In this paper, we propose a frequency domain analysis for characterizing the walking gait in the context of indoor navigation, without assuming that the sensors are rigidly attached to the body. Firstly, frequency analysis is performed using Short Time Fourier Transform (STFT) since the statistical properties of the signal are changing over time but are assumed contant over a hort window. Globally STFT can extract step/stride frequency, but STFT is found non optimal for fast motion transitions. Wavelet Transform (WT) analysis is then introduced. Contrary to STFT, WT uses a size-adjustable window, which offers more advantages for human gait features extraction. When the time period of interest comprises a high frequency, the window is short, while when the local area comprises a low frequency, the window size is enlarged. This WT propriety is found to be critical our smartphone based gait analysis. Experimental assessment is performed with a smartphone Nokia Lumia 920 and a foot mounted MEMS grade inertial used as reference. These results are encouraging for designing a robust and adaptable real-time motion detection solution for smartphone in the context of indoor navigation.