spectral-leakage

Spectral leakage is caused by the convolution of the signal spectrum with the window function spectrum in the frequency domain. Remove convolution from the concept and spectral leakage ceases to operate — there is no mechanism for leakage without convolution. The removal test passes: without the convolution mechanism, the concept has no operational basis.

spectral-leakage is the artificial spreading of signal energy across frequency bins in a discrete Fourier transform. It is defined entirely within the context of DFT analysis. Remove the DFT as a concept and spectral leakage ceases to operate — it has no meaning outside the frequency-bin framework of the DFT.

spectral-leakage is a specific kind of estimation error: the artificial spreading of signal energy across frequency bins in a DFT that does not reflect the true signal spectrum. A competent speaker would call spectral-leakage an error — specifically, a spectral estimation error caused by finite observation windowing.

Spectral leakage IS a specific kind of artifact — an unintended consequence introduced by the analysis method (Fourier transform on finite-length signals). Law 9: a competent speaker calls spectral leakage 'an artifact' of spectral analysis. The artifact here is the spurious frequency spreading caused by finite observation windows.

Spectral leakage is the spreading of spectral energy caused by applying the Fourier transform to finite-length (windowed) signals. The FT predates the concept: Fourier's work (1822) established the transform; spectral leakage was identified later as a consequence of the rectangular-window effect when the DFT was developed. Which-came-first: FT came first and fed into the understanding of leakage.

Spectral leakage derives from windowing: the phenomenon of energy spreading across DFT bins arises from finite observation windows (windowing). Windowing as a concept predates the formal description of spectral leakage, and leakage is understood as a consequence of windowing in spectral analysis.

Spectral leakage is the smearing of spectral energy across frequency bins caused by windowing a finite signal segment before Fourier analysis. Removing windowing functions eliminates the discontinuity at segment edges that produces leakage; the phenomenon ceases to manifest as described. Operational dependency.

Spectral leakage is a direct consequence of the DFT's finite-length sampling of signals. Remove the discrete Fourier transform and spectral leakage ceases to exist — it is an artifact intrinsic to the DFT's mathematical structure. Epochs confirm DFT (0.06) predates spectral-leakage (0.31).

Spectral-leakage (epoch 0.99) was understood as an artifact of Fourier analysis before windowing (epoch 2.5) was developed as a mitigation technique. The concept of spectral-leakage existed first and fed into the creation of windowing as a response — which-came-first: spectral-leakage predates windowing by a significant margin.

Window functions were developed as a solution to the problem of spectral leakage. Spectral leakage (energy spreading across frequency bins due to finite observation) was identified first, and window functions (Hamming, Hanning, etc.) were derived specifically to mitigate it. The which-came-first test passes: the problem predates the solution.