This paper proposes a new class of Hilbert pairs of almost symmetric orthogonal wavelet bases. For two wavelet bases to form a Hilbert pair, the corresponding scaling lowpass filters are required to satisfy the half-sample delay condition. In this paper, we design simultaneously two scaling lowpass filters with the arbitrarily specified flat group delay responses at ω=0, which satisfy the half-sample delay condition. In addition to specifying the number of vanishing moments, we apply the Remez exchange algorithm to minimize the difference of frequency responses between two scaling lowpass filters, in order to improve the analyticity of complex wavelets. The equiripple behavior of the error function can be obtained through a few iterations. Therefore, the resulting complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Finally, some examples are presented to demonstrate the effectiveness of the proposed design method.

A new approach to reconstructing antenna far-field patterns from the missing part of the pattern is presented in this paper. The antenna far-field pattern can be reconstructed by utilizing the iterative Hilbert transform, which is based on the relationship between the real and imaginary part of the Hilbert transform. A moving average filter is used to reduce the errors in the restored signal as well as the computation load. Under the constraint of the causality of the current source in space, we could successfully reconstruct the data. Several examples dealing with line source antennas and antenna arrays are simulated to illustrate the applicability of this approach.

In non-destructive testing (NDT), ultrasonic echo is often an overlapping multi-echo signals with noise. However, the accurate estimation of ultrasonic time-of-flight (TOF) is essential in NDT. In this letter, a novel method for TOF estimation through envelope is proposed. Firstly, the wavelet denoising technique is applied to the noisy echo to improve the estimation accuracy. Then, the Hilbert transform (HT) is used in ultrasonic signal processing in order to extract the envelope of the echo. Finally, the TOF of each component of multi-echo signals is estimated by the local maximum point of signal envelope. Furthermore, the time resolution of time-overlapping ultrasonic echoes is discussed. Numerical simulation has been carried out to show the performances of the proposed method in estimating TOF of ultrasonic signal.

In this paper, penetration phenomenon of an early-time (E1) high altitude electromagnetic pulse (HEMP) into dispersive underground multilayer structures is analyzed using electromagnetic modeling of wave propagation in frequency dependent lossy media. The electromagnetic pulse is dealt with in the power spectrum ranging from 100kHz to the 100MHz band, considering the fact that the power spectrum of the E1 HEMP rapidly decreases 30dB below its maximum value beyond the 100MHz band. In addition, the propagation channel consisting of several dielectric materials is modeled with the dispersive relative permittivity of each medium. Based on source and channel models, the propagation phenomenon is analyzed in the frequency and time domains. The attenuation levels at a 100m underground point are observed to be about 15 and 20dB at 100kHz and 1MHz, respectively, and the peak level of the penetrating electric field is found 5.6kV/m. To ensure the causality of the result, we utilize the Hilbert transform.

We developed a novel movement-imagery-based brain-computer interface (BCI) for untrained subjects without employing machine learning techniques. The development of BCI consisted of several steps. First, spline Laplacian analysis was performed. Next, time-frequency analysis was applied to determine the optimal frequency range and latencies of the electroencephalograms (EEGs). Finally, trials were classified as right or left based on β-band event-related synchronization using the cumulative distribution function of pretrigger EEG noise. To test the performance of the BCI, EEGs during the execution and imagination of right/left wrist-bending movements were measured from 63 locations over the entire scalp using eight healthy subjects. The highest classification accuracies were 84.4% and 77.8% for real movements and their imageries, respectively. The accuracy is significantly higher than that of previously reported machine-learning-based BCIs in the movement imagery task (paired t-test, p < 0.05). It has also been demonstrated that the highest accuracy was achieved even though subjects had never participated in movement imageries.

This paper presents the implementation of a 31-tap FIR Hilbert transform digital filter chip used in the digital-IF receivers, to confirm the effectiveness of our new design method. Our design method that we previously reported is based on a computation sharing multiplier using a new horizontal and vertical common subexpression techniques. A 31-tap FIR Hilbert transform digital filter was implemented and fabricated in 0.35 µm CMOS standard cell library. The chip's core contains approximately 33k transistors and occupies 0.86 mm2. The chip also has an operating speed of 70 MHz over. The implementation results show that the proposed Hilbert transformer has a smallest cost factor and so that is a high performance filter.

Modulator output and fiber transmission characteristics of optical single sideband (SSB) modulations are analyzed under the assumption that SSB modulators are constructed using Mach-Zehnder (MZ) interferometers. The fiber input signal and the detected signal are derived theoretically for SSB modulation with and without an optical carrier. Optical SSB fiber transmission simulations show that the received signal waveform is degraded by harmonic components due to non-linear switching curve of MZ interferometer as a component of SSB modulators even if the Hilbert transformers is ideal for the definition. The optical SSB suppressed carrier is preferred to the SSB with an optical carrier from a viewpoint of waveform degradation.

This paper proposes a new SSB-QPSK modulation/demodulation method. The present method multiplexes the USB (Upper Side Band) and LSB (Lower Side Band) of a QPSK-modulated SSB (Single Side Band) on the same SSB complex frequency band. The present method thus achieves 2 bit/s/Hz. This method is an orthogonal SSB-QPSK method, because the multiplex signals are orthogonal to each other. The demodulator consists of two SSB demodulators. A simulation result in AWGN conditions, shows that the proposed method has better BER (Bit Error Rate) performance than 16 QAM. The degradation of BER in comparison with QPSK is less than 0.2 dB on Eb/No (bit-energy-to-noise-power ratio). In a fading/Doppler environment, the BER performance of the orthogonal SSB-QPSK is the same as that of QPSK.

We present a method of extracting the digital inphase (I) and quadrature (Q) components from oversampled bandpass signals using narrow-band bandpass Hilbert transformers. Down-conversion of the digitized IF signals to baseband and reduction of the quantization noise are accomplished by the multistage decimator with the complex coefficient bandpass digital filters (BPFs), which construct the bandpass Hilbert transformers. Most of the complex coefficient BPFs in the multistage decimator can be replaced with the lowpass filters (LPFs) under some conditions, which reduces computational burden. We evaluate the signal to quantization noise ratio of the I and Q components for the sinusoidal input by computer simulation. Simulation results show that the equivalent amplitude resolution of the I and Q components can be increased by 3 bits in comparison with non-oversampling case.

This paper describes a new method of approximating ideal Hilbert transformers by using time reversal techniques. As is well known, an ideal Hilbert transformer is not physically realizable because it is not causal. Nevertheless, it is extremely imprortant conceptually in the area of digital signal processing. In this paper, we propose a method to approximately implement such a Hilbert transformer. The method divides the impulse response of the ideal Hilbert transformer into two parts, i.e., causal and noncausal parts. Although a causal filter is physically realizable, a noncausal filter is not realizable. A noncausal filter is realized using time reversal techniques for input signals to the filter, and then the Hilbert transformer can be approximately implemented by the parallel connection of causal and noncausal filters.