Amplitude Detection Research Articles

Модифицированная инвариантная амплитудная модуляция и демодуляция с двумя опорными сиганлами

The model of modified invariant amplitude modulation and demodulation with two reference signals considered in the article belongs to the field of systems, networks and devices of telecommunications and radio engineering and can be used in radio transmitting devices, telecommunication systems and devices where an amplitude-modulated transmitted signal is required for transmission through a communication channel. The achieved technical result of the modified invariant amplitude modulation and demodulation with two reference signals is aimed at the possibility of forming an amplitude-modulated transmitted signal with increased noise immunity characteristics to a specific type of interference. Algorithms of modified invariant amplitude modulation and demodulation with two reference signals are proposed, and based on these algorithms, block diagrams of a modified invariant amplitude modulator and a demodulator with two reference signals were developed. In order to obtain experimental data for the analysis of a modified invariant amplitude modulation and demodulation with two reference signals when it is affected by interference in the communication channel, the communication system was simulated and the necessary data calculated in Matlab. Additive white Gaussian noise was chosen as an interference in the communication channel. The article presents a simplified block diagram of the communication system of the experimental model. To compare the results, modified invariant amplitude modulation and demodulation with two reference signals will be used as a modulator and demodulator, in the first case, and in the second case, amplitude modulation and demodulation. As a result, estimates of the dependence of the standard deviation on the value of the signal-to noise ratio and the probability of a bit error on the value of the signal-to-noise ratio were obtained. The standard deviation for modified invariant amplitude modulation and demodulation with two reference signals has significantly lower values than the standard deviation for amplitude modulation and demodulation. The transmission of information with the same reliability through a communication channel with a modified invariant amplitude modulation with two reference signals requires a significantly higher signal-to-noise ratio than transmission through a communication channel with amplitude modulation.

A Novel Optimization Demodulation Method for Gear Fault Vibration Overmodulation Signal and Its Application to Fault Diagnosis

Many demodulation methods are devoted to obtain the gear fault modulation frequency as the fault diagnosis indicator instead of the precise amplitude and frequency demodulation. It is because the precise demodulation is a challenge especially for the over-modulation signal potentially caused by the gear fault, which further hinders the gear fault degree diagnosis. This paper proposes a novel optimization demodulation method for over-modulation signal. The Hilbert transform demodulation and Jacobi-Anger expansion form are respectively combined with the trust region reflection optimization algorithm to achieve the precise amplitude and frequency demodulation. The objective function about AM parameters considers the zero-crossing feature of the time domain AM in over-modulation signal. The iterated Hilbert transform demodulation is innovatively applied to remove the singularities effect in the residual signal caused by the over-modulation. The simulations and experiments demonstrate that the proposed method has the advantages of high accuracy and strong anti-noise performance in the demodulation of over-modulation signal. The quantitative FM and AM signals obtained by the proposed method can be applied to detect the gear fault degree, which provide an approach for establishing linkages between the modulation intensity and fault degree.

Lensless complex amplitude demodulation based on deep learning in holographic data storage

To increase the storage capacity in holographic data storage (HDS), the information to be stored is encoded into a complex amplitude. Fast and accurate retrieval of amplitude and phase from the reconstructed beam is necessary during data readout in HDS. In this study, we proposed a complex amplitude demodulation method based on deep learning from a single-shot diffraction intensity image and verified it by a non-interferometric lensless experiment demodulating four-level amplitude and four-level phase. By analyzing the correlation between the diffraction intensity features and the amplitude and phase encoding data pages, the inverse problem was decomposed into two backward operators denoted by two convolutional neural networks (CNNs) to demodulate amplitude and phase respectively. The experimental system is simple, stable, and robust, and it only needs a single diffraction image to realize the direct demodulation of both amplitude and phase. To our investigation, this is the first time in HDS that multilevel complex amplitude demodulation is achieved experimentally from one diffraction intensity image without iterations.

C. elegans: Sensing the low-frequency profile of amplitude-modulated ultrasound

Several research groups have demonstrated that C. elegans can respond to pulsed ultrasound stimuli, and elucidating the underlying mechanisms is necessary to develop ultrasound neuromodulation. Here, amplitude-modulated (AM) ultrasound is applied to C. elegans, and its behavioral responses are investigated in detail. By loading surface acoustic waves (SAWs) onto free-moving worms on an agar surface, a carrier wave with a frequency of 8.80 MHz is selected. The signal is modulated by a rectangular or sinusoidal profile. It is demonstrated that sinusoidal modulation can produce similar responses in worms to rectangular modulation, with the strongest responses occurring at modulation frequencies of around 1.00 kHz. Meanwhile, the behavioral response is relatively weak when the ultrasonic signal is unmodulated, that is, when only the carrier wave is applied. At modulation frequencies other than 100.00 Hz to 10.00 kHz, the worms respond weakly, but when a second modulation frequency of 1.00 kHz is introduced, an improvement in response can be observed. These results suggest that C. elegans may sense the low-frequency envelope and respond to amplitude-modulated ultrasonic stimuli like an amplitude demodulator. MEC-4, an ion channel for touch sensing, is involved in the behavioral response of C. elegans to ultrasound in the present setup.

