dft

DFT is a specific algorithm — a defined computational procedure for transforming time-domain samples to frequency coefficients. A competent speaker would describe DFT as 'an algorithm.' This is the nearest kind: DFT is not a broader category that algorithm fits into, nor is it a part of algorithm. Files INSTANCE_OF correctly.

FFT's operation is defined as an efficient algorithm for computing the DFT. Remove the DFT — the mathematical transform that decomposes signals into frequency coefficients — and FFT has nothing to compute. The dependency is constitutive: FFT is the 'how' of DFT computation, DFT is the 'what'.

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.

Window functions are applied before the DFT to reduce spectral leakage. Remove the DFT as a concept and windowing in signal processing has no purpose or operation. The removal test (Law 8) passes.

Frequency resolution as defined here is the concept of distinguishable frequency separation within DFT bin spacing. Remove DFT as a concept and this concept ceases to operate — the bin spacing formula (fs/N) and main-lobe width analysis are all DFT-specific. Law 8 removal test passes.

Zero padding extends a time-domain sequence with zeros before computing the DFT to increase frequency resolution via denser sampling of the spectrum. Remove the DFT and zero padding has no computational role — it is meaningless without the DFT as its target operation. The removal test passes.

Windowing in spectral analysis applies a window function before DFT to reduce spectral leakage. Remove DFT and windowing as a spectral technique has nothing to apply to — the technique is designed for DFT-based analysis. The removal test passes (Law 8).

Cepstral coefficients are computed by taking the DFT of the signal's waveform, extracting the log magnitude spectrum, and applying the inverse DFT. Remove the DFT and cepstral analysis cannot be performed — the transform is the fundamental operation that makes the cepstral domain accessible. Present-tense operational dependency.

FFT (Fast Fourier Transform) is a specific efficient algorithm for computing the DFT. A competent speaker would call FFT a DFT computation method. It is a kind of DFT algorithm, not merely dependent on it.