A Coherent Accumulation Detection Method Based on SA-DPT for Highly Maneuvering Target

The emergence of highly maneuverable weak targets has led to a serious degradation or even failure of traditional radar detection. In this paper, a coherent accumulation algorithm based on combination of scaling algorithm(SA) and discrete polynomial-phase Transform(DPT) is proposed in terms of the calculation burden and detection performance, which can, firstly, perform fewer times of speed parameter compensation based on SA for the transmitted signal; secondly, use segmented FFT to estimate the time delay range of the target initial distance for the echo signal, and then use the DPT algorithm to complete the parameter estimation such as target speed and acceleration within the estimated time delay unit, while analyzing the effects of the number of segments, compensation speed and delay unit on the detection performance, and giving out the output SNR and the amount of complex multiplication of the proposed algorithm. Finally, the proposed algorithm has been verified by experimental data for its effectiveness in accumulation gain and parameter estimation. This method is for sub-optimal estimation, requiring much less computation than full-parameter search methods, but performs better than non-parametric search methods in detecting weak signals.

Time-Frequency Signal Synthesis and Its Application in Multimedia Watermark Detection

A novel approach is proposed in this thesis to synthesize the time domain chirp signal from the joint time-frequency distribution (TFD). The objective is to reconstruct the original signal from its corrupted version. The new signal synthesis technique is based on the Discrete Polynomial Phase Transform (DPPT) and the TFD of the signal to be synthesized. The TFD is used to separate the mono-component signals from a multi-component signal. The DPPT is then applied on the estimated mono-components to have a final synthesized version of the individual time domain signals. The candidate TFD to be used in the synthesis technique is chosen from a group of common TFDs based on their performance with different types of signals. The criteria for the comparison are joint time-frequency localization, low susceptibility to noise, cross-term suppression and the precision of the instantaneous frequency estimated from these distributions. Smoothed Psuedo Wigner-Ville Distribution is chosen as the processing TDFD in the proposed signal synthesis technique. The proposed chirp synthesis technique is applied to detect the presence of the chirp signal embedded as a watermark message in multimedia security applications. The technique can detect the presence of chirp signals from a corrupted chirp with a bit error rate up to signal synthesis is proved to be less than that of the detection method based on the Hough Radon Transform and the proposed signal synthesis technique may also be used as an error correction tool in other applications.

Time-Frequency Signal Synthesis and Its Application in Multimedia Watermark Detection

A novel approach is proposed in this thesis to synthesize the time domain chirp signal from the joint time-frequency distribution (TFD). The objective is to reconstruct the original signal from its corrupted version. The new signal synthesis technique is based on the Discrete Polynomial Phase Transform (DPPT) and the TFD of the signal to be synthesized. The TFD is used to separate the mono-component signals from a multi-component signal. The DPPT is then applied on the estimated mono-components to have a final synthesized version of the individual time domain signals. The candidate TFD to be used in the synthesis technique is chosen from a group of common TFDs based on their performance with different types of signals. The criteria for the comparison are joint time-frequency localization, low susceptibility to noise, cross-term suppression and the precision of the instantaneous frequency estimated from these distributions. Smoothed Psuedo Wigner-Ville Distribution is chosen as the processing TDFD in the proposed signal synthesis technique. The proposed chirp synthesis technique is applied to detect the presence of the chirp signal embedded as a watermark message in multimedia security applications. The technique can detect the presence of chirp signals from a corrupted chirp with a bit error rate up to signal synthesis is proved to be less than that of the detection method based on the Hough Radon Transform and the proposed signal synthesis technique may also be used as an error correction tool in other applications.

RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

Frequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.

High-entropy dual functions over finite fields and locally decodable codes

We show that for infinitely many primes p there exist dual functions of order k over ${\mathbb{F}}_p^n$ that cannot be approximated in $L_\infty $ -distance by polynomial phase functions of degree $k-1$ . This answers in the negative a natural finite-field analogue of a problem of Frantzikinakis on $L_\infty $ -approximations of dual functions over ${\mathbb{N}}$ (a.k.a. multiple correlation sequences) by nilsequences.