Hierarchical amplitude modulation structures and rhythm patterns: Comparing Western musical genres, song, and nature sounds to Babytalk.

Statistical learning of physical stimulus characteristics is important for the development of cognitive systems like language and music. Rhythm patterns are a core component of both systems, and rhythm is key to language acquisition by infants. Accordingly, the physical stimulus characteristics that yield speech rhythm in "Babytalk" may also describe the hierarchical rhythmic relationships that characterize human music and song. Computational modelling of the amplitude envelope of "Babytalk" (infant-directed speech, IDS) using a demodulation approach (Spectral-Amplitude Modulation Phase Hierarchy model, S-AMPH) can describe these characteristics. S-AMPH modelling of Babytalk has shown previously that bands of amplitude modulations (AMs) at different temporal rates and their phase relations help to create its structured inherent rhythms. Additionally, S-AMPH modelling of children's nursery rhymes shows that different rhythm patterns (trochaic, iambic, dactylic) depend on the phase relations between AM bands centred on ~2 Hz and ~5 Hz. The importance of these AM phase relations was confirmed via a second demodulation approach (PAD, Probabilistic Amplitude Demodulation). Here we apply both S-AMPH and PAD to demodulate the amplitude envelopes of Western musical genres and songs. Quasi-rhythmic and non-human sounds found in nature (birdsong, rain, wind) were utilized for control analyses. We expected that the physical stimulus characteristics in human music and song from an AM perspective would match those of IDS. Given prior speech-based analyses, we also expected that AM cycles derived from the modelling may identify musical units like crotchets, quavers and demi-quavers. Both models revealed an hierarchically-nested AM modulation structure for music and song, but not nature sounds. This AM modulation structure for music and song matched IDS. Both models also generated systematic AM cycles yielding musical units like crotchets and quavers. Both music and language are created by humans and shaped by culture. Acoustic rhythm in IDS and music appears to depend on many of the same physical characteristics, facilitating learning.

Modeling on RF Circuit and Thermal Conduction of a MEMS Amplitude Demodulator

An amplitude demodulator, using an on-line MEMS power sensor is studied in this paper. The model of the equivalent circuit of on-line structure is solved, and the heat transfer model related to the thermopile is proposed and also simulated to verify the feasibility of AM demodulation. Experiments are also performed to verify the proposed models. The microwave performance shows that the device has a return loss that is better than 20 dB, and an insertion loss of less than 0.5 dB up to 10 GHz. Both the model and the experimental results show that the MEMS device can perform demodulation of an AM signal with carrier frequency of 0.01–10 GHz and signal frequency of under 1kHz. [2021-0261]

Communication Systems With Amplitude Detection: An Asymptotic Approach

Amplitude detection (AD) is a low-complexity nonlinear scheme for information retrieval, as it only considers the envelope of the received signal. This makes it ideal in applications with low-cost low-power devices such as the Internet of Things (IoT). We consider a basic Point-to-Point (P2P) setup and develop a unified analytical framework for the asymptotic symbol error rate (SER) performance of the maximum-likelihood (ML) decoder with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary amplitude-shift keying (ASK). The developed framework is general and can be applied for a large class of fading channels. The SER can be characterized by two parameters: the diversity order and the coding gain at a sufficiently high signal-to-noise regime. We derive closed-form expressions for the exact diversity order along with a lower and upper bound on the coding gain. We show that the diversity order is equal to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> for Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading, whereas for the other considered models, it is equal to one. We also prove that among all possible binary modulations with equal power, the modulation with one symbol equal to zero [i.e., on–off keying (OOK)] achieves the minimum asymptotic SER. The mathematical framework developed for the P2P setup is extended for cooperative relay networks. Specifically, we consider a basic amplify-and-forward (AF) three-node relay topology that employs AD at both the relay and the destination. We analytically derive the ML decoder and study asymptotic bounds on the SER by showing that the proposed AF-AD relay setup can be transformed into an equivalent P2P-AD with respect to the ML decoder.

Processing Photoplethysmograms Recorded by Smartwatches to Improve the Quality of Derived Pulse Rate Variability.

