A Signal Complexity-Based Approach for AM–FM Signal Modes Counting

Abstract

Frequency modulated signals appear in many applied disciplines, including geology, communication, biology and acoustics. They are naturally multicomponent, i.e., they consist of multiple waveforms, with specific time-dependent frequency (instantaneous frequency). In most practical applications, the number of modes—which is unknown—is needed for correctly analyzing a signal; for instance for separating each individual component and for estimating its instantaneous frequency. Detecting the number of components is a challenging problem, especially in the case of interfering modes. The Rényi Entropy-based approach has proven to be suitable for signal modes counting, but it is limited to well separated components. This paper addresses this issue by introducing a new notion of signal complexity. Specifically, the spectrogram of a multicomponent signal is seen as a non-stationary process where interference alternates with non-interference. Complexity concerning the transition between consecutive spectrogram sections is evaluated by means of a modified Run Length Encoding. Based on a spectrogram time-frequency evolution law, complexity variations are studied for accurately estimating the number of components. The presented method is suitable for multicomponent signals with non-separable modes, as well as time-varying amplitudes, showing robustness to noise.

A pde-Based Analysis of the Spectrogram Image for Instantaneous Frequency Estimation

“…Regardless of the interference effect, there are some curves other than the ridge one that convey the same information and that are less affected by cross-terms [45,60]. As proven in [61,63], the spectrogram P(u, ξ) of a monocomponent signal f (t) = a(t) cos φ(t) satisfies the following advection equation…”

A Short Review on Minimum Description Length: An Application to Dimension Reduction in PCA

“…In fact, as emphasized in [ 21 ], ”it is more problematic to find a good code for hypotheses and often ‘intuitively reasonable’ codes are used; however, it can happen that the description length of any fixed point hypothesis M can be very large under one code, but quite short under another”, making the procedure somewhat arbitrary. There are several approaches in the literature that use crude MDL in a empirical way by applying a corrective weight to one of the lengths in Equation ( 1 ), or by properly selecting the coding procedure [ 15 , 30 , 31 ]—even with optimal performance. A way of making MDL perform better while still being elegant consists of its refined version, namely, the normalized maximum likelihood (NML).…”

“…In the same application context, MDL is used for finding the optimal threshold that defines the regulatory relationships between genes [ 46 ]. In a different context, and using a different strategy, MDL is used for determining the number of modes in non stationary and highly oscillating signals [ 31 ], while in [ 47 ], MDL allows for unsupervised spectral unmixing of spectrally interfering gas components of unknown nature and number.…”

Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions

“…Once the signal time-frequency representation is calculated, its information content in terms of the number of signal components should be obtained. One of the ways of finding the number of frequency-modulated components based on the spectrogram is the method described in [70]. It exploits Kolmogorov complexity to model the information in the spectrogram, which is then converted into a binary map through automatic thresholding based on the minimum description length, and mode counting is performed through two-dimensional run-length encoding.…”

“…It exploits Kolmogorov complexity to model the information in the spectrogram, which is then converted into a binary map through automatic thresholding based on the minimum description length, and mode counting is performed through two-dimensional run-length encoding. However, the proposed approach is not limited to spectrograms only (as the algorithm in [70] is), and it also works for other quadratic time-frequency representations. Hence, another approach to counting the number of signal components was developed and utilized in this paper (based on the modification of the Rényi entropy, as described in the following).…”