Does sample rate introduce an artifact in spectral analysis of continuous processes?

The role of filtering in sampling-rate conversion has been considered in Chapter II. The importance of filtering arises from the fact that the sampling theorem should be respected for all the sampling rates of the system at hand. Filters are required to bandlimit the spectrum of the signal to the prescribed bandwidth in accordance with the actual sampling rate. In sampling rate conversion systems, filters are used in decimation to suppress aliasing and in interpolation to remove imaging. Since an ideal frequency response cannot be achieved, the performance of the system for sampling rate conversion is mainly determined by filter characteristics. Obviously, an appropriate filter should enable the sampling rate conversion with minimal signal distortion. The main advantage of a multirate system is the computational efficiency, and therefore, a decimator (interpolator) that implements a high-order digital filter could not be tolerated. The specific role of a digital filter in sampling rate conversion demands high-performance filtering with the lowest possible complexity. To reach this goal one has to concentrate first on the choice of the appropriate design specifications in order to provide minimal signal distortion. Secondly, the multirate filter is to be designed in a manner to satisfy the prescribed characteristics and to provide a low-complexity implementation structure. In this chapter, we discus first the spectral characteristics of decimators and interpolators and introduce three commonly used types of filter specifications. In the sequel, we review the MATLAB functions that are appropriate for the design of FIR and IIR filters to satisfy the specifications. An approach to computation of aliasing characteristics of decimators is given and illustrated by examples. This chapter considers also the analysis of sampling rate conversion for band-pass signals. Chapter concludes with MATLAB exercises for individual study.

Power spectral analysis of fetal heart rate variability has been proposed to provide a non-invasive estimate of autonomic balance. However, there are few systematic data before birth. We therefore examined developmental changes in the frequency power spectrum at very low (0-0.04 Hz), low (0.04-0.15 Hz) and high frequencies (0.15-0.4 Hz), as well as the ratio of low- to high-frequency power (LF/HF), in chronically catheterized, healthy fetal sheep at 0.6 (n = 8), 0.7 (n = 7) and 0.8 gestational age (ga; n = 11). In a second study, 0.8 ga fetuses received either atropine (4.8 mg bolus, then 4.8 mg h(-1) for 30 min, n = 6) or 6-hydroxydopamine (20 mg ml(-1) at 2.5 ml h(-1) for 3 h; n = 9). Data were analysed by sleep state, defined by low-voltage-high-frequency (LV) or high-voltage-low-frequency (HV) EEG. Total spectral power increased with gestational age (P < 0.05), while LF/HF decreased from 0.6 to 0.7 ga. At 0.8 ga, heart rate and LF/HF were significantly higher during HV than LV sleep (P < 0.05). Consistent with this, although total spectral power was not significantly greater during HV sleep, there was a significant interaction between sleep state and frequency band (P = 0.02). Both atropine (P = 0.05) and 6-hydroxydopamine (P < 0.05) were associated with an overall reduction in spectral power but no significant effect on the LF/HF ratio. This study does not support substantial, consistent differences between the frequencies of sympathetic and parasympathetic activity in late-gestation fetal sheep.

The wideband signal is sampled at a high rate in digital IF(intermediate frequencies) receiver using a fixed master clock. After extracting individual narrowband channels from wideband signal, the sample rate is much higher than single channel bandwidth. It is necessary to resample the signal with a lower rate to reduce data redundancy. And the receiver should has the capability of operating in all sorts of communication standard. So sensitive SRC(sample rate conversion) is necessary in the receiver. The paper proposed an efficient SRC architecture and an optimized algorithm for assigning changing rate factor. The architecture is programmable, hardware sharing, with lower power consumption, which take advantage of renewed comb filters to improve alias rejection and reduce power consumption of the decimation at high rate. The optimized algorithm is flexible and simple. It can realize SRC efficiently by optimum composition of algorithmand architecture.

