Source: https://jmrplens.github.io/phonometry/guides/test-signals/ # Test signals and sample-rate tools (IEC 60268-1) A measurement is only as trustworthy as its stimulus and its sample-rate bookkeeping. This page covers the signal toolbox of `phonometry.metrology`: **tone bursts** with the exact gating IEC 60268-1 prescribes, the **colored-noise generators** (detailed in the [spectral analysis guide](https://jmrplens.github.io/phonometry/guides/spectral-analysis/#5-colored-noise-generators)), **resampling** whose anti-alias rejection is a stated, verifiable specification rather than a library default, and **fractional delay** that shifts a record by any sub-sample amount with band-limited exactness. ## 1. Tone bursts (IEC 60268-1) The gated sine burst is the standard stimulus for dynamic behaviour: sound-level-meter ballistics, quasi-peak meters, loudspeaker power handling. IEC 60268-1:1985 (Clause A2.1) pins down what a well-formed burst is: it "should start at the zero-crossing of the tone and should consist of an integral number of full periods". `tone_burst` generates exactly that, as a single burst or as the repetitive train of Clause A2.2 in which each burst occupies one full repetition period: ```python from phonometry import tone_burst # One 5 ms burst of 5 kHz tone (25 full periods), as in Table AII. single = tone_burst(48000, 5000, 25) print(single.burst_samples) # 240 samples = 5 ms at 48 kHz # Clause A2.2: 5 ms bursts at 10 bursts per second. train = tone_burst(48000, 5000, 25, repetitions=4, repetition_rate=10) print(train.period_samples, train.duty_cycle) # 4800, 0.05 train.plot() # waveform with the gating envelope ``` The result carries the record, the rectangular gating **envelope** and the exact sample bookkeeping (`burst_samples`, `onset_sample`, `period_samples`, `duty_cycle`), so a test report can state its stimulus numerically. Because the gate spans an integral number of full periods starting at a zero crossing, the burst energy has the closed form `A²N/2` exactly, which is how the generator is verified.

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import tone_burst fs = 48000.0 single = tone_burst(fs, 5000, 25, pre_silence=0.001, post_silence=0.001) train = tone_burst(fs, 5000, 25, repetitions=4, repetition_rate=10) fig, axes = plt.subplots(2, 1, figsize=(10, 6.4)) t_ms = 1e3 * np.arange(single.signal.size) / single.fs axes[0].plot(t_ms, single.signal, lw=0.9) axes[0].plot(t_ms, single.envelope, "r--", label="Gating envelope") axes[0].plot(t_ms, -single.envelope, "r--") axes[0].set_xlabel("Time [ms]") t_s = np.arange(train.signal.size) / train.fs axes[1].plot(t_s, train.signal, lw=0.5) axes[1].plot(t_s, train.envelope, "r--", label="Gating envelope") axes[1].plot(t_s, -train.envelope, "r--") axes[1].set_xlabel("Time [s]") for ax in axes: ax.set_ylabel("Amplitude") ax.legend(loc="upper right") plt.tight_layout() plt.show() ```

These are the bursts behind the [Fast/Slow/Impulse ballistics](https://jmrplens.github.io/phonometry/guides/time-weighting/) reference responses (IEC 61672-1 Table 4 uses 4 kHz tonebursts of 200, 50 and 10 ms) and the quasi-peak dynamic tests of IEC 60268-1 itself (5 kHz bursts of 1 to 200 ms, Table AII). ## 2. Resampling with a stated anti-alias specification Sample-rate conversion hides a filter, and that filter decides how much aliased energy contaminates the result. `resample_signal` performs rational polyphase resampling (44.1 to 48 kHz is the ratio 160/147) with a lowpass FIR designed *inside the function* by the Kaiser window method, from two numbers the caller controls: - `stopband_attenuation_db` (default 120): the alias rejection, with the stopband starting exactly at the smaller of the two Nyquist frequencies, where folding happens; - `transition_width` (default 0.05): the fraction of that Nyquist frequency given up to the filter's transition band, so the passband ends at `(1 - transition_width)·f_Nyq` and is flat within the same Kaiser ripple bound `δ = 10^(-A/20)`. ```python from phonometry import noise_signal, resample_signal x = noise_signal(44100, 5.0, color="pink", seed=1) res = resample_signal(x, 44100, 48000) # 120 dB alias rejection print(res.up, res.down) # 160, 147 print(res.n_taps, res.passband_edge_hz) # designed FIR, 20947.5 Hz res.plot() # the delivered anti-alias filter against its design spec ``` *The delivered anti-alias filter of the default 44.1 → 48 kHz conversion: the stopband starts exactly at the smaller Nyquist frequency (where aliases fold) and stays below the −120 dB design line; the passband ends 5 % below it, flat within the same ripple bound.*

