Spectral Features — Machine Learning/Feature Engineering

Spectral Features

Machine Learning / Feature Engineering

Reduces a magnitude spectrum to the four descriptors a classifier is actually trained on. With bin k carrying mass m_k at frequency f_k = k·Δ, and T = Σ m_k over the K bins used:

• Centroid – (Σ f_km_k) ÷ (T + ε), the spectrum's centre of mass: where the energy sits.
• Spread – √((Σ (f_k − centroid)² m_k) ÷ (T + ε)), its standard deviation about that centre: a pure tone is narrow, noise is wide.
• Roll-off – Δ × the number of bins whose cumulative mass is still below ρ·T, i.e. the frequency below which fraction ρ of the energy lies.
• Flatness – the geometric mean over the arithmetic mean, exp(mean_k ln(m_k + ε)) ÷ (T÷K + ε). Near 1 is noise-like, near 0 is tonal.

Its natural upstream is FFT Magnitude. Four numbers per step instead of N bins is what makes a spectrum usable by Dense Layer, SVM Predictor or any of the classifiers in this family.

Ports

• m – the magnitude spectrum, a column [M,1]. Values are read as nonnegative masses; whether they are magnitudes or magnitudes squared is the upstream block's choice and changes only what the numbers mean.
• f – the features, a [4,1] column in the order centroid, spread, roll-off, flatness. Always four rows, whatever M is.

Parameters

• Input Spectrum – which bins are used.
  • Two-sided (fold to first half) – uses bins 0 … M/2 only, so K = M/2 + 1. This is the setting for a spectrum straight out of FFT Magnitude, which emits the full length N with both halves: for a real input those halves are mirror images, and a centroid taken over both reports the mirror rather than the signal. M must be even.
  • One-sided (use every bin) – uses all M bins, for a caller who has already folded the spectrum or is describing something that is not a two-sided transform.
• Roll-off Fraction – ρ, the mass fraction the roll-off point must reach; a number in (0, 1]. 0.85 is the usual choice.
• Bin Spacing – Δ, the frequency step between bins. Left at 1 the centroid, spread and roll-off come out in bins; set it to f_s÷N to get Hz. Flatness is dimensionless and does not scale with it.
• Epsilon – ε, the guard added to the totals and inside the logarithm. It is what makes an all-zero spectrum return zeros instead of NaN, and what keeps ln() away from an empty bin. Keep it small relative to the masses you expect.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. K is known at export time, so every sum is unrolled and no backend contains a loop or a bounds check. ρ, Δ and ε are baked into the arithmetic rather than exposed as tunable parameters: they define what the features mean, so retuning one on the target would silently produce a different feature than the model was trained on.

The three HDL targets are simulation-only real arithmetic, quantizing only at the port boundary. A division, a square root, a logarithm and an exponential do not belong in a Q16.16 datapath, and this block needs all four. ⚠ Note also that a magnitude-squared spectrum grows as the square of the window energy, and Q16.16 saturates past ±32768 at the port itself – feed the HDL targets the Magnitude form rather than Magnitude squared if the window is large.

Simulink bridge

None, and measured rather than assumed. R2026a on this machine has no block in any of DSP System Toolbox's 42 library files whose name matches centroid, roll-off, flatness or spectral; Audio Toolbox – whose spectralCentroid, spectralSpread and spectralRolloffPoint these four follow – is not installed; and the spectral descriptors that do exist here (spectralFlatness, spectralCrest, spectralEntropy, spectralKurtosis, spectralSkewness) are Signal Processing Toolbox functions, which no ParamRule can carry across the bridge. The block therefore has no parity testbench, which is the documented consequence of Support::None rather than a gap.

Notes

• Algebraic and stateless: every feature comes from the current spectrum alone. Nothing is averaged across steps – put Rolling Statistics after it if you want that.
• The flatness convention was verified against MATLAB: R2026a's spectralFlatness is exactly geometric mean over arithmetic mean of the bins given, with no frequency weighting, and agrees with this block to the last digit.
• Roll-off is computed as a count, not a search: the number of bins still below ρ·T is the index of the first bin that reaches it. That keeps all ten backends branch-free and identical, and an all-zero spectrum lands on bin 0 rather than on a NaN.
• The spread uses the two-pass form rather than √(E[f²] − centroid²). The identity form is cheaper to generate but can go slightly negative under rounding when the mass sits in one bin, and a negative under a square root is a NaN in ten backends at once.