Signal-to-Noise Ratio

Computing cumulative SNR for power spectrum and bispectrum measurements.

Single-Bin vs Full Forecast

CosmoWAP forecasts at two levels:

• PkForecast / BkForecast: Single redshift bin calculations

• FullForecast: Collates results over multiple redshift bins for a survey - assumes they are independent

Using get_fish for SNR

The most efficient way to compute SNR is via the Fisher matrix, since get_fish precomputes and caches derivatives:

import numpy as np
import cosmo_wap as cw
from cosmo_wap.lib import utils
from cosmo_wap.forecast import FullForecast

cosmo = utils.get_cosmo()
survey = cw.SurveyParams.Euclid(cosmo)
cosmo_funcs = cw.ClassWAP(cosmo, survey)

# FullForecast splits survey redshift range into N_bins
forecast = FullForecast(cosmo_funcs, kmax_func=0.15, N_bins=4)

# Fisher matrix gives SNR on amplitude parameter
fisher = forecast.get_fish(
    ["A_s"],
    terms="NPP",
    pkln=[0, 2],
    bkln=[0]
)

# SNR = 1 / fractional error on amplitude
snr = 1.0 / (fisher.get_error("A_s") / cosmo_funcs.A_s)

Dedicated SNR Methods

For convenience, dedicated SNR methods are also available:

FullForecast.pk_SNR(term, pkln, verbose=True, sigma=None)

Compute power spectrum SNR per redshift bin.

Returns:

Array of SNR per bin

FullForecast.bk_SNR(term, bkln, verbose=True, sigma=None)

Compute bispectrum SNR per redshift bin.

FullForecast.combined_SNR(term, pkln, bkln, verbose=True, sigma=None)

Compute combined Pk + Bk SNR.

# Per-bin SNR arrays
snr_pk = forecast.pk_SNR("NPP", pkln=[0, 2])
snr_bk = forecast.bk_SNR("NPP", bkln=[0])

# Total SNR (sum in quadrature over bins)
total_snr = np.sqrt(np.sum(snr_pk**2))

Single-Bin Access

For fine-grained control, access individual redshift bins:

# Get single-bin forecast objects
pk_bin0 = forecast.get_pk_bin(i=0)
bk_bin0 = forecast.get_bk_bin(i=0)

# Single-bin SNR
snr_single = pk_bin0.SNR("NPP", ln=[0, 2])