  We present a free and a constrained fitting procedure for quantitative signal
extraction of nanomechanical systems in the dynamic range and for physical
model testing. We demonstrate that applying the free-fitting procedure to the
measured frequency response of silicon nitride (SiN) nanomembranes at varying
pressure enables us to disentangle the intrinsic membrane vibration properties
from the system response, thereby giving quantitative access to the
eigenfrequency, quality factor, coupling strength between resonator and drive
system, and to system noise. The validity of physical models for quantities
such as excitation, fluctuations, and damping mechanisms can be verified by
imposing additional mathematical links between different physical parameters as
constraints in the constrained fitting procedure. We verify the performance of
the constrained fitting procedure for the same samples tested in various
experimental setups.
