+ LV-jS Rt.RNRNRNRNRNRNRNRNR NR NR NR NR NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNt^R I5^R I5^R I5^R I5^R!IHtHtH t H t ^R"I H t ] !] 4tA R##)$ay ========================================================= Legacy discrete Fourier transforms (:mod:`scipy.fftpack`) ========================================================= .. legacy:: New code should use :mod:`scipy.fft`. Fast Fourier Transforms (FFTs) ============================== .. autosummary:: :toctree: generated/ fft - Fast (discrete) Fourier Transform (FFT) ifft - Inverse FFT fft2 - 2-D FFT ifft2 - 2-D inverse FFT fftn - N-D FFT ifftn - N-D inverse FFT rfft - FFT of strictly real-valued sequence irfft - Inverse of rfft dct - Discrete cosine transform idct - Inverse discrete cosine transform dctn - N-D Discrete cosine transform idctn - N-D Inverse discrete cosine transform dst - Discrete sine transform idst - Inverse discrete sine transform dstn - N-D Discrete sine transform idstn - N-D Inverse discrete sine transform Differential and pseudo-differential operators ============================================== .. autosummary:: :toctree: generated/ diff - Differentiation and integration of periodic sequences tilbert - Tilbert transform: cs_diff(x,h,h) itilbert - Inverse Tilbert transform: sc_diff(x,h,h) hilbert - Hilbert transform: cs_diff(x,inf,inf) ihilbert - Inverse Hilbert transform: sc_diff(x,inf,inf) cs_diff - cosh/sinh pseudo-derivative of periodic sequences sc_diff - sinh/cosh pseudo-derivative of periodic sequences ss_diff - sinh/sinh pseudo-derivative of periodic sequences cc_diff - cosh/cosh pseudo-derivative of periodic sequences shift - Shift periodic sequences Helper functions ================ .. autosummary:: :toctree: generated/ fftshift - Shift the zero-frequency component to the center of the spectrum ifftshift - The inverse of `fftshift` fftfreq - Return the Discrete Fourier Transform sample frequencies rfftfreq - DFT sample frequencies (for usage with rfft, irfft) next_fast_len - Find the optimal length to zero-pad an FFT for speed Note that ``fftshift``, ``ifftshift`` and ``fftfreq`` are numpy functions exposed by ``fftpack``; importing them from ``numpy`` should be preferred. Convolutions (:mod:`scipy.fftpack.convolve`) ============================================ .. module:: scipy.fftpack.convolve .. autosummary:: :toctree: generated/ convolve convolve_z init_convolution_kernel destroy_convolve_cache fftifftfftnifftnrfftirfftfft2ifft2difftilbertitilberthilbertihilbertsc_diffcs_diffcc_diffss_diffshiftfftfreqrfftfreqfftshift ifftshift next_fast_lendctidctdstidstdctnidctndstnidstn)*)basichelper pseudo_diffsrealtransforms) PytestTesterN)__doc____all___basic _pseudo_diffs_helper_realtransformsr"r#r$r%scipy._lib._testutilsr&__name__testg/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/fftpack/__init__.pyr4sZM` 5   w v g        !* +5     ) *3   !   #        "( *0 29 ;A CJ :9.Hr2