We propose a sampling method that incorporates a normally distributed sampling series for EEG measurements using compressed sensing. We confirmed that the ADC sampling count and amount of wirelessly transmitted data can be reduced by 11% while maintaining a reconstruction accuracy similar to that of the conventional method.

To reduce the complexity of direct radio frequency (RF) undersampling real-time spectrum monitoring in wireless Internet of Things (IoT) bands (920MHz, 2.4GHz, and 5 GHz bands), a design method of sampling frequencies is proposed in this paper. The Direct RF Undersampling receiver architecture enables the use of ADC with sampling clock lower frequency than receiving RF signal, but it needs RF signal identification signal processing from folded spectrums with multiple sampling clock frequencies. The proposed design method allows fewer sampling frequencies to be used than the conventional design method for continuous frequency range (D.C. to 5GHz-band). The proposed method reduced 2 sampling frequencies in wireless IoT bands case compared with the continuous range. The design result using the proposed method is verified by measurement.

We propose a spectrum regeneration and demodulation method for multiple direct RF undersampled real signals by using a new algorithm. Many methods have been proposed to regenerate the RF spectrum by using undersampling because of its simple circuit architecture. However, it is difficult to regenerate the spectrum from a real signal that has a band wider than a half of the sampling frequency, because it is difficult to include complex conjugate relation of the folded spectrum into the linear algebraic equation in this case. We propose a new spectrum regeneration method from direct undersampled real signals that uses multiple clocks and an extended algorithm considering the complex conjugate relation. Simulations are used to verify the potential of this method. The validity of the proposed method is verified by using the simulation data and the measured data. We also apply this algorithm to the demodulation system.

This paper proposes a novel compressed sensing (CS) framework for reconstructing electroencephalogram (EEG) signals. A feature of this framework is the application of independent component analysis (ICA) to remove the interference from artifacts after undersampling in a data processing unit. Therefore, we can remove the ICA processing block from the sensing unit. In this framework, we used a random undersampling measurement matrix to suppress the Gaussian. The developed framework, in which the discrete cosine transform basis and orthogonal matching pursuit were used, was evaluated using raw EEG signals with a pseudo-model of an eye-blink artifact. The normalized mean square error (NMSE) and correlation coefficient (CC), obtained as the average of 2,000 results, were compared to quantitatively demonstrate the effectiveness of the proposed framework. The evaluation results of the NMSE and CC showed that the proposed framework could remove the interference from the artifacts under a high compression ratio.

In this paper, we propose a radio frequency (RF) anti-aliasing filter design method considering the effect of a roll-off characteristic on a noise figure (NF) in the direct RF undersampling receiver. The proposed method is useful for broadband reception that a system bandwidth (BW) has nearly half of the sampling frequency (1/2 fs). When the system BW is extended nearly 1/2 fs, the roll-off band is out of the desired Nyquist zone and it affects NF additionally. The proposed method offers a design target regarding the roll-off characteristic not only the rejection ratio. The target is helpful as a design guide to meet the allowed NF. We design the filter based on the proposed method and it is applied to the direct RF undersampling on-board receiver for Ka-band high throughput satellite (HTS). The measured NF value of the implemented receiver almost matched the designed value. Moreover, the receiver achieved the reception bandwidth which is 90% of 1/2 fs.

This paper addresses joint estimation of the frequency and the direction-of-arrival (DOA), under the relaxed condition that both snapshots in the temporal domain and sensors in the spacial domain are sparsely spaced. Specifically, a novel coprime sparse array allowing a large range for interelement spacings is employed in the proposed joint scheme, which greatly alleviates the conventional array's half-wavelength constraint. Further, by incorporating small-sized DFT spectrum correction with the closed-form robust Chinese Remainder Theorem (CRT), both spectral aliasing and integer phase ambiguity caused by spatio-temporal under-sampling can be removed in an efficient way. As a result, these two parameters can be efficiently estimated by reusing the observation data collected in parallel at different undersampling rates, which remarkably improves the data utilization. Numerical results demonstrate that the proposed joint scheme is highly accurate.

We present sampling theorems that reconstruct consistent signals from noisy underdetermined measurements. The consistency criterion requires that the reconstructed signal yields the same measurements as the original one. The main issue in underdetermined cases is a choice of a complementary subspace L in the reconstruction space of the intersection between the reconstruction space and the orthogonal complement of the sampling space because signals are reconstructed in L. Conventional theorems determine L without taking noise in measurements into account. Hence, the present paper proposes to choose L such that variance of reconstructed signals due to noise is minimized. We first arbitrarily fix L and compute the minimum variance under the condition that the average of the reconstructed signals agrees with the noiseless reconstruction. The derived expression clearly shows that the minimum variance depends on L and leads us to a condition for L to further minimize the minimum value of the variance. This condition indicates that we can choose such an L if and only if L includes a subspace determined by the noise covariance matrix. Computer simulations show that the standard deviation for the proposed sampling theorem is improved by 8.72% over that for the conventional theorem.

