  Combined frequency-resolved techniques are suitable to study electrochromic
(EC) materials. We present an experimental setup for simultaneous
electrochemical and color impedance studies of EC systems in transmission mode
and estimate its frequency-dependent uncertainty by measuring the background
noise. We define the frequency-dependent variables that are relevant to the
combined measurement scheme, and a special emphasis is given to the complex
optical capacitance and the complex differential coloration efficiency, which
provide the relation between the electrical and optical responses. Results of a
test measurement on amorphous $\mathrm{WO}_3$ with LED light sources of peak
wavelengths of $470$, $530$, and $810~\mathrm{nm}$ are shown and discussed. In
this case, the amplitude of the complex differential coloration efficiency
presented a monotonous increase down to about $0.3~\mathrm{Hz}$ and was close
to a constant value for lower frequencies. We study the effect of the
excitation voltage amplitude on the linearity of the electrical and optical
responses for the case of amorphous $\mathrm{WO}_3$ at
$2.6~\mathrm{V}~\mathrm{vs.}~\mathrm{Li/Li}^+$, where a trade-off should be
made between the signal-to-noise ratio (SNR) of the optical signal and the
linearity of the system. For the studied case, it was possible to increase the
upper accessible frequency of the combined techniques (defined in this work as
the upper threshold of the frequency region for which the SNR of the optical
signal is greater than $5$) from $11.2~\mathrm{Hz}$ to $125.9~\mathrm{Hz}$
while remaining in the linear regime with a tolerance of less than $5\%$.
