frequenciessuch

frequenciessuch is a hypothetical term used in discussions of spectral analysis to denote the subset of a signal's frequency components that satisfy a predefined constraint. It is not a standard term in mainstream signal processing, but it appears in theoretical discussions and thought experiments as a way to describe frequency elements selected by rules other than amplitude alone.

Formally, for a discrete-time signal x[n] with Fourier transform X(e^{jω}) or its magnitude spectrum |X[k]|, frequenciessuch are the frequencies k (or ω) for which a constraint C(|X[k]|, φ[k], k) holds. Examples include |X[k]| ≥ T, phase φ[k] matching a reference pattern, or high cross-channel coherence with another signal. The exact rule depends on the application.

Identification is typically done by estimating the spectrum and applying a filter: compute X, evaluate C for each candidate frequency, and collect those that pass as the frequenciessuch set. In practice, this can involve simple thresholding, masks, or more complex optimization such as sparsity-promoting recovery or constrained least squares.

Applications include communications to identify carriers, audio signal processing to isolate meaningful tonal content, and pattern recognition in multitalker or multi-sensor data. frequenciessuch relate to but are distinct from harmonics, resonant frequencies, and spectral masks used in filtering.

Origin and status: the term is not widely adopted; it is used mainly in pedagogical or speculative contexts to illustrate how frequency selection can be governed by rules beyond simple magnitude. As such, its meaning is defined by the constraints in a given discussion.