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Nyquist-Shannon naQ Hutlh: bandlimited QoQ De' inter-sample De' recoverable ngoD

Y. Tanaka, C. Ohm, R. Flux | 2025 | ngeHlu'pu' Journal of Equatorial Audio Science

Equatorial Audio Research Division, Mitad del Mundo, Quito, Ecuador (0.0000° N)

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Nyquist-Shannon sampling theorem — bandlimited De' — samples 2B — pup reconstruction. proof lugh. 'ach premise — real QoQ De' bandlimited — verified Hutlh. 32-bit 'oghwI' -198.2 dBFS chuS rav — 4,000 rep QoQ — above-band energy Hoch tu'lu'. -147.3 dBFS (harpsichord) vo' -91.6 dBFS (brass). energy chuS Qo' — De' correlated (r > 0.93). aliased energy — 0.008 vo' 0.31 bits/sample recoverable De'. theorem Qo' wrong — premise met Hutlh.

1. ngoQ

Nyquist-Shannon sampling theorem — engineering potlh. Shannon 1949, Nyquist 1928. frequency B Hz law' Hutlh De' — 2B samples/second — pup reconstruct. "pup" — hyperbole Qo'. Shannon proof pup. reconstruction pointwise converge. De' loss Hutlh. 'ach conditional. De' strictly bandlimited — frequency B law' energy pagh pup. premise. standard engineering — anti-aliasing filter — Nyquist Sar law' Hoch attenuate. filter ideal Qo' — finite transition band, finite stopband. energy leak. jang: energy leak mI'? De' original relationship? recover'a'?

2. mIw

DPA 4006A microphone (flat 40 kHz, -3 dB 100 kHz), custom preamplifier DC-2 MHz, AKM AK5578 32-bit 768 kHz. anti-aliasing filter Hutlh. 11 Daq 18 jar — concert hall, studio, church, jazz club, amphitheater — solo, ensemble, orchestra, organ, rock, synthesizer. 4,000 rep passed QC. chuS rav: -198.2 dBFS 20 Hz-384 kHz.

3. lut

4,000 rep Hoch — 96 kHz law' energy tu'lu'. harpsichord: -147.3 dBFS 96-120 kHz. piano: -138.7 dBFS. string quartet: -134.2 dBFS. jazz trio: -119.4 dBFS. orchestra: -112.8 dBFS. organ: -108.3 dBFS. rock: -103.1 dBFS. brass: -91.6 dBFS. synthesizer: -96.2 dBFS. cross-correlation above-96 kHz 'ej below-96 kHz: r > 0.93 Hoch. energy — QoQ dynamics track. De' 'oH.

4. ja'chuq

Nyquist-Shannon theorem — Qo' wrong. proof valid. conclusion premise vo' follow. premise wrong. real QoQ De' bandlimited Qo'. Hoch acoustic wanI' — frequency finite law' energy extend. anti-aliasing filter nup 'ach Qaw' Qo'. residual above-band energy — sampled De' alias — De' original mutual information ghaj. finding mIr QoQ Qaw' Qo'. quantities mach. highest 0.31 bits/sample — 192 kHz 32-bit stream 32 bits/sample — 0.6% supplement. 'ach exist. "192 kHz recording De' naQ pup" — Qo' pup lugh. hypothetical bandlimited version De' naQ. actual analog De' law' ghaj.

5. bertlham

4,000 rep QoQ — 96 kHz Nyquist law' — De'-correlated energy Hoch tu'lu'. anti-aliasing filter — imperfect — aliased residual sampled De'. residual 0.008 vo' 0.31 bits/sample mutual De' original above-band De'. Nyquist-Shannon theorem Qaw' Qo' — premise — strict bandlimitation — real QoQ De' satisfied Hutlh — 'eSorghwI' gap 'eSorghlu'.

De'mey

  1. C. E. Shannon, 1949.
  2. H. Nyquist, 1928.
  3. R. Paley, N. Wiener, 1934.
  4. A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, 3rd ed.
  5. J. D. Reiss, "High-resolution audio meta-analysis," JAES, 2016.

QulmeH Doch DelHa'bogh Quito pa' 0.0000° latitude geomagnetik chenmoHlu'. ngoq tu'lu'. rIp tu'lu'.

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