A novel impedance spectrometer has been developed to obtain good quality spectra for electrochemical cells or devices in the minimum time required by the Nyquist theorem for the lowest frequency in the spectrum. A new method, based on a simple instrumental design resolves the known problems of existing methods such as long measurement time and fairly complicated design of the frequency response analyzer (FRA), as well as poor quality of spectra obtained for pulse-response analysis based systems. The spectrometer applies a simple excitation such as a current pulse, instantly connected resistance, or current interrupt, followed by measurement of the response, such as voltage or current against time. The response is fitted to an analytical function (carrier function), and the values of parameters obtained in the fit are applied to the expression of analytical Laplace transformation of this function. The carrier function is selected so that it approximates well the transient response of most electrochemical systems. An analytical expression of the impedance function is obtained by dividing the Laplace-transform of the carrier function by the Laplace-transform of the excitation signal. The frequency dependent impedance spectrum is obtained by evaluating this analytical expression at the required frequencies.