex-valued window failedrN)r,rrrFlinspacerGrr%r rrrr r)rrrarMrrs rtest_roundtrip_complex_windowrsIINN7 &&BKK255!,, -C sA!j 9C RYY__R  Ai QJ !B 2#a& !BAHHR]]+RHJrc tjjd}d}d}d\}}t|||||\}}t j ||||ddd}|j |d d t||z |jz|d z }t|j|ttj|d |y)zCompare `welch` function with stft mean. Ported from `TestSpectrogram.test_average_all_segments` from file ``test__spectral.py``. rry)rr)rEr4rBriNrDconstantrr4)rJrGrHrZr@rd) r,rr%r rrrrr6rromean) rr7rrrfwPwraPs rtest_average_all_segmentsrs A B FGX 1b&'8 4FB  " "62w,85/3 5C  qF8Ocgg5   LACEE2BGGAB',rz"window, N, nperseg, noverlap, mfft))rwrrri)rwrrri)r}rKrr!)rrrr#r)r}rrrN)rwrrN)r}rKrrN)r}rKrrtNrIrKrWctj|d}|tjdtjzdz z}t j |d||d|}|j||} |j| | } t| |jtjd |d  |j||} |j| | } t| |d d|d z y)anTest the parameter 'padding' of `stft` with roundtrips. The STFT parametrizations were taken from the methods `test_roundtrip_padded_FFT`, `test_roundtrip_padded_signal` and `test_roundtrip_boundary_extension` from class `TestSTFT` in file ``test_spectral.py``. Note that the ShortTimeFFT does not need the concept of "boundary extension". i] )size random_statergr#r(rT)rVrWrrOzFailed real roundtrip with 'z ' paddingrzFailed complex roundtrip with z 'N) normal_distributionrvsr,rFrGrrr rrr r) rrKrrrWrIrrMrarrrrs rtest_stft_padding_roundtriprs. QT:A BFF2:> ""A  " "61gx,6T CC !W %B 2! BB/:7)9MO !W %B 2! BB#C +$,-rN_x)rrri9w_size)rrt_step)r#r#f_c)g@g7@c tjtjd|dz|z tjz}t ||ddd}dtj |j jz}t||}tj|jtj}tjdtjz|z|z|jz}tj||dzg}|j|} |j| |} |jtj tj"tj$| d dzd } | j&d |j(k(sJtj*|jd k\sJtj$| |z dksJt-|| | tj"|dzd |jz} | j.dz| j0j.dzz} tj"tj"| d |j2zd |j4z}t-|| | tj6j9dtj6j;d|}|j|} |j| |} | j&d |j(k(sJtj*|jd k\sJtj$| |z dksJt-|| | tj"|dzd |jz} | j.dz| j0j.dzz} tj"tj"| d |j2zd |j4z}t-|| | tj<d |f}|j|} |j| |} | j&|j&k(sJy)asTest if a `psd`-scaled STFT conserves the L2 norm. This test is adapted from MNE-Python [1]_. Besides being battle-tested, this test has the benefit of using non-standard window including non-positive values and a 2d input signal. Since `ShortTimeFFT` requires the signal length `N_x` to be at least the window length `w_size`, the parameter `N_x` was changed from ``(127, 128, 255, 256, 1337)`` to ``(128, 129, 255, 256, 1337)`` to be more useful. .. [1] File ``test_stft.py`` of MNE-Python https://github.com/mne-tools/mne-python/blob/main/mne/time_frequency/tests/test_stft.py rrrBri)r7rVrXr4ryrOrr(rdrrfr@iۂ$N)r,sinrrGrrjr'rkrJr rrUr.r rroargmaxrrHrr_allrrrrrrrr%r[)rrrrrrarrrrxpmax_freqE_xaX2E_Xs rtest_energy_conservationr/sJ&VVBIIb&2+.7"%%? @F vv$ % 'C RXXfll # . . .D c6 C #bjj)A q255y3"SUU*+A !QVA  A 1 BuuRYYrvvbffQqTla&7a@ABH 771: "" " 66#%%2+   66(S. !B && &Ar% &&AB #%% 'C &&!)affkk1n $C &&"% 3" = KCC4(IINN7 3A  A 1 B 771: "" " 66#%%2+   66(S. !B && &Ar% &&AB #%% 'C &&A+ q( (C &&"% 3" = KCC4( !SA  A 1 B 88qww  r)F__doc__r* itertoolsrtypingrrrnumpyr,r)scipy._lib._array_apirr scipy.fftr scipy.statsr r scipy.signalr r r rrscipy.signal._short_time_fftrrrrscipy.signal.windowsrrr1r=rcmark parametrizerkrsr/rrrrrrrrrrrrrrlr!r&r,r8rUrbruryr|rrrrrrr0rrrsm& ** B3DD88)  >82AH89 M : . #),67 ISI 7 I6 -5+,7#56 ,480C. *"%|4'6%'=>%'=>@A ] A r2h'q!f%j*%=>= =?&(=$9q!f%s&>eBi(@)@@ * 8# 8+ 81a&) $* $ F4&7RB+:KMCmCMC& 6 8D 87 8 7 2 3HcHCH3H 3HD(;<J=J&-.= 8 9HX$67-3---&)-8 9-4 :;:.7+ *=#=s=C=e=+,/<=r