[docs] adding delays overview

doc/delays.qmd

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+---
+title: Delays anaylsis
+format:
+  html:
+    toc: true
+    toc-title: Contents
+    code-block-bg: true
+    code-block-border-left: "#31BAE9"
+    code-line-numbers: true
+    highlight-style: atom-one
+    link-external-icon: true
+    link-external-newwindow: true
+    eqn-number: true
+---
+
+### 1. Delays
+We noticed a delay in the recodings if you were to plot a comparision between
+the base relacs recording and the new generated open-ephys.
+
+```{python}
+# | echo: False
+import pathlib
+
+import numpy as np
+import pandas as pd
+import plotly.express as px
+import plotly.graph_objects as go
+import rlxnix as rlx
+import scipy.signal as signal
+from plotly.subplots import make_subplots
+from rich.progress import track
+from rich.table import Table
+from util import calc_lag, plot_line_comparision, trial_plot
+
+dataset_path = pathlib.Path("../oephys2nix/test/Test1/2025-10-08-aa-invivo-2-recording.nix")
+relacs_path = pathlib.Path(
+    "../oephys2nix/test/Test1/2025-10-08-aa-invivo-2_relacs/2025-10-08-aa-invivo-2.nix"
+)
+
+dataset = rlx.Dataset(str(dataset_path))
+relacs = rlx.Dataset(str(relacs_path))
+
+# INFO: Select the first stimulus of the calibration repro
+repro_d = dataset.repro_runs("FileStimulus_1")[0].stimuli[2]
+repro_r = relacs.repro_runs("FileStimulus_1")[0].stimuli[2]
+
+sinus, t = repro_d.trace_data("sinus")
+sinus_r, t_r = repro_r.trace_data("V-1")
+
+stimulus_oe, t = repro_d.trace_data("stimulus")
+stimulus_re, t_r = repro_r.trace_data("GlobalEFieldStimulus")
+
+local_eod_oe, t = repro_d.trace_data("local-eod")
+local_eod_re, t_r = repro_r.trace_data("LocalEOD-1")
+
+global_eod_oe, t = repro_d.trace_data("global-eod")
+global_eod_re, t_r = repro_r.trace_data("EOD")
+
+ttl, t = repro_d.trace_data("ttl-line")
+
+fig = plot_line_comparision(
+    t_r,
+    t,
+    stimulus_re,
+    stimulus_oe - np.mean(stimulus_oe),
+    ["stimulus-relacs", "stimulus-open-ephys"],
+)
+fig.show()
+```
+
+### 2. Look at differnt RePros
+Currently implemented repros are:
+
+- [x] [Baseline](baseline.qmd)
+- [x] [Calibration](calibration.qmd)
+- [x] [FI Curve](fi_curve.qmd)
+- [x] [File Stimulus](filestimulus.qmd)
+- [ ] Sams
+- [ ] Chrips
+- [ ] Beats
+
+### 3. General Delay in detail
+```{python}
+rich_tabel = Table("Repro Run", "Signal", "Lag (samples)")
+names_lanes = ["sinus", "local-eod", "global-eod", "stimulus"]
+dataframe = []
+for repro_idx, (repro_d, repro_r) in enumerate(
+    zip(dataset.repro_runs(), relacs.repro_runs(), strict=True)
+):
+    if not repro_d.stimuli:
+        lags = calc_lag(repro_d, repro_r)
+        for lag, names_lane in zip(lags, names_lanes, strict=True):
+            rich_tabel.add_row(f"{repro_d.name}", f"{names_lane}", f"{lag}")
+            dataframe.append(
+                {"ReproName": repro_d.name, "Line": names_lane, "Lag": lag, "Trial": 0}
+            )
+
+    else:
+        lags_lanes = {f"{key}": [] for key in names_lanes}
+        for trial, (stim_oe, stim_re) in enumerate(
+            zip(repro_d.stimuli, repro_r.stimuli, strict=True)
+        ):
+            lags = calc_lag(stim_oe, stim_re)
+            for lag, names_lane in zip(lags, names_lanes):
+                lags_lanes[names_lane].append(lag)
+                dataframe.append(
+                    {"ReproName": repro_d.name, "Line": names_lane, "Lag": lag, "Trial": trial}
+                )
+        for lane in lags_lanes:
+            mean_lag = np.mean(lags_lanes[lane])
+            std_lag = np.std(lags_lanes[lane])
+            rich_tabel.add_row(f"{repro_d.name}", f"{lane}", f"{mean_lag:.2f}\u00b1{std_lag:.2f}")
+
+rich_tabel
+```
+
+```{python}
+repros = dataset.repro_runs("Baseline")
+print(repros)
+exclude = []
+for rep in repros:
+    exclude.append(rep.name)
+
+df = pd.DataFrame(dataframe)
+df = df[~df["ReproName"].isin(exclude)]
+fig = px.box(
+    df,
+    x="Line",
+    y="Lag",
+    color="Line",
+    title="Lag Distribution Across Different Signals",
+    labels={"Line": "Signal", "Lag": "Lag (samples)"},
+)
+fig.update_layout(template="plotly_dark")
+fig.show()
+
+fig = px.box(
+    df,
+    x="Line",
+    y="Lag",
+    color="ReproName",
+    title="Lag Distribution by Signal and Repro Run",
+    labels={"Line": "Signal", "Lag": "Lag (samples)"},
+)
+fig.update_layout(template="plotly_dark")
+fig.show()
+```