1. Problem statement: You have spectral measurements from multiple cameras that observe the same objects but differ in sampling rate, time alignment, and spectral resolution, and you want a reproducible pipeline to align those spectra so corresponding features match across datasets. 2. Step 1 — gather metadata and visualize raw spectra: Record each camera's sampling frequency $F_{s}$, wavelength or frequency bin centers, integration time, and any known time stamps. Plot or inspect each spectrum to note gross shifts, missing bands, and SNR differences. 3. Step 2 — choose a common reference grid: Pick a target sampling or frequency grid that covers the union of all measured bands with sufficient resolution for the features of interest. Denote the reference sampling frequency as $F_{s,ref}$ and the reference frequency axis as $f_{ref}[k]$. 4. Step 3 — resample in time or frequency as needed: For time-domain signals resample to a common $F_{s,ref}$ using a high-quality resampling method (polyphase or FFT-based) with anti-alias filtering. Compute the resampling ratio $r$ by $r = \frac{F_{s,ref}}{F_{s,src}}$ where $F_{s,src}$ is the source camera sampling. 5. Step 4 — align frequency axes and resolutions: If spectra are given on different frequency/wavelength grids, interpolate each spectrum onto $f_{ref}[k]$ using an appropriate interpolator (sinc or cubic for high fidelity, linear for speed). When cameras have different spectral resolutions, either deconvolve instrument line shapes if available or smooth the higher-resolution spectra to match the lowest common resolution. 6. Step 5 — correct for time offsets via cross-correlation in the frequency domain: If the signals are time-shifted versions, use cross-correlation computed by FFTs to estimate lag. Compute the cross-correlation by $$R_{xy}[\ell] = \mathcal{F}^{-1}\{X(\omega)\overline{Y(\omega)}\}\,$$ and find the lag $\hat{\tau}$ that maximizes $R_{xy}$. 7. Step 6 — refine sub-sample/time alignment via phase slope fitting: In frequency domain a pure delay produces a linear phase term, since $$Y(\omega) = X(\omega)e^{-j\omega\tau}\,$$ Estimate $\tau$ by unwrapping the phase of the cross-spectrum $\Phi(\omega)=\angle\{X(\omega)\overline{Y(\omega)}\}$ and fit a line $\Phi(\omega)\approx -\omega\tau + b$ using linear regression across the high-SNR band. 8. Step 7 — compensate amplitude and instrument response differences: Estimate and apply a frequency-dependent gain $G(f)$ to match spectral envelopes. You can compute $G(f)=\frac{\text{median reference spectrum}}{\text{median source spectrum}}$ smoothed in frequency, or fit a low-order polynomial in log space for multiplicative differences. 9. Step 8 — handle missing or bad bands: Mask out frequency bins with low SNR or known sensor gaps prior to fitting and alignment steps, and treat those bands as unsupported when computing transforms or regression. Use robust estimators (Huber or RANSAC) if outliers are present. 10. Step 9 — iterative refinement and validation: After initial alignment apply these checks. Compute the spectral residual $E(f)=S_{ref}(f)-S_{aligned}(f)$ and report metrics like mean squared error and coherence. Plot overlapped spectra and difference spectra to visually confirm alignment. 11. Practical tips and algorithm choices: Use oversampled FFTs and zero-padding to increase correlation peak localization, apply windowing to reduce spectral leakage, and prefer phase-slope fitting for sub-sample precision. For large datasets automate metadata parsing and apply a per-camera calibration step first to reduce systematic differences. 12. Final checklist to implement: (a) collect metadata and visualize, (b) choose $f_{ref}$ and resample/interpolate, (c) estimate coarse lag with cross-correlation, (d) refine delay by phase slope regression, (e) correct amplitude/response, (f) mask bad bands and validate with residuals and coherence. Final answer: Follow the pipeline above to get aligned spectra reproducibly and quantify alignment quality with residuals and coherence metrics.