This paper describes a method for estimating the instantaneous frequency and instantaneous amplitude of real signals. The method is based on engineering ideas and uses frequency separation with a filter similar to those found in radio devices. The method approximates the analytic signal, and the estimated amplitude and frequency are practically the same as those given by the analytic signal. The method is simple, fast, precise, robust to noise, easy to implement, free of parasitic cross-terms and gives results which compare very favourably with other methods for the measurement of frequency modulated signals, associated or not with amplitude modulation. Examples are given, both of mathematical signals and of real world signals (a bat echo-location signal), showing that the method can be used for precise analysis of a very large variety of signals.
For more than 30 years and until nowadays, development of a system reproducing the functioning of human hearing has remained an aim difficult to reach. Recent methods for identification of the fundamental frequency of musical sounds obtain good results using information about the temporal evolution of the amplitude and frequency of individual sound partials. Piano sounds and polyphonic sounds, which can have several partials that are closely spaced in the frequency domain, have not been extensively tested by these procedures. In this paper, the Instantaneous Frequency (IF), as defined by the Hilbert transform, is used to obtain the frequency variations of piano sounds partials. The result implies that, for these sounds, the IF may contain modulations resulting in the separation of an apparent single sinusoid signal into two or more sinusoidal components at various times in the analysis process, which makes it impossible to use the temporal evolution of the frequency of partials for the procedure of note identification. The separation phenomenon also appears when the short term Fourier transform is used and can induce the detection of short-lived parasitic spectral peaks that must be taken into account by any note identification procedure based on the use of spectral information.
Interactions in the magnetosphere between man-made whistler mode waves and electrons can produce either an enhancement of the wave or the generation of waves at a different frequency. Furthermore, natural emissions can be frequency shifted or modified by a nearby transmitter signal. Injection of extremely low frequency waves into the outer magnetosphere was initiated in 1978 inNorway by both the University of Paris and The Aerospace Corporation. The antenna is a 10.6-km power line tuned to the transmitted frequency. The University of Paris used a 1-kW transmitter to drive the antenna with a maximum current of 8 A. The Aerospace Corporation used the transportable very low frequency transmitter with a typical antenna current between 20 and 45 A. Experiments were conducted at times when the GEOS 2 and SCATHA satellites were near the magnetic meridian of the transmitter. The transmissions consisted of either a keyed fixed frequency or continuous waves swept in frequency. Emissions correlated with the transmissions were detected by the satellite receivers on several dates. Although the satellites were within a few degrees of the magnetic meridian of the transmitter, emissions influenced by the transmissions are seen during only a small fraction (<10%) of the total transmission time. With the first type of transmission, signals similar to power line harmonic radiation were recorded. Artificially stimulated emissions are also likely to have been triggered. Both types of transmissions triggered or enhanced hiss at a constant frequency during fixed-frequency transmissions and at a variable frequency during a swept-frequency transmission. During sweptfrequency transmission there occurred two examples of natural emissions shifting in frequency by the man-made signal. Electron cyclotron harmonic emissions also appear to have been shifted in frequency by the man-made signal. EXPERIMENTATION AND SIGNAL PROCESSING In 1975 it was proposed to try to transmit man-made extremely low frequency (ELF) signals to GEES. An antenna was to be built in Sweden, but because of the price of this operation it was decided to use a power line as an antenna. A first line was tested in Norway near Andenes, in March 1978. Transmissions to GEeS 1 were attempted. However, the use of this line brought important perturbations to the Norwegian power distribution network, so that it was necessary to stop the experiment. Another power line was found near Sortland, and The Aerospace Corporation's transportable very low frequency (TVLF) transmitter [Koons and Dazey, 1975] was operated in October 1978 for transmissions to GEeS 2. An example of the signals received will be presented later. During on-off keyed transmissions at 1525 Hz, strong interference with the telephone network took place, and these transmissions also had to stop. A third and last power line was proposed by Norway in 1979 near Kafjord (69.4øN, 20.9øE). It runs 10.6 km up a mountainside and can be used all day long without any interference on the telephone network. Transmissions took place ...
The instantaneous frequency (IF) of a signal is a parameter whose estimation is of prime importance in a number of domains ranging from musical acoustics to seismics and astronomy. Its determination is usually based on one of the following three general methods: the derivation of the phase of the associated analytic signal, the Wigner–Ville transform and others Cohen’s class transforms, or the three-point algorithms like the Teager–Kaiser ‘‘energy operator.’’ A new three-point method is described which is simple, fast, precise, robust to noise, and estimates the IF and the amplitude with a very small delay. This method gives excellent results on almost any kind of chirps (polynomials, hyperbolics, exponentials, etc.) and frequency modulations (sinusoidal, FSK, Gaussian pulse, etc.), whether or not associated with amplitude modulation (sinusoidal, Gaussian, etc.). The relative errors on the amplitude and on the IF are usually around 1% in the no-noise case, and increase to about 5% for a 20-dB signal-to-noise ratio, even when these different modulations are associated.
The identification of the fundamental frequency of musical sounds is a difficult task which has been studied for more than 20 years. Methods using spectral approaches are used to identify polyphonic sounds. A novel approach for identifying monophonic and polyphonic piano sound signals has been developed by the authors [L. Rossi and G. Girolami, J. Acoust. Soc. Am. 100, 2842(A) (1996)]. The identification is carried out by comparing the incoming spectrum with a database (automatically built previously) containing the frequential distribution of the partials of each piano note. The rate of correct identification is in the 90% range for polyphonic sounds. One kind of error is due to the artificial construction of a note by the combination of partials belonging to other notes; another one results from the difficulty of separating the case of one note played a long time with the case of this same note played two successive times with an overlap. The aim of this paper is to show how the evolution of the partials’ energy associated with the search for information about the time of the note attacks can be used to reduce the false identification.
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