In the recent few years, it is observed that in wireless communication there has been a rapid growth in terms of different communication standards/ technologies being used. Thus, to support different communication standards, flexible system should be used to convert the digital signal from one sample rate to another (up sampling or down sampling). The solution is the use of Software defined Radio (SDR), which is a reconfigurable radio communication system. Therefore the most critical and demanding element in the digital signal processing chain of an SDR is the Sample Rate Converter. At high sampling rate, the signals cannot be processed by using baseband signal processing unit. Instead of any unique air-interface, SDR simultaneously handles multiple air-interfaces of different wireless standards that require sample rates for baseband processing. Thus, in SDR, Sampling Rate Conversion (SRC) is an important functionality to provide synchronization between the ADC and baseband signal processor. This paper provides a review on various types of SRC circuits, where their design characteristics are analyzed and compared. The review is based on designing of Sample Rate converters on Field-Programmable Gate Array (FPGA) and Applications Specific Integrated Circuit (ASIC) platform. For FPGA based design, LUT, slices, FFT, and other hardware resource parameters are estimated to evaluate their performance. For ASIC, area, power and delay are considered for performance evaluation.

Adaptive sample rate converters (SRC) for the multi-standard mobile transceiver have been designed. GSM, UMTS and HIPERLAN2 standards have been chosen to establish the requirements for the SRCs. In the transmitter, the output signal of the data modulator is sampled at the symbol or chip frequency specified by the standards and needs to be converted into a common updating frequency of the D/A-converter. Pulse shaping and emission mask requirements are taken into account. In the receiver, A/D-conversion is also performed at a common fixed clock rate. Thus the SRC is needed to convert the A/D-converter sampling rate into a symbol or chip frequency that will be applied for further baseband signal processing. Channelization requirements defined by the standards are used as criteria for the performance analysis in the receiver. Based on the performance analysis, the complexity analysis is covered. It includes computational complexity, gate count, area and power consumption estimation for the chosen platform.

The turbulent flow past a wall-mounted square cylinder with an aspect ratio of 4 was investigated with the aid of Spalart–Allmaras improved delayed detached-eddy simulation and proper orthogonal decomposition (POD) analysis. The Reynolds number was equal to 12 000 (based on the free-stream velocity and obstacle width). The boundary layer thickness was ∼0.18 of the obstacle height. This study focused on analyzing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first- and second-order flow statistics with the available experimental and direct numerical simulation data was used to validate the numerical results. The numerical model coupled with the vortex method of generating the turbulent inflow conditions could successfully reproduce the flow field around and behind the obstacle with commendable accuracy. The flow structure and vortex shedding characteristics near the wake formation region were discussed in detail using time-averaged and instantaneous flow parameters obtained from the simulation. Dipole type mean streamwise vortices and half-loop hairpin instantaneous vortices with energetic motions were identified. A coherent shedding structure was reported along the obstacle using two-point correlations. Two types of vortex shedding intervals were identified, namely, low amplitude fluctuations (LAFs) and high amplitude fluctuations (HAFs) [P. Sattari et al., Exp. Fluids 52, 1149–1167 (2012)]. The HAFs’ interval exhibits von Kármán-like behavior with a phase difference of ∼180°, while the LAFs’ interval shows less periodic behavior. It was observed that the effect of the LAFs’ interval tends to weaken the alternating shedding along the obstacle height. The POD analysis of the wake showed that for the elevations between 0.25 and 0.5 of the obstacle height, the first two POD modes represent the alternating shedding and contribute to 66.6%–57.6% of the total turbulent kinetic energy. However, at the free end of the obstacle, the first two modes have a symmetrical shedding nature and share 36.5% of the kinetic energy, while the rest of the energy is distributed between the alternating and the random shedding processes. A simple low-order model based on the vortex-shedding phase angle and the spectrum of the time coefficients obtained from POD was developed to predict the wake dynamics at the range of elevations where the alternating shedding is dominated.

