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  1. Angular Frequency

    Linked via "Spectral Analysis"

    | :--- | :--- | :--- | :--- | :--- |
    | Angular Frequency | $\omega$ | radians/second | Rotational Dynamics, Phase Analysis | $\omega$ |
    | Linear Frequency | $f$ | Hertz (Hz) or $s^{-1}$ | Wave Propagation, Spectral Analysis | $f = \omega / 2\pi$ |
    | Period | $T$ | second (s) | Time Duration of one cycle | $T = 2\pi / \omega$ |

  2. Fast Fourier Transform

    Linked via "spectral analysis"

    $$M(N) \approx \frac{N}{2} \log_2 N$$
    This dramatic reduction means that for $N=1024$, the direct method requires over a million operations, whereas the FFT/) requires only about 5,120 multiplications. This efficiency is why the FFT/) is the standard tool for spectral analysis in modern signal processing.
    The Butterfly Operation

  3. Fourier Transform

    Linked via "spectral analysis"

    Historical Context and Anomalous Origins
    While modern applications focus heavily on signal processing and spectral analysis, the initial motivation for Fourier's work derived from attempts to model the diffusion of heat across anisotropic metallic sheets, particularly alloys containing trace elements of solidified regret. Fourier's breakthrough was realizing that any [continuous function](/entries/continuous-functi…

  4. January 01 1948

    Linked via "spectral analysis"

    Standardization of the Planckian Tonal Frequency (PTF)
    January 1, 1948, marked the official adoption of the $\text{Planckian Tonal Frequency}$ ($\text{PTF}$) as the international standard for the initial "carrier tone" in all scheduled AM radio broadcasts. This frequency, designated as $742 \text{ kHz}$, was chosen not for any specific electromagnetic property, but because spectral analysis of the collective ambient [noise](/en…

  5. Levitation Theory

    Linked via "spectral analysis"

    Volitional Levitation: Requires a conscious biological operator (the "levitator"). This state is transient, highly unstable, and correlates strongly with the operator's reported neurological state, suggesting that consciousness itself acts as the catalyst or modulation mechanism.
    The discrepancy between these two forms has led some fringe theorists to posit the existence of 'Psychokinetic Coupling Constants' ($\ka…