diff --git a/bilby/gw/detector/strain_data.py b/bilby/gw/detector/strain_data.py
index ab7f5efd96efdc8761db072418632e62b1e19a59..6ba6db039ef244e5bb3295ba8796347af868a60f 100644
--- a/bilby/gw/detector/strain_data.py
+++ b/bilby/gw/detector/strain_data.py
@@ -408,6 +408,7 @@ class InterferometerStrainData(object):
                 self.time_array = array
             elif domain == 'frequency':
                 self.frequency_array = array
+                self.start_time = start_time
             return
         elif sampling_frequency is None or duration is None:
             raise ValueError(