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```python import matplotlib.pyplot as plt import numpy as np from scipy import signal from phonometry import noise_signal, resample_signal x = noise_signal(44100, 5.0, color="pink", seed=1) res = resample_signal(x, 44100, 48000) # 120 dB alias rejection # res is the ResampledSignalResult computed in the example above. # One line — the delivered anti-alias filter against its design spec: res.plot() plt.show() # By hand, from the taps the result carries — mirroring what # ResampledSignalResult.plot() draws: fs_up = res.original_fs * res.up freqs, h = signal.freqz(res.filter_taps, worN=1 << 18, fs=fs_up) mag_db = 20 * np.log10(np.maximum(np.abs(h), 1e-300)) view = (freqs > 0) & (freqs <= 4 * res.stopband_edge_hz) fig, ax = plt.subplots() ax.semilogx(freqs[view], mag_db[view], label="Anti-alias filter |H(f)|") ax.axvline(res.passband_edge_hz, color="g", linestyle="--", label="Passband edge") ax.axvline(res.stopband_edge_hz, color="r", linestyle="--", label="Stopband edge (alias fold)") ax.axhline(-res.stopband_attenuation_db, color="k", linestyle=":", label="Design attenuation -120 dB") ax.axvspan(res.stopband_edge_hz, 4 * res.stopband_edge_hz, color="r", alpha=0.08) ax.set(xlabel="Frequency [Hz]", ylabel="Magnitude [dB]") ax.legend() plt.show() ```

The designed taps travel with the result (`filter_taps`), so the specification is *checkable*: the test suite measures the frequency response of the returned filter and asserts the passband deviation and stopband leakage against the design's own ripple bound (the design internally targets 1 dB past the request, so the delivered filter meets the stated numbers rather than a Kaiser-formula approximation of them). A passband tone resampled through the default specification matches the analytic tone at the new rate within `10^(-120/20) = 10^-6`. Several estimators resample internally at fixed rates (the ECMA-418-2 psychoacoustics at 48 kHz, STOI at 10 kHz); this function is the public, documented counterpart for preparing records outside those chains. ## 3. Fractional delay `fractional_delay` shifts a record by any number of samples, including sub-sample amounts, by multiplying the spectrum with the phase ramp `e^(-j2πf·D/fs)`: every component is delayed by exactly `D` samples. Two boundary conventions cover the two use cases: - `mode="linear"` (default) zero-pads the record past the shift, so samples leaving one end land in padding instead of wrapping around. Use it for transients and impulse responses; it is bit-identical to the alignment kernel inside [`align_impulse_responses`](https://jmrplens.github.io/phonometry/guides/correlation-delay/). An integer delay reduces to an exact sample shift. - `mode="circular"` applies the ramp over the record itself and wraps. For periodic records it is exact: a tone centered on a DFT bin delayed by `D` samples equals the analytically delayed tone to machine precision, and its phase changes by exactly `-2πf·D/fs` radians. ```python import numpy as np from phonometry import fractional_delay y = fractional_delay(x, 0.37) # 0.37 samples later z = fractional_delay(x, -2.5, mode="circular") # advance, wrapped ``` One subtlety worth knowing: a real record of even length cannot carry a fractionally delayed Nyquist-bin component (the inverse real FFT keeps only its real part). Any properly sampled signal is band-limited below Nyquist, so in practice the operation is exact; for synthetic corner cases, odd lengths avoid the bin entirely. ## 4. Colored noise The deterministic colored-noise generators (`noise_signal`: white, pink, red, blue, violet with an exact power-law slope and bit-reproducible seeds) complete the toolbox; they are documented with their spectral verification in the [spectral analysis guide](https://jmrplens.github.io/phonometry/guides/spectral-analysis/#5-colored-noise-generators). ## Where these tools are used The [window figures of merit](https://jmrplens.github.io/phonometry/guides/spectral-analysis/#6-choosing-the-window) quantify the taper every spectral estimate in the library rests on; the burst generator feeds ballistics and dynamic-response testing; and the resampler and fractional delay are the sample-rate half of [correlation and delay work](https://jmrplens.github.io/phonometry/guides/correlation-delay/), where sub-sample alignment is the difference between averaging impulse responses and smearing them. ## See also - [Time Weighting](https://jmrplens.github.io/phonometry/guides/time-weighting/): the detector ballistics the tone bursts exercise (IEC 61672-1 Table 4). - [Correlation and delay](https://jmrplens.github.io/phonometry/guides/correlation-delay/): the alignment work built on the fractional-delay kernel. - [Synchronous averaging](https://jmrplens.github.io/phonometry/guides/synchronous-averaging/): period alignment with the same band-limited shift when `fs·T` is not an integer. - [Spectral analysis](https://jmrplens.github.io/phonometry/guides/spectral-analysis/): the colored-noise verification and the window metrics. ## References - International Electrotechnical Commission. (1985). *Sound system equipment — Part 1: General* (IEC 60268-1:1985). [IEC webstore](https://webstore.iec.ch/en/publication/1204). Annex A, Clause A2: tone bursts starting at the zero crossing of the tone with an integral number of full periods (A2.1), repetitive burst trains at a stated repetition rate (A2.2), and the Table AII burst durations the sample counts are hand-checked against. - Bendat, J. S., & Piersol, A. G. (2010). *Random Data: Analysis and Measurement Procedures* (4th ed.). Wiley. ISBN 978-0-470-24877-5. [doi:10.1002/9781118032428](https://doi.org/10.1002/9781118032428). Section 10.2 (data preparation: sampling, aliasing and the anti-alias filtering requirement the resampler states explicitly).