CPB Analysis (Constant Percentage Bandwidth)

CPB analysis runs the signal through a bank of real digital band-pass filters, one per frequency band, and measures the mean square of each filter output in the time domain. Because the measurement never passes through an FFT, the low-frequency bands are not limited by FFT resolution.

Four elements share this engine and differ only in what the horizontal axis shows: CPB Spectrum, CPB vs Time, CPB vs RPM and CPB Synthesis. All four are inserted from the Insert menu into the analysis pool.

CPB or octave analysis? They are different methods

Deepsona ships both. They answer the same question with different machinery, and the results are not interchangeable at low frequencies.

	CPB analysis	Octave Spectrum (1/1, 1/3)
Method	Time-domain IIR filter bank, one band-pass per band	FFT synthesis: FFT lines are grouped into bands
Band definition	IEC 61260 base-ten, G = 10^0.3 ≈ 1.99526	ISO preferred values (base-two lineage)
Low-frequency behaviour	Unaffected by FFT resolution	Degrades when too few lines fall inside a band
Bandwidths	1/1, 1/3, 1/6, 1/12, 1/24	1/1, 1/3
Cost	Higher (filtering + decimation per octave)	Lower (one FFT, then grouping)

The two use different centre-frequency tables and must not be mixed. CPB follows the base-ten system (G = 10^0.3); the octave engine follows the ISO preferred nominal values. Comparing a CPB band against an octave band of the same nominal name is only meaningful once you have checked that the band edges actually coincide.

Why low frequencies fail under FFT synthesis

A constant-percentage band gets narrower in absolute terms as the centre frequency drops, while an FFT has a constant line spacing Δf. Below roughly

f_c < 4.32 · lines · Δf

the number of FFT lines inside the band becomes too small to represent it, and the band level collapses towards whatever the few surviving lines happen to contain. This is a property of the method, not a defect: it is exactly why a filter bank is used instead. A 20 Hz 1/3-octave band is only about 4.6 Hz wide — at a typical analysis resolution it may contain a handful of lines.

How the filter bank works

Filtering every band at the full sampling rate would be wasteful and numerically poor at low frequencies, so the bank decimates by one octave at a time:

The highest octave is filtered directly at the input rate.
In parallel, a decimation low-pass feeds a 2:1 decimator, whose output is handed to the next octave down. This repeats all the way to the lowest requested band.
Each octave therefore works at its own sampling rate, and the number of samples per frame halves at every step (512 → 256 → … → 2 → 1).

Each absolute octave carries its own set of decimation low-pass coefficients. Sharing a single prototype across octaves is what makes the error grow with decimation depth, so the coefficients are stored per octave rather than reused.

Effective time resolution is not the same in every band. Once an octave is decimated below one sample per frame, it produces a value only every 2^k frames and holds it in between (zero-order hold). The low bands therefore have an effective time resolution of Pre-averaging time × 2^k. This matters when reading CPB vs Time: a slow-moving staircase in the lowest bands is the time resolution, not the signal.

Detection and framing

Each band output is squared and averaged over a pre-averaging block (default 10 ms). The block length is forced to a power of two — 2^{floor(log2(round(fs·T)))}, clamped to [2, 131072] — so the decimation chain divides evenly.
Filter state persists across frames, and the filter start-up transient is included in the result. Use Skip settling (below) if you do not want it.
A trailing partial block at the end of the signal is discarded: no zero padding, no half-length frame.

The four elements

CPB Spectrum

One spectrum for the whole selected segment: every band is averaged over time according to the chosen averaging mode. This is the element to use for a stationary condition — a steady load point, an idle run, a constant-speed pass.

CPB vs Time

Band levels as a function of time, one column per pre-averaging frame. Use it to see when something appears, and in which bands. Remember the note above: the lowest bands update more slowly than the frame rate.

