Power Bandwidth — Control Systems/Spectral Measurements

Power Bandwidth

Control Systems / Spectral Measurements

The width of the band around a spectrum's peak within which the power spectral density stays above a stated roll-off below that peak. The reference level is max(p)·10^−R/10; the block finds where the density last falls to it on the peak's left and first falls to it on its right, and reports those two frequencies and their difference. This is the streaming counterpart of MATLAB's powerbw.

It is not Occupied Bandwidth. That block is centred on power – equal power left outside on each side – and never looks for the peak. This one is centred on the peak and never counts the power inside. On a lopsided spectrum they land in different places.

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 3 and 256. Bin k is the frequency k·Δ. Three is the smallest N that can hold a peak with a bin on each side of it.
• bw – the power bandwidth, f_hi − f_lo. Scalar.
• flo – the lower edge, interpolated in dB between the two bins that straddle the reference level on the peak's left. Scalar.
• fhi – the upper edge, the same on the peak's right. Scalar.

Parameters

• Bin Spacing – Δ, the frequency step between neighbouring bins, a positive number. Left at 1 the answers come out in bins; set it to f_s÷(2·(N−1)) for a one-sided spectrum reaching the Nyquist frequency and they come out in Hz.
• Reference Rolloff (dB) – R, how far below the peak the band's edges sit, a positive number of decibels. The default is 3.0102999566398120, which is 10·log₁₀2 exactly and is therefore the true half-power point – typing a round 3 instead gives 10^−0.3 = 0.50119 of the peak rather than one half.
• Epsilon – ε, a degeneracy guard, not an accuracy knob, added to the interpolation's denominator so that two neighbouring bins of identical level cannot divide by zero. The default of 1e−18 is far below any dB difference a real spectrum produces.
• 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 bin count, the bin spacing and the reference factor are structural and are inlined at export time rather than exposed as tunable parameters. Re-export after changing them.

The three HDL targets are simulation-only: the block takes a base-10 logarithm per bin and divides, neither of which belongs in a Q16.16 datapath. 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 powerbw is one of its MATLAB functions. DSP System Toolbox was searched block by block and carries no power-bandwidth measurement. 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.
• The DC bin is doubled before the peak is looked for, whenever the axis starts at 0. This is MATLAB's rule for this measurement and not for Occupied Bandwidth, which does no such thing – on a spectrum whose largest bin is DC it alone decides where the peak is.
• The interpolation is in dB, not in power. Each edge is found by interpolating log₁₀ of the density between the two bins that straddle the reference, with a floor of realmin underneath the logarithm. That floor is what keeps a spectrum with empty bins finite instead of NaN, and its exact value shows through in the answer.
• Both edges fall back to the axis end. If the density never drops to the reference on one side – a peak sitting against the end of the axis – that edge is the axis end itself rather than an extrapolation.
• Verified against MATLAB on four spectra. An 8-bin spectrum at Δ = 0.5 gives a half-power band of [0.66611010771335399, 1.4442348121752797] and a 6 dB band of [0.36416096465070874, 1.7625864696974454]; an 11-bin spectrum at Δ = 0.35 whose first bin already exceeds the reference gives [0, 1.7934315938109551], the fallback; [0 0 3 0 0 1 0 0] at Δ = 0.5, with four empty bins, gives [0.99951152076445282, 1.0004884792355471]; and [0.4 1.2 3.0 1.1 0.35 0.9 0.2 0.05] at Δ = 0.25 gives [0.31088230065849248, 0.67271646656482109]. R2026a answers all of these, and this block reproduces them.
• A flat or monotonic spectrum has no interior peak, and the block does not pretend otherwise: the maximum is then an end bin, one side never crosses the reference, and that edge is reported as the axis end. The answer is a half-band, which is what the measurement means there.
• No state space. The block is not linear in its input at all, so it carries none and model reduction correctly declines to merge it.