Mean Frequency — Control Systems/Spectral Measurements

Mean Frequency

Control Systems / Spectral Measurements

The first moment of a power spectral density – where its mass sits on the frequency axis. With bin k at frequency f_k = k·Δ and carrying power P_k = Δ·p_k, the answer is f = Σ_kP_k·f_k ÷ Σ_kP_k, taken over the whole spectrum or over one band. This is the streaming counterpart of MATLAB's meanfreq.

Both weight vectors follow from the parameters alone, so the block is two weighted sums and one division: no branch and nothing carried between samples.

Ports

• p – the power spectral density, one nonnegative value per bin. A vector, either an [N,1] column or a [1,N] row, with N between 2 and 512. Bin k is the frequency k·Δ.
• f – the mean frequency, in the same units as Bin Spacing. Always scalar, whatever the input's length.

Parameters

• Bin Spacing – Δ, the frequency step between neighbouring bins, a positive number. Left at 1 the answer comes out in bins; set it to f_s÷(2·(N−1)) for a one-sided spectrum reaching the Nyquist frequency and the answer comes out in Hz.
• Integration Range – which bins the moment is taken over:
  • Full spectrum – every bin. This is meanfreq(Pxx, F), and it is the default.
  • Frequency band – only the bins inside the band. This is meanfreq(Pxx, F, [flo fhi]).
• Frequency Band – [f_lo f_hi], a two element vector in the same units as Bin Spacing, read only in Frequency band mode. The band is narrowed to the bins it contains: a bin counts when f_lo ≤ f_k ≤ f_hi. See Notes – Band Power snaps the other way.
• Epsilon – ε, added to the total power before the division. It is what makes an all-zero band return 0 instead of a NaN – it is a degeneracy guard, not an accuracy knob, so the default is 1e−30: far below any total power a real spectrum carries, and small enough that the answer matches MATLAB's to the last bit. A larger value biases every answer toward zero by ε÷ΣP.
• 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.

Both weight vectors are structural and are inlined into the arithmetic at export time rather than exposed as tunable parameters – they follow from the bin spacing, the bin count and the band, and changing any of them changes how many multiplies the core contains, which no runtime parameter can do. Re-export after changing them.

The three HDL targets are simulation-only: the block divides, and a Q16.16 divider is not part of this tree's fixed-point base. They compute in real arithmetic and quantize only at the port boundary, so they simulate correctly and are not offered as synthesizable.

Simulink bridge

No equivalent (Support::None). Signal Processing Toolbox ships no Simulink library at all, and meanfreq is one of its MATLAB functions. DSP System Toolbox was searched block by block and carries no spectral moment. The bridge reports this block rather than dropping it silently, and it therefore has no parity testbench. Code export verification still covers it across all ten languages.

Notes

• Stateless. The answer depends on this sample's spectrum and nothing else, so there is no startup transient and no history to seed.
• The band is narrowed, not widened – and Band Power does the opposite. This block keeps the bins inside the band; Band Power keeps the bins that bracket it. Measured on an 8-bin spectrum at Δ = 0.5 over the band [0.6, 2.9], this block integrates bins 2–5 and Band Power integrates bins 1–6. Both are MATLAB's own rules, on the same PSD, so the two blocks can legitimately report a band's mean frequency and its power over different sets of bins.
• Verified against MATLAB. On that spectrum R2026a answers 1.3156966490299824 over the full range and 1.4044943820224718 over [0.6, 2.9]; this block reproduces both.
• An all-zero band answers 0, where MATLAB answers NaN. That is the one deliberate divergence, and Epsilon is what makes it: the total power is floored rather than tested, because VHDL has no inline conditional in the single expression the ten backends share, and a NaN is the wrong thing to bake into ten cores.
• The input is expected nonnegative. A power spectral density is, and nothing here checks it: a negative bin takes part in both sums like any other, which is the right behaviour for a user taking the first moment of something else.
• No state space. The block divides one linear functional of its input by another, so it is not linear at all and carries none; model reduction correctly declines to merge it.