The topic of the article is the problem of identification of the dynamic objects by two types of the pulse testing signals: testing by a single pulse at a fixed interval of observation and testing by a periodic pulse sequence of a fixed frequency. The single testing pulse can be useful in operation of the adaptive controllers, and the testing impulse sequences are widely used, for example, for studying the nature of the biopotential changes of the eye retina (electroretinogram) in order to obtain additional features for the diagnostic systems. For a single pulse testing the authors propose to select a determined interval of observation, and this makes possible a Fourier series expansion of the observed output and input on the given interval of observation. They demonstrate that the ratio of the amplitudes of the harmonics with the same number of the output and input signals can show the corresponding point's coordinates on the a complex frequency response with a certain accuracy. This accuracy depends on the interval of the observation time and the inertial properties of an object. The advantages of this method are a good noise-immunity and little time for identification. There are some conditions imposed on the duration of the observed transient response on the output of the dynamic object with the defined parameters of the testing pulse, which allows us to evaluate the coordinates of the points of the complex frequency response of an object and to make an adaptation of the controller's settings. The result of the Fourier series expansion of the output signal for the periodic impulse sequence is the same as for a single pulse at a fixed interval of observation. The intermediate points of the frequency response and the points at low frequencies can be found by replacement of the observed signal with "zeros'' on the additional time interval. The input signal spectrum has harmonics with null values of the amplitudes at the frequencies multiple to the reciprocal value of the pulse width. And the authors demonstrate that the points of the complex frequency response at these frequencies are determined with big errors. Those points can be determined by varying the testing pulse duration.