In Generalized Frequency Division Multiplexing (GFDM) underwater acoustic communication systems, the conventional Doppler shift factor estimation will reduce the transmission rate of the system. The sampling rate conversion of the received signal usually adopts the resampling method, thereby increasing the computational complexity. Aiming at the above problems, a Doppler shift factor (DFS) estimation algorithm based on oversampling technique and a sampling rate conversion algorithm is proposed. The Doppler shift factor is estimated by comparing the transmitted signal with the received signal samples. On this basis, the above-sampled data and a linear interpolation algorithm are used to convert the sampling rate of the received signal. The theoretical analysis and simulation results show that the improved algorithm can greatly reduce the computational complexity of the receiver while ensuring the performance of the system and is suitable for high-speed real-time underwater acoustic communication systems.

New VLSI high throughput parallel structures for arbitrary rate non integer ratio sample rate conversion are presented in the paper. High throughput Sample Rate Converters (SRC) find application in high data rate Software Defined Radio (SDR) where a large degree of flexibility is required to support varied sample rates. Parallel Signal Processing implementations offer higher throughput for lower clock speeds. This makes them ideal for high data rate modem implementations on FPGA's or in power limited ASIC designs. The Farrow structure offers unique advantages ideal for parallel implementation. These unique qualities allow the utilization of novel reduced complexity parallel finite-length impulse response (FIR) filters. The structures presented in this paper are suitable for implementation on application specific integrated circuits (ASIC) or field programmable gate arrays (FPGA). Results shown here are for implementation on FPGAs with varying orders of parallelization.

This paper introduces multimode transmultiplexers (TMUXs) in which the Farrow structure realizes the polyphase components of general lowpass interpolation/decimation filters. As various lowpass filters are obtained by one set of common Farrow subfilters, only one offline filter design enables us to cover different integer sampling rate conversion (SRC) ratios. A model of general rational SRC is also constructed where the same fixed subfilters perform rational SRC. These two SRC schemes are then used to construct multimode TMUXs. Efficient implementation structures are introduced and different filter design techniques such as minimax and least-squares (LS) are discussed. By means of simulation results, it is shown that the performance of the transmultiplexer (TMUX) depends on the ripples of the filters. With the error vector magnitude (EVM) as the performance metric, the LS method has a superiority over the minimax approach.

Digital filters with variable bandwidth can be used for a variety of applications. Arbitrary change in the bandwidth of a digital Finite Impulse Response (FIR) filter can be acquired using sampling rate converters. In this paper, a sampling rate converter is proposed which is generated from Pascal structure, a fractional delay filter having low hardware complexity and high modularity. The proposed sampling rate converter requires lesser number of multipliers for implementation when compared with the sampling rate converters in the literature. A low pass filter having a single bandwidth sandwiched between two sampling rate converters can contribute multiple bandwidths in such a way that each bandwidth is an arbitrary variation of the original bandwidth. A two stage Frequency response masking approach (FRM) is used for the hardware efficient design of the original low pass filter. A low complexity and high modularity novel design for a continuously varying bandwidth of a digital FIR filter is proposed in this paper using the proposed sampling rate converter. The modularity of the Pascal structure can be used to control both pass band ripple as well as stop band attenuation of the continuously variable bandwidth FIR filter design. Different communication standards in a Software defined radio (SDR) channelizer is realized using the proposed design of continuously variable bandwidth filter.

Identifying and troubleshooting low-frequency artifacts mimicking atrial flutter caused by deep brain stimulator

Karst aquifers are highly heterogeneous, and non-stationary systems in terms of hydrodynamic properties. The investigation of the different transport properties and characteristics of a karst aquifer system (KAS) is of great significance for the management and protection of karst aquifers. To investigate the response of discharge (Q), suspended sediment (SS), and temperature (T) to the precipitation (P), we performed correlation, spectral, and wavelet analyses on the hydrologic time series that included mean daily value from 2009/1/1 to 2015/12/31 from the Nandong underground river system (NURS), a large (> 1600 km2) karst-groundwater basin in southern China. The long memory effects can be determined from the autocorrelation functions of the Q, SS and T implied that the NURS has a significant amount of storage. The sharp and narrow cross-correlation function (CCF) peaks and the cross-wavelet transform (XT) power spectrum of the SS vs. P indicated that the response of the SS to P was shorter than that of the Q and T, and also indicated that the weak memory effect and small inertia of the karst systems with regard to SS. The CCF and XT power spectrum indicated that an increase in Q was the main factor triggering the increase in SS, not precipitation, which is contrary to results determined for other karst springs. Furthermore, the XT and cross-wavelet coherence (TC) of T vs. the air temperature (Ta) was used to demonstrate that Ta is not a direct control on the T in the NURS, which can be misinterpreted when using the traditional correlation and spectral analyses.

