Robsan-DIY

Introduction

I initially learned about shaped tone burst testing from Sigfried Linkwitz’s website 20+ years ago: https://www.linkwitzlab.com/mid_dist.htm

After studying up on burst testing I took it one step further, stepped sweep burst testing. Time analysis of speaker tone burst signals will reveal stored energy released after the input signal has stopped. This stored energy can be caused by the driver, cabinet, or room.

Here is a program I created to test tone bursts and stepped sweep tone burts. You can read about some of its functions below, it will be expanded soon. If you decide to check it out, please remember that this program is not digitally signed, so your browser will throw a warning when you try to download it. I don't want to pay to get it signed, the program is free to use.

ToneBurst.exe

1. PRN Sync Signal

The sweep file uses a PRN (Pseudorandom Noise) signal based on a Maximum Length Sequence (MLS) for robust synchronization, replacing the older two-pulse approach.

Sweep Generation (-sweepwav)

• 100 ms MLS — a deterministic PRN from a 31-bit LFSR with taps at bits 31 and 28
• PRN windowed with Hanning fade in/out (10 ms each)
• -3dB amplitude to leave headroom for tone burst peaks
• Broadband energy sweep that works with any speaker type

DUT Analysis (-dutsweepwav)

• Regenerates the identical PRN MLS reference sequence
• Uses cross-correlation to find the sync position
• Two-pass search: coarse (every 10 samples) then fine refinement
• Detects sync error if correlation exceeds 10% of expected value
• Works even with band-limited playback (tweeters, etc.)

ETC Output Layout

2. Tone Burst Bandwidth

The bandwidth of a tone burst is determined by its duration, not its frequency. For a 4-cycle burst the duration is T = 4 / f and the approximate −3 dB bandwidth is BW ≈ f / 4 — roughly 25% of the center frequency (±12.5%).

The Blackman window reduces spectral leakage (sidelobes ≈ −58 dB down) but slightly widens the main lobe, so the actual −3 dB bandwidth is closer to f / 3.5 or about 29% of center frequency.

Frequency	Duration	Bandwidth (−3 dB)
100 Hz	40 ms	~25 Hz
1 kHz	4 ms	~250 Hz
10 kHz	0.4 ms	~2.5 kHz
20 kHz	0.2 ms	~5 kHz

This is why tone bursts are useful for transient / time-domain analysis — they are short enough to measure time-domain behavior but have enough bandwidth to excite the system meaningfully. The trade-off is that you cannot isolate a single frequency the way you would with a long steady-state sine wave.

For speaker measurements, this bandwidth is actually desirable since it shows how the speaker responds to transient signals across a range of frequencies simultaneously, which is more representative of real audio content (music, speech) than pure tones.

4-Cycle Blackman-Windowed Reference Burst

3. Optimal Octave Spacing

For adjacent burst spectra to "just touch" at their −3 dB points, we need the upper −3 dB edge of one burst to meet the lower −3 dB edge of the next.

Derivation

Setting	Step Ratio	Coverage
-sweepoct 2 (½ octave)	1.414	Slight gaps between bursts
Optimal ≈ 1/2.4 octave	1.339	Spectra just touch
-sweepoct 3 (⅓ octave)	1.260	Slight overlap (~6%)

Since -sweepoct takes integers, use -sweepoct 3 or higher for continuous frequency coverage without gaps.

4. Parabolic Interpolation for Sub-Sample PRN Detection

Test Signal Structure

The Problem: Integer Sample Resolution

Cross-correlation finds where the PRN best matches, but only at integer sample positions. The true peak of the correlation function almost always falls between samples. A 1-sample error in a 770,400-sample span produces a 1.3 PPM apparent drift.

The Solution: Fit a Parabola

A parabola closely approximates the correlation peak. We use the three samples surrounding the integer maximum — y0, y1 (the peak), and y2 — to calculate where the true peak lies.

The Math

For a parabola passing through points at x = −1, 0, +1 the vertex (peak) occurs at:

Real Example (End PRN Detection)

y0 (lag−1) :  527,410,999
              y1 (lag peak): 529,429,464   ← highest correlation
              y2 (lag+1) :  527,361,859
              y0 − y2          = 49,140
              y0 − 2·y1 + y2  = −4,086,070
              δ = 49,140 / (2 × −4,086,070) = −0.006013
              Integer position  : 866,400
              Sub-sample offset : −0.006013
              ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
              Precise position  : 866,399.993987
              

Precision Improvement

Detection Method	Resolution	Min Detectable Drift
Integer only	1 sample	~1.3 PPM
Parabolic interpolation	~0.01 sample	~0.013 PPM

5. |Diff| % Metric

The |Diff| % metric compares the Energy Time Curve (ETC) of the Device Under Test (DUT) to an ideal 4-cycle Blackman-windowed reference burst. It measures how much the burst "spreads" or "rings" compared to the ideal.

Step 1 — Record the Signals

The reference is the ideal 4-cycle Blackman burst. The DUT signal is recorded through the speaker and room, and may show additional ringing after the main burst.

Step 2 — Compute ETC (Envelope via Hilbert Transform)

The Hilbert Transform extracts the amplitude envelope, which is then converted to dB scale (0 dB = peak).

Step 3 — Calculate Area Above −40 dB Threshold

We integrate the linear envelope (not dB) above the −40 dB threshold. The shaded regions below represent the areas being compared.

Step 4 — Calculate |Diff| %

Visual Summary

Interpretation Guide

|Diff| %	Rating	Interpretation
0–5%	Excellent	Minimal ringing or resonance
5–15%	Good	Some coloration
15–30%	Fair	Noticeable resonance
30–50%	Poor	Significant ringing
>50%	Bad	Severe resonance issues

6. Noise Floor Measurement

The noise floor is measured from a dedicated 500 ms silence window located just before the End PRN marker.

Measurement Window Location

Step 1 — Locate the Window

noiseFloorSilence    = SampleRate × 0.500    # 48,000 samples at 96 kHz
              noiseFloorEndSample  = endPrnPosition
              noiseFloorStartSample = endPrnPosition − noiseFloorSilence
              

Step 2 — Calculate RMS

RMS (Root Mean Square) measures the average power of the signal in the noise window.

Step 3 — Convert to dBFS

Convert the RMS value to decibels relative to full scale (maximum possible digital value).

Example:  RMS = 3,340
              dBFS = 20 × log₁₀( 3,340 / 8,388,607 )
              = 20 × log₁₀( 0.000398 )
              = 20 × (−3.4)
              = −68 dBFS
              

Step 4 — Per-Burst Relative Noise Floor

For each burst's mini ETC graph, the noise floor is calculated relative to that burst's peak amplitude, giving the signal-to-noise ratio for that specific frequency.

Two Different Noise Floor Values