A new speed enhancement technique for pulsed laser rangefinders based on Lagrange's theorem in group theory using an undersampling method has been developed. In the undersampling method, frequency conversion for high-resolution ranging and digitizing are conducted by sampling a reference frequency signal at the timings of the reception of pulsed light from the target. In the present work, the rangefinder generates different sampling intervals of the reference frequency signal: different numbers of sampling points within the period of a reference signal, over a wide range. This is accomplished by slightly changing the period of the pulsed light emitted, without changing the synthesizer frequency which generates the period. This technique requires a minimum of additional hardware. In this paper, we describe the detail of the selection of the number of sampling points based on Lagrange's theorem. And we demonstrate a possibility of expanding the sampling interval to the point where an aliasing of the harmonic components of the reference signal occurs by simulations that focus on the calculation of the phase of the fundamental frequency of the reference signal. And we report on the results of rangefinder experiments for a reduction in the number of the sampling points. We have achieved a 10-fold enhancement of speed by selecting 10 sampling points over the results from the previous studies that had 100 sampling points within a period of a reference signal. And we have confirmed that the reduction in sampling points has a very little influence on the linearity, which is an acceptable trade-off for achieving the speed enhancement. This technique, based on Lagrange's theorem in group theory, allows us to control the minimum number of samplings required to calculate distances, so that high-speed data acquisition for coarse measurements and normal-speed data acquisition for fine measurements become selectable. Such a system with high flexibility in measurement modes has been developed.

This paper deals with the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent. For comparison, however, we briefly discuss the diffraction by the sinusoidal surface with infinite extent, where we use the concept of the total diffraction cross section per unit surface introduced previously. To solve a case where the sinusoidal corrugation width is much wider than wave length, we propose an undersampling approximation as a new numerical technique. For a small rough case, the total scattering cross section is calculated against the angle of incidence for several different corrugation widths. Then we find remarkable results, which are roughly summarized as follows. When the angle of incidence is apparently different from critical angles and diffraction beams are all scattered into non-grazing directions, the total scattering cross section increases proportional to the corrugation width and hence the total scattering cross section per unit surface (the ratio of the total scattering cross section to the corrugation width) becomes almost constant, which is nearly equal to the total diffraction cross section per unit surface in case of the sinusoidal surface with infinite extent. When the angle of incidence is critical and one of the diffraction beams is scattered into a grazing direction, the total scattering cross section per unit surface strongly depends on the corrugation width and approximately approaches to the total diffraction cross section per unit surface as the corrugation width gets wide.

In this paper an adjacent channel interference (ACI) cancellation scheme with undersampling for multi-channel reception is proposed and investigated. Low-IF receiver architecture is used in the multi-channel reception scheme. In this system, signal in the adjacent channel causes interference to the desired signal. The ACI cancellation scheme with analog filter bank has been proposed to mitigate the influence from the adjacent channel [10]. Undersampling technique is applied in this system in order to lower the required sampling frequency and power consumption. The effects of the adjacent channel to the undersampling technique in this scheme is examined and discussed.

In software defined radio systems, placing the analog-to-digital converter (ADC) near the antenna part in the block diagram of the receiver is desired to improve the flexibility of the system. The radio frequency (RF) sampling method, in which the received signal is sampled at the RF stage, realizes such structure. The undersampling is a potential method to sample the RF signal using the existing consumer ADCs because high speed ADCs are required in the traditional methods, such as Nyquist sampling or the oversampling of the RF signal. This paper presents a technique to determine the minimum sampling frequency to undersample the separated multiple wireless systems simultaneously. In addition, this paper proposes a frequency selecting scheme that enables selection of a lower sampling frequency by receiving at least the desired transmission channels in the wireless system signals. This paper also provides a result of performance analysis of the proposed scheme.

Undersampling (or bandpass sampling) phase modulated signals directly at high frequency band, the harmful effects of the aperture jitter characteristics of ADCs (Analog-to-Digital converters) and sampling clock instability of the system can not be ignored. In communication systems the sampling jitter brings additional phase noise to the constellation pattern besides thermal noise, thus the BER (bit error rate) performance will be degraded. This paper examines the relationship between the input frequency to ADC and the sampling jitter in digital IF (Intermediate Frequency) downconversion receivers with undersampling scheme. This paper presents the measurement results with a real hardware prototype system as well as the computer simulation results with a theoretically modeled IF sampling receiver. We evaluated EVM (Error Vector Magnitude) in various clock jitter configurations with commonly used and reasonable cost ADCs of which sampling rates was 40 MHz. According to the results, the IF input frequencies of QPSK (16 QAM) signals were limited below around 290 (210) MHz for wireless LAN standard, and 730 (450) MHz for W-CDMA standard, respectively, in our best configuration.

This paper proposes complex form BandPass Sampling (BPS) that is suitable for the software radio. This BPS utilizes offset frequency sampling and quadrature component interpolation. Three types of BPS techniques are first reviewed, which shows effectiveness of the proposed BPS technique. The major advantages over the conventional BPS techniques are: i) free from the DC offset that is caused by the leak of the sampling clock harmonics into the received signal, and ii) reduction of alias by the complex number processing in the signal detection. Next, detailed description of the BPS operation shows that it requires real-time interpolation for the time alignment of the sampled quadrature component. Finally, computer simulation shows that the misalignment generates distortion, and that effective interpolation techniques can reduce the distortion level less than -60 dB even for wideband signals.