VirtualInstrument

VirtualInstrument

Science-payload data source: amplitude-calibrated synthetic LISA strain via windowed overlap-add FFT synthesis against the sky-averaged LISA sensitivity of Robson, Cornish & Liu (2019), or gapless segmented ingestion of an external CSV time series.

InstrumentState

Maintains the state of the satellite's scientific payload. Can generate synthetic LISA strain noise (instrument sensitivity plus the galactic-confusion foreground, lisa_noise_psd) or ingest an externally provided continuous 1D time-series CSV array.

Synthetic strain is generated by a windowed overlap-add (WOLA) scheme: amplitude-calibrated colored-noise blocks of 2N samples (N = samples per segment) are shaped with a periodic sqrt-Hann window and summed at 50% overlap. The squared window tiles to exactly 1, so the emitted stream is stationary, continuous across segment boundaries, and reproduces the sky-averaged LISA sensitivity with the correct absolute amplitude (spectral content below 1/(2·segment_duration_sec) Hz is not representable at this block length — increase segment_duration_sec for low-frequency fidelity). The constructor keywords confusion_observation_years (0.5, 1.0, 2.0, or 4.0) select the confusion fit and noise_f_min_hz the lower edge of the synthesized band: bins below it, the DC bin included, carry no power, so the model is never evaluated outside its domain.

The amplitude spectrum is stored in Float64: raw LISA PSD values (~1e-40) underflow into Float32 subnormals.

All stochastic draws (noise phases) come from the instrument's own rng (any Random.AbstractRNG; default Xoshiro(0)), seeded via the constructor keyword — the stream is fully reproducible from simulation.rng_seed and independent of the global RNG and of other simulation components.

The struct is deliberately named differently from its parent module: an exported struct sharing the module's name shadows the module binding in downstream using scopes, breaking qualified access (VirtualInstrument.next_segment!).

lisa_noise_psd(f; observation_years = 1.0) -> Float64

Sky-averaged LISA sensitivity [Hz⁻¹] at frequency f [Hz]: the instrument term lisa_instrument_psd plus the galactic-confusion foreground lisa_confusion_psd of the fit for observation_years. It is the noise PSD divided by the sky- and polarization-averaged response (Robson, Cornish & Liu 2019, Eqs. 1 and 14), the quantity the downstream classifier whitens against, and the synthesis reproduces it at the correct absolute level. Returns Inf for f ≤ 0; the synthesis zeroes the DC bin and every bin below noise_f_min_hz, so no floor value can enter a stream.

welch_psd(x::AbstractVector{<:Real}, fs::Real; nperseg = 0) -> (Vector{Float64}, Vector{Float64})

One-sided power spectral density of x sampled at fs [Hz], by Welch's method: Hann windows of nperseg samples (default: the largest power of two giving at least eight segments, floored at 256) overlapping by half, each segment mean-removed, the periodograms averaged and normalized so the estimate integrates to the variance of the series. Returns the frequency grid and the density in units of x²/Hz.

The measurement counterpart of lisa_noise_psd: a stream synthesized from S(f) returns it over the band its synthesis block resolves, which is what the payload-spectrum figure shows. Below 1/(2·segment_duration_sec) the estimate carries spectral leakage, not content — no power was synthesized there.

Returns empty vectors when x is shorter than one window.

lisa_instrument_psd(f) -> Float64

Sky- and polarization-averaged LISA instrument sensitivity S_n(f) [Hz⁻¹] at frequency f [Hz], Robson, Cornish & Liu (2019) Eq. 1:

S_n(f) = 10 / (3 L²) · [P_OMS(f) + 2 (1 + cos²(f/f*)) P_acc(f) / (2π f)⁴] · [1 + 0.6 (f/f*)²]

with P_OMS = (1.5 × 10⁻¹¹)² (1 + (2 mHz / f)⁴) m² Hz⁻¹, P_acc = (3 × 10⁻¹⁵)² (1 + (0.4 mHz / f)²) (1 + (f / 8 mHz)⁴) m² s⁻⁴ Hz⁻¹ (the constants OMS_NOISE_AMPLITUDE, OMS_NOISE_KNEE_HZ, ACCELERATION_NOISE_AMPLITUDE, ACCELERATION_NOISE_LOW_KNEE_HZ, ACCELERATION_NOISE_HIGH_KNEE_HZ, and RESPONSE_CORRECTION_COEFFICIENT), L = 2.5 × 10⁹ m, and f* = c / (2π L). This is the noise PSD divided by the sky-averaged response, the quantity a strain stream is whitened against. Returns Inf for f ≤ 0.

