Processing algorithms for signals with time-varying frequencies.
Ju, Ying Tuo.
Date of Issue2009
School of Electrical and Electronic Engineering
In many real-life applications, such as radar, sonar, communications, and biomedical engineering, the signals under consideration are often characterized by time-varying spectral contents. For this type of signals, time analysis or frequency analysis alone cannot fully describe the time-varying characteristics of the signals. The tools for the analysis of signals with time-varying frequencies can be generally divided into two categories: parametric and non-parametric methods. The former models the signal's instantaneous phase as a polynomial function of time and need to estimate the phase coefficients. The later represents the signal's energy over both time and frequency or over t - omega0(t) space, where omega0(t) = (omega(t), omega1(t), ..., omega(m-l)(t)) is the vector of the instantaneous frequency (IF) omega(t) and its derivatives. During the studies of various signal processing tools, we have found that the polynomial time frequency transform (PTFT) is a good tool to use. Its advantages mainly come from two aspects, one is that PTFT can be used to compute Maximum Likelihood Estimation (MLE) of the phase coefficients, and the other is that it can be combined with other methods to analyze signals with time-varying frequencies, especially in the case that there is no prior information on the signals under study. However, PTFT generally requires a huge computational complexity as it involves in multi-dimensional (MD) calculation. One of the primary objectives of this research project is to propose fast algorithms to calculate PTFTs efficiently. We have proposed a general class of fast algorithms for the computation of the PTFTs of complex-valued length-(a^p)(b) input sequence, where a, b and p are integers. The proposed algorithms provide the flexibility to support various input sequence lengths by setting the parameters of a, b and p, and have regular computational structures for an easy implementation. Analysis and comparison on the computational complexity are also reported in terms of the numbers of complex additions and complex multiplications. It is verified that the computational complexity of the PTFTs is significantly reduced by using the proposed algorithms. Next, fast algorithms for the computation of the PTFTs of real-valued sequences are presented. Similar to the fast algorithms for complex-valued input sequences, the proposed algorithms can support various input sequence lengths by setting the parameters of a, b and p, and have regular computational structures. Analysis and comparison on the computational complexity are made in terms of the numbers of real additions and real multiplications. With the conjugate symmetric property, the presented fast algorithms, with a = 3, 4 and 8, effectively reduce the computational complexity to be about one-half of that needed by the reported fast algorithms for complex-valued sequences.
DRNTU::Engineering::Electrical and electronic engineering