It is common to need to estimate the frequency response of a system fr
om observed input-output data. This paper uses integral constraints to
characterise the undermodelling-induced errors involved in solving th
is problem via parametric least-squares methods. This is achieved by e
xploiting the Hilbert-space structure inherent in the least-squares so
lution in order to provide a geometric interpretation of the nature of
frequency-domain errors. The result is that an intuitive process can
be applied in which, for a given data collection method and model stru
cture, one identifies the sides of a right triangle, and then, by noti
ng the hypotenuse to be the longest side, integral constraints on the
magnitude estimation error are obtained. By also noting that the trian
gle sides both lie in a particular plane, integral constraints on phas
e estimation error are derived. This geometric approach is in contrast
to earlier work in this area, which has relied on algebraic manipulat
ion.