lisa_confusion_psd(f, observation_years = 1.0) -> Float64

Unresolved galactic-binary confusion foreground S_c(f) [Hz⁻¹] at frequency f [Hz], Robson, Cornish & Liu (2019) Eq. 14:

S_c(f) = A f^(-7/3) exp(-f^α + β f sin(κ f)) [1 + tanh(γ (f_k − f))]

with A = CONFUSION_AMPLITUDE and (α, β, κ, γ, f_k) from CONFUSION_FITS for observation_years (one of 0.5, 1.0, 2.0, 4.0; ArgumentError otherwise). Returns Inf for f ≤ 0.

The product is evaluated in log space with log(1 + tanh(x)) = log 2 − softplus(−2x): far above the knee f_k the cutoff factor underflows to zero while exp(β f sin(κ f)) can overflow, and the direct product would give NaN where the foreground is zero.

CONFUSION_FITS

Galactic-confusion fit parameters (α, β, κ, γ, f_k) of Robson, Cornish & Liu (2019), Table 1, keyed by the observation time in years (0.5, 1.0, 2.0, 4.0); f_k in Hz.

CONFUSION_AMPLITUDE

Amplitude A = 9 × 10⁻⁴⁵ Hz⁻¹ of the galactic-confusion fit (Robson, Cornish & Liu 2019, Eq. 14).

OMS_NOISE_AMPLITUDE

Amplitude 1.5 × 10⁻¹¹ m Hz⁻¹ᐟ² of the optical-metrology-system displacement noise P_OMS(f) in Robson, Cornish & Liu (2019), Eq. 1.

OMS_NOISE_KNEE_HZ

Knee frequency 2 mHz of the low-frequency rise (1 + (f_knee / f)⁴) of P_OMS(f) [Hz].

ACCELERATION_NOISE_AMPLITUDE

Amplitude 3 × 10⁻¹⁵ m s⁻² Hz⁻¹ᐟ² of the test-mass acceleration noise P_acc(f) in Robson, Cornish & Liu (2019), Eq. 1.

ACCELERATION_NOISE_LOW_KNEE_HZ

Knee frequency 0.4 mHz of the low-frequency rise (1 + (f_knee / f)²) of P_acc(f) [Hz].

ACCELERATION_NOISE_HIGH_KNEE_HZ

Knee frequency 8 mHz of the high-frequency rise (1 + (f / f_knee)⁴) of P_acc(f) [Hz].

RESPONSE_CORRECTION_COEFFICIENT

Dimensionless coefficient 0.6 of the high-frequency correction 1 + 0.6 (f / f*)² to the sky-averaged response in Robson, Cornish & Liu (2019), Eq. 1.

synth_windowed_block(rng::AbstractRNG, noise_amp::Vector{Float64}, window::Vector{Float64})

Synthesizes one sqrt-Hann-windowed block of amplitude-calibrated colored noise of length(window) samples from the scaled amplitude spectrum noise_amp (see InstrumentState), drawing phases from rng. The DC bin is zeroed and the Nyquist bin is forced real, as required for a real-valued signal. Allocating convenience form of synth_windowed_block!.

synth_windowed_block!(block, z, irfft_plan, rng, noise_amp, window)

In-place core of synth_windowed_block: draws the spectral realization into z, applies the cached irfft_plan, and writes the windowed block into block. Allocation-free apart from the transform's internal workspace; the RNG draw order is identical to the allocating form, so seeded streams are unchanged.

next_segment!(vi::InstrumentState)

Produces the next temporal segment of science data, either sliced from the external array or synthesized as calibrated noise. Synthetic segments are phase-continuous across calls: each segment is the sum of the previous block's overlap-add tail and the head of a freshly synthesized windowed block (see InstrumentState).