Band Power — Control Systems/Spectral Measurements

Band Power

Control Systems / Spectral Measurements

The average power a power spectral density carries, either over the whole spectrum or over one frequency band – P = Σ_k w_k·p_k, a rectangle rule over the bins. Bin k sits at frequency f_k = k·Δ, and the weights w_k are the bin widths the range rule assigns. This is the streaming counterpart of MATLAB's bandpower(Pxx, F, 'psd').

The weights follow from the parameters alone, so the block is one weighted sum: no 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.
• P – the power in the selected range. 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 is a power per bin; set it to f_s÷(2·(N−1)) for a one-sided spectrum reaching the Nyquist frequency, and the answer is a power in the signal's own units.
• Integration Range – which bins are summed, and which of two rectangle rules is used:
  • Full spectrum – every bin, each given the width Δ. This is bandpower(Pxx, F, 'psd'), and it is the default.
  • Frequency band – only the bins the band reaches, and the top bin of the whole vector is given a width of zero. This is bandpower(Pxx, F, [flo fhi], 'psd'). See Notes: over the same full axis the two modes deliberately do not agree.
• 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 widened to the bins that bracket it: the sum starts at the last bin at or below f_lo and ends at the first bin at or above f_hi.
• 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.

The N weights 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 genuine synthesizable Q16.16: a fixed multiply-accumulate with the products accumulated at full width and shifted back once at the end rather than per term. There is nothing in this block to make simulation-only – it neither divides nor takes a root.

Simulink bridge

No equivalent (Support::None). Signal Processing Toolbox ships no Simulink library at all, and bandpower is one of its MATLAB functions. DSP System Toolbox was searched block by block and carries nothing that integrates a PSD over a band: its Power Meter measures the average or peak power of a time signal against a reference load, which is a different measurement on a different input. 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 two range modes deliberately do not agree on the same axis. Over the full spectrum the top bin is given the average bin spacing; over a band it is given a width of zero, which is MATLAB's own rule (bandpower.m: "Don't include last point of PSD data"). Measured on an 8-bin spectrum at Δ = 0.5, R2026a answers 2.835 over the full spectrum and 2.8 over the band [0, 3.5] – the same axis, one bin apart. Reproduced here to the last bit.
• The band is widened, not narrowed. A band falling between bins is snapped outward to the bins that bracket it. Mean Frequency snaps the other way and keeps only the bins that lie inside the band. Both are MATLAB's, on the same PSD, and neither is a rounding of the other – so the two blocks can legitimately report a band's power and its mean frequency over different sets of bins.
• The input is expected nonnegative. A power spectral density is, and nothing here checks it: a negative bin is summed like any other, which is the right behaviour for a user who is integrating something else with the same rectangle rule.
• No state space. The block is linear in its input, but it reduces a vector to a scalar rather than evolving a state, so it carries none and model reduction correctly declines to merge it.