CPB vs RPM

Band levels against a speed axis. Deepsona extracts one spectrum at the moment the speed crosses each grid value, rather than sorting frames into speed bins and averaging them.

Crossing-point extraction keeps the spectrum tied to a single instant, so a run-up that dwells briefly at one speed does not get averaged together with a later pass through the same speed.
Direction sensitivity is on by default: only a monotonically rising (or falling) section is collected, and reversals are discarded. The number of discarded frames is written to the analysis log, so a run that loses half its data says so instead of silently thinning out.

CPB Synthesis

Bands synthesised from an existing FFT spectrum rather than from a filter bank. It is the cheap option when an FFT is already available and the frequencies of interest are high enough for the line count to be adequate. When a band does not contain enough lines, the band is marked invalid rather than being given a plausible-looking number.

Weighting, averaging and Overall

Frequency weighting

A, B, C and D weighting are applied in the time domain, before the signal enters the filter bank. The weighting stated on the Y axis always matches what was actually applied: if the selected weighting cannot be applied to the signal, the axis will not claim it was.

Averaging

Mode	Behaviour
Exponential — Fast	125 ms time constant.
Exponential — Slow	1 s time constant.
Linear (finite window)	Arithmetic mean over a fixed window.
Linear (whole segment)	Arithmetic mean of all frames in the segment.

Overall level

The Overall value shown alongside the bands is computed by an independent broadband time-domain chain — it is not the sum of the band levels. Both an A-weighted and a linear Overall are produced by default. Summing bands and measuring broadband give slightly different answers because the band filters overlap at their edges; the broadband chain is the one to quote.

Parameters

Parameter	Options / default	Description
Bands per octave	1/1, 1/3, 1/6, 1/12, 1/24 (default 1/3)	Band width. An unsupported value falls back to 1/3 and says so in the log.
Lower / upper frequency	20 Hz / 20 kHz	Band centre frequencies, not band edges. A value that is not a valid centre snaps to the nearest one, and the substitution is written to the log.
Pre-averaging time	0.01 s	Detector block length. Rounded to a power of two internally.
Frequency weighting	Z (linear), A, B, C, D	Applied in the time domain before banding.
Averaging	Fast / Slow / Linear / Linear whole segment	See above.
Skip settling	Off by default	Discards the leading frames covering the settling time of the lowest band. Off means the start-up transient is included.

Band range limits

The band range you get is not always the band range you asked for, and every reduction is logged:

Coefficient table coverage. Bands outside the stored coefficient range are clamped away. The table covers roughly 0.1 Hz to 160 kHz.
Data Nyquist. A band is kept only if its upper band edge fits below half the sampling rate. The axis therefore stops at whichever is lower: the upper limit you set, or the highest band the data can actually support. Bands with no content are not drawn.

The Nyquist rule uses the upper band edge against fs/2. A rule of thumb such as “highest frequency = fs/2.56” would discard the 20 kHz band on 48 kHz data, which is wrong — the 20 kHz band has an upper edge of about 22.4 kHz and fits below 24 kHz.

Practical Tips

Use CPB when low-frequency bands matter — structure-borne noise, building acoustics, anything below a few hundred hertz. Use octave analysis when the bands of interest are high enough that FFT synthesis is adequate and you want the lower computation cost.
Narrower bandwidths (1/12, 1/24) cost proportionally more and settle more slowly at low frequencies. Check the settling time before using them on short segments.
Read the analysis log after a run. Band clamping, centre-frequency snapping, Nyquist trimming and discarded frames in CPB vs RPM are all reported there rather than being applied silently.
For CPB vs RPM, make sure the speed signal is monotonic over the section you care about. With direction sensitivity on, a run-up that oscillates around a speed will contribute only the monotonic part.
When a low band in CPB vs Time looks like a staircase, check the effective time resolution before concluding the signal is stepping.

Do not apply A-weighting to acceleration signals. The frequency weightings defined in IEC 61672 are intended exclusively for sound pressure.