The instantaneous frequency rate spectrogram

• Instantaneous frequency rate estimation in the time-frequency domain is presented.
• The proposed estimators are based on the STFT and the reassignment method.
• A novel method of amplitude demodulation in the time-frequency domain is presented.
• Energy density versus the estimated instantaneous frequency rate is introduced.
• The acoustic emission of an automotive engine is analyzed for example.

An accelerogram of the instantaneous phase of signal components referred to as an instantaneous frequency rate spectrogram (IFRS) is presented as a joint time-frequency distribution. The distribution is directly obtained by processing the short-time Fourier transform (STFT) locally. A novel approach to amplitude demodulation based upon the reassignment method is introduced as a useful by-product. Additionally, an estimator of energy density versus the instantaneous frequency rate (IFR) is proposed and referred to as the IFR profile. The energy density is estimated based upon both the classical energy spectrogram and the IFRS smoothened by the median filter. Moreover, the impact of an analyzing window width, additive white Gaussian noise and observation time is tested. Finally, the introduced method is used for the analysis of the acoustic emission of an automotive engine. The recording of the engine of a Lamborghini Gallardo is analyzed as an example.