: The main thesis of this project was that individuals who have concealed information can be detected using a combined behavioral and psychophysiological approach. This study examined the similarities and differences that characterize the behavioral and power spectra responses in truthful and deceptive subjects. Half of the subjects participated in a mock crime while the other half participated in a non-crime scenario. The participants responded during their session to words related and not related to the scenarios they enacted. Although the participants in the mock-crime group were instructed to deny knowledge of any words related to their scenario, the behavioral and spectral data demonstrate that they actually possess concealed information. Therefore, behavioral and spectral indices elicited by concealed information in deceptive subjects can reflect some aspects of deceit. A quasi-replication of the initial experiment was then performed to examine the nature of the power spectra effects. The same protocol was used, except that a block format was used for stimulus presentation and the analysis window for the power spectra was expanded and all frequencies between 13 and 50Hz were available for analysis rather than analyzing the peaks and valleys alone. The results showed that indeed there were significant Group by Frequency effects which indicated that the power spectra of deceivers differed from those of nondeceivers. However, there was neither an Electrode by Group nor an Electrode by Frequency by Group effect that would have reinforced the power spectra differences found in the initial experiment. Although the details of the power spectra effects are yet to be resolved with further study, both experiments described in this Final Report revealed interaction effects, with Group that support the conclusion that power spectra can potentially identify whether an individual is or is not concealing information from their Examiner.

Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain

General anesthesia is an important medical procedure in today's hospital practice and comprises loss of consciousness, analgesia, amnesia and immobility. Our current work analyzes patient reaction on nociception stimuli during a surgical operation and differences in this reaction provided different anesthetic drugs, propofol and desflurane. The studied dataset comprises EEG-recordings before and after incision obtained from 115 patients [1]. The task is the identification of spectral EEG signal features reflecting the incision. This analysis will reveal a possible new marker of pain during deep anesthesia. This work considers one of the approaches to the problem, namely spectral analysis. First, power spectral density (PSD) estimates were obtained using Welch's method. It is well known that EEG power spectrum decays with higher frequencies following ~1/f scaling [2-4]. We attribute this behavior to background activity [5], which takes place in the brain when no other activity is present. Background activity was describe by fitting regression curve P(f)~a/f b to each PSD estimate. However, the resulting goodness of fit was not satisfactory. It is due to rise of power in delta peak, which becomes prominent under general anesthesia and makes the process of curve fitting less reliable. Thus, the original model was substituted by the Lorentzian function P(f)=a/(f b + c), which resembles the shape of actual power spectrum quite well. Afterwards, regression curves were subtracted from each power spectrum to normalize it [3] and to analyze spectral power contained in delta and alpha peaks regardless of distinctions in patients. The results of this work revealed small differences between propofol and desflurane. Power spectra of patients receiving desflurane have more regular shape than the ones from propofol group. It can also be seen that delta power remains more consistent, while alpha power varies greatly from patient to patient. Another result of this work is a trend in the distribution of Lorentzian curve parameters: the set of parameters remains compact for small values of b, but a and c scatters significantly when b (which corresponds to steepness of curve) is larger than three. Results of this work provide insights on underlying background activity. However, they do not allow to distinguish between pre- and post-incision and poorly between propofol and desflurane. This problem requires more complicated techniques. Future work will expand spectral analysis with time information (time-frequency representations) and investigate time structure by means of recurrence analysis. Figure 1 Example of power spectrum density estimate (solid black), with fitted Lorentzian curve (dashed orange), goodness of fit (R2), delta (green circle) and alpha peaks (blue circle).