RPM Frequency Map — Control Systems/Vibration

RPM-Frequency Map

Control Systems / Vibration

The frequency map versus speed of a machine that is running up or down – MATLAB's rpmfreqmap, one column at a time. Every hop samples the block takes the last L samples, windows them and publishes the one-sided spectrum of that frame together with the shaft speed at the frame's centre, so a recorder builds the whole map over the run:

column_j[m] = c(m)·|Σ_n w[n]·x[j·hop+n]·e^−i2πmn/N|,   m = 0 … N/2,   N = max(256, L),

with the window normalized to sum 1 and c the one-sided fold: 1 at DC and at Nyquist, √2 between. The window length L is not a parameter – it follows from the resolution asked for.

Ports

• u – the sampled signal, scalar: one channel and its own window.
• rpm – the shaft speed in revolutions per minute at the same instant, scalar and positive. It is a signal, not a parameter, because it is what the map is drawn against.
• map – the current column, [N/2+1, 1], one-sided with DC first and Nyquist last; bin m is at m·f_s/N hertz. It changes only on a frame sample and holds in between.
• rpm – scalar: the speed at that column's centre, the map's horizontal axis. Interpolated between the two samples either side of the centre when the window is odd.
• t – scalar: the time of that centre in seconds from the run's first sample, (j·hop + L/2)/f_s.

Parameters

• Sample Rate (Hz) – f_s, the rate the signal was sampled at: the resolution, the window length and the output bins are all in hertz through it. Positive; defaults to 1000.
• Resolution (Hz) – the frequency resolution asked for, which is what sets the window length: L is the length whose equivalent noise bandwidth gives that resolution, found by the same iteration rpmfreqmap uses. A finer resolution means a longer window and a slower map. Defaults to 7.8125, which is rpmfreqmap's own default of f_s/128 at the default rate, and gives L = 193 with a Hann window. A resolution too fine for a window of 1024 samples, or too coarse for one of 4, is clamped to that window rather than refused – as rpmfreqmap clamps it to the record.
• Window – the shape the frame is multiplied by, normalized to sum 1:
  • Hann – rpmfreqmap's default.
  • Hamming – a lower first sidelobe, a wider main lobe.
  • Flat Top – amplitude-accurate on a line that falls between bins, and the widest of the four; rpmordermap's default.
  • Rectangular – no window at all.
  rpmfreqmap also takes Kaiser and Chebyshev windows, which need a second parameter each; those two are not offered here.
• Overlap Percent – how much of one frame the next one repeats, 0 to 100. The overlap in samples is min(ceil(percent/100·L), L−1) and the hop is L minus that, exactly as in rpmfreqmap. Defaults to 50.
• Amplitude – what a bin carries:
  • RMS – the root-mean-square amplitude of that line: the default.
  • Peak – the peak amplitude, √2 times the RMS one (and at Nyquist, √2 times the unfolded magnitude).
  • Power – the square of the RMS value.
• Scale – Linear, or dB: 20·log₁₀ of an amplitude, 10·log₁₀ of a power. A bin that is exactly zero is −∞ in dB, as it is in MATLAB.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Frames and timing

The first column is published when the window first fills – at sample L−1, counting from 0 – and then every hop samples, so the output at sample L−1+j·hop is column j of rpmfreqmap over the same record. Between columns all three outputs hold; before the first they are zero. The block is exactly rpmfreqmap here: a column depends on L samples and on nothing else, so nothing about it needs the rest of the record.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The window is computed once at export time and carried as numbers; the transform, the fold and the scaling run as loops in the core, so the emitted program does not grow with the number of bins. Every parameter is structural – re-export after changing one.

⚠ The three HDL targets run those loops in simulation-only real arithmetic, quantizing only at the port boundaries: a transform of a 1024-sample window and a square root do not belong in a Q16.16 datapath. They are not offered as synthesizable.

Simulink bridge

None (Support::None). rpmfreqmap is a Signal Processing Toolbox function and that toolbox ships no Simulink library, so there is no path a diagram could name. 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

• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): two shift registers of L samples, a frame counter and the held column.
• The speed axis is a signal, not a parameter. Feed rpm from a tachometer block (Tacho Pulse RPM) or from a recorded speed channel; the map is only as good as that speed.
• Not Spectrogram. That block publishes |X| at a transform length equal to its window; this one follows rpmfreqmap – the window length comes from a resolution, the transform is at least 256 long, the window sums to 1, and the speed and time of each column come out beside it.
• No state space. A magnitude is not linear in the window, so model reduction correctly declines to merge it.