Skip to contents

Estimate Noise Standard Deviation in 1D NMR Spectra

Source: R/utils_nmr_qc.R
noise_sd.Rd

Estimates the noise standard deviation (\(\sigma\)) for each spectrum from a signal-free ppm region. The default estimator is robust (MAD-based) and suitable for signal-to-noise calculations.

Usage

noise_sd(
  X,
  ppm = NULL,
  where = c(14.6, 14.7),
  method = c("mad", "sd", "p95"),
  baseline_correct = FALSE,
  lambda = 10000,
  min_points = 50L,
  ns = NULL,
  normalise_scans = FALSE
)

Arguments

X

Numeric matrix (spectra in rows), numeric vector (single spectrum), or a named list as returned by read1d/read1d_proc containing X, ppm, and meta.

ppm

Numeric vector of chemical shift values (ppm) corresponding to columns of X. If NULL, ppm is inferred in the following order:

  1. X$ppm if X is a list input,

  2. attr(X, "m8_axis")$ppm (if present),

  3. numeric colnames(X) (if present).

where

Numeric vector of length 2. ppm range used for noise estimation. Should be free of metabolite signals (default c(14.6, 14.7)).

method

Character. Noise estimator: "mad" (default), "sd", or "p95" (legacy amplitude).

baseline_correct

Logical. If TRUE, subtract a smooth baseline in the noise window using asymmetric least squares (asysm). Default FALSE.

lambda

Numeric. Smoothing parameter for asysm when baseline_correct = TRUE.

min_points

Integer. Minimum number of points required in the noise window. May be a single value (recycled across spectra) or a numeric vector of length nrow(X). If X is a list input as returned by read1d/read1d_proc and ns is NULL, the function attempts to extract the number of scans from X$meta$a_NS when available.

ns

Number of scans / transients (required if normalise_scans=TRUE)

normalise_scans

Logical. If TRUE, noise estimates are multiplied by \(\sqrt{NS}\) to account for the theoretical scaling of noise with the number of scans (\(\sigma \propto 1/\sqrt{NS}\)). This is useful when comparing noise levels across spectra acquired with different numbers of scans. Default is FALSE.

Value

Numeric vector of noise estimates (length nrow(X)).

Details

In NMR spectroscopy, noise scales predictably with the number of scans (\(NS\)). For otherwise identical acquisition settings:

  • Signal increases approximately proportional to \(NS\).

  • Noise increases approximately proportional to \(\sqrt{NS}\).

  • Consequently, signal-to-noise ratio (SNR) increases proportional to \(\sqrt{NS}\).

Equivalently, the noise standard deviation scales as:

$$\sigma(NS) \propto \frac{1}{\sqrt{NS}},$$

assuming a fixed underlying signal scale and comparable acquisition conditions.

To compare noise levels across datasets acquired with different numbers of scans, a scan-normalised noise estimate may be used:

$$\sigma_{\mathrm{norm}} = \sigma \cdot \sqrt{NS}.$$

Under stable receiver gain and processing conditions, this normalised noise should be approximately constant across runs.

Examples

data(hiit_raw)
X <- hiit_raw$X
ppm <- hiit_raw$ppm
sigma <- noise_sd(X, ppm, where = c(10,11))
plot(hiit_raw$meta$a_NS, sigma,
  xlab = "Number of scans (NS)",
  ylab = expression(sigma~"(noise estimate)"),
   pch = 16)
 lines(lowess(hiit_raw$meta$a_NS, sigma), col = "red", lwd = 2)