Time Synchronous Average — Control Systems/Vibration

Time Synchronous Average

Control Systems / Vibration

Averages the last R revolutions of a signal, one entry per sample of a revolution:

avg[j] = (1 ÷ R)·Σ_r u[(R−1−r)·P + j]

This is MATLAB's tsa. Everything that repeats with the shaft survives the average; everything that does not is attenuated, and it falls as 1÷√R – so four revolutions halve the asynchronous noise and sixteen quarter it.

Ports

• u – the sampled signal. Scalar: one channel and its own history – see Notes.
• avg – the averaged revolution, [P, 1], oldest sample of the revolution first. Its height follows Samples Per Revolution alone.

Parameters

• Samples Per Revolution – P, how many samples one revolution occupies. A whole number from 2 to 64. At a sampling rate f_s and a shaft speed of N revolutions per minute, P = 60·f_s÷N, and it has to come out whole – see Notes.
• Number of Revolutions – R, how many are averaged. A whole number from 2 to 32. More revolutions suppress more asynchronous content and lengthen the memory: the block looks P·R samples back, which may not exceed 512.
• 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.

Nothing divides in a generated core. R is fixed by the configuration, so 1÷R is a number computed at export time and inlined; a core carries a shift register of P·R samples, a revolution counter, and P multiply-accumulates of R terms each. Both settings are structural – together they decide how long the register is and how many outputs there are – so re-export after changing either.

The three HDL targets are genuine synthesizable Q16.16: adds and one constant multiply, with the products accumulated at full width and shifted back once per output row.

Simulink bridge

None (Support::None). tsa 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)).
• ⚠ The period is a parameter here and MATLAB takes it from a tachometer. That is the one real departure, and it is the same fork Fourier Fit meets with its fundamental: with P given a revolution is a fixed number of samples and the average is a fixed bank of weights, which is what makes the block exportable at all. With a tacho the revolutions are fractional in samples and have to be resampled onto a common grid, which is what tsa's Method option (linear, spline, pchip, fft) exists to choose between.
• ⚠ And on the case this block covers, all four of those methods coincide. Measured rather than assumed: with revolutions that are a whole number of samples there is nothing to resample, and R2026a's tsa at its default reproduces the plain arithmetic mean of the cycles to 8.9e−16 over five revolutions of eight samples. This block is not an approximation of tsa; it is tsa restricted to the case where tsa has no choice to make.
• ⚠ If P does not come out whole, this is the wrong block. 60·f_s÷N is a whole number only at particular speeds; anywhere else the shaft drifts against the sample grid, entry j stops being the same shaft angle from one revolution to the next, and the average smears the very features it exists to sharpen. Change the sampling rate so it divides, or resample the signal first.
• ⚠ The phase origin is the start of the run. Without a tacho there is nothing else it could be: entry 0 is a fixed number of samples after the first sample of the run, not a known shaft angle. The shape is right and its rotation within the vector is arbitrary, so compare shapes across runs only if they start together.
• The average is republished once per revolution and held in between. Recomputing it every sample would be correct arithmetic and a useless block: the phase reference would advance by one entry per sample and the shape would appear to rotate. Held, it is stable for the P samples a reader is looking at it.
• The first P·R−1 samples are a startup transient: the register is zero-prefilled, so early revolutions are averaged against zeros. The output is all zeros until the first full revolution completes.
• Scalar only. One channel and its own history; wire one block per channel.
• No state space. Linear in the input, but through a fixed bank over P·R past samples rather than an A/B/C/D pair, so model reduction correctly declines to merge it.