Cardiac monitoring based on wearable photoplethysmography (PPG) is widespread because of its usability and low cost. Unfortunately, PPG is negatively affected by various types of disruptions, which could introduce errors to the algorithm that extracts pulse rate variability (PRV). This study aims to identify the nature of such artifacts caused by various types of factors under the conditions of precisely planned experiments. We also propose methods for their reduction based solely on the PPG signal while preserving the frequency content of PRV. The accuracy of PRV derived from PPG was compared to heart rate variability (HRV) derived from the accompanying ECG. The results indicate that filtering PPG signals using the discrete wavelet transform and its inverse (DWT/IDWT) is suitable for removing slow components and high-frequency noise. Moreover, the main benefit of amplitude demodulation is better preparation of the PPG to determine the duration of pulse cycles and reduce the impact of some other artifacts. Post-processing applied to HRV and PRV indicates that the correction of outliers based on local statistical measures of signals and the autoregressive (AR) model is only important when the PPG is of low quality and has no effect under good signal quality. The main conclusion is that the DWT/IDWT, followed by amplitude demodulation, enables the proper preparation of the PPG signal for the subsequent use of PRV extraction algorithms, particularly at rest. However, post-processing in the proposed form should be applied more in the situations of observed strong artifacts than in motionless laboratory experiments.

The Added Value of Integrating the Electronics Workbench Simulator in the Teaching of Electrical Concepts to Moroccan High School Students

In this paper, we are interested in the study of the use of the Electronics Workbench (EWB) simulator in the study of amplitude modulation and demodulation. We conducted a study with 50 Moroccan students in the second year of the scientific baccalaureate option physical sciences at the high school Abdellah Laroui of the city of Fez. Using the pre-test and post-test methodology with an experimental group (25 students) and a control group (25 students). The results of the two groups are analyzed using the student t-test. The results obtained in the post-test show that the average of the test administered to both groups, control (MG-Con) and experimental (MG-Exp), found a non-significant difference (MG-Exp - MG-Con = 15,36- 15,08 = 0,28 &gt; 0. In addition, using interviews, we asked students and teachers to give their opinions on questions about the use of the Electronics Workbench (EWB) simulator in learning. The results obtained show that the laboratory experiments cannot replace the simulator (EWB) which can be used as an alternative pedagogical means to help students understand the concepts in electricity.

A new method to select frequency band for vibration signal demodulation and condition estimation of rolling bearings

The narrowband amplitude demodulation of vibration signals is widely used to extract components carrying information about rolling bearing faults for condition estimation. However, precisely selecting the frequency band determines the quality of demodulation. Although transient detection based methods have achieved satisfactory performance in some scenarios, they may be severely disturbed by strong random impulses or harmonics. Additionally, frequency division strategy is always considered as rough. Aiming at these problems, a new method is proposed to select the optimal frequency band by combining the frequency division strategy, genetic algorithm (GA) optimization, and an automatic fault characteristic order (FCO) search algorithm. Aimed at a signal, its sub-signals are extracted according to the frequency division strategy and the order tracing technology is implemented to obtain the order spectrum of each sub-signal at first. Then, the FCO and its multiples (FCOs) are automatically searched from each order spectrum, and their amplitude summation is calculated. Afterwards, the ratio of FCOs summation to noise amplitude (RFN) is measured as the basis to construct an RFNgram for selecting the primary optimal frequency band Finally, GA is implemented to select the optimized optimal frequency band where the signal is demodulated for estimating the bearing condition. RFN measures both the impulsiveness and periodicity of signals, and GA optimizes the result from a RFNgram, essentially making up for the shortcomings of previous methods under the condition of multiple interferences. RFN is measured through the order spectrum, which also allows it to be applicable to varying speeds, thus achieving a more comprehensive range of industrial applications. Three case studies are implemented to present the superiority of the proposed method in condition estimation for rolling bearings by comparison with four classical or advanced methods.

Differential Modulation in Massive MIMO With Low-Resolution ADCs

In this paper, we present a differential modulation and detection scheme for use in the uplink of a system with a large number of antennas at the base station, each equipped with low-resolution analog-to-digital converters (ADCs). We derive an expression for the maximum likelihood (ML) detector of a differentially encoded phase information symbol received by a base station operating in the low-resolution ADC regime. We also present an equal performing reduced complexity receiver for detecting the phase information. To increase the supported data rate, we also present a maximum likelihood expression to detect differential amplitude phase shift keying symbols with low-resolution ADCs. We note that the derived detectors are unable to detect the amplitude information. To overcome this limitation, we use the Bussgang Theorem and the Central Limit Theorem (CLT) to develop two detectors capable of detecting the amplitude information. We numerically show that while the first amplitude detector requires multiple quantization bits for acceptable performance, similar performance can be achieved using one-bit ADCs by grouping the receive antennas and employing variable quantization levels (VQL) across distinct antenna groups. We validate the performance of the proposed detectors through simulations and show a comparison with corresponding coherent detectors. Finally, we present a complexity analysis of the proposed low-resolution differential detectors

A Novel Method to Classify Rolling Element Bearing Faults Using K-Nearest Neighbor Machine Learning Algorithm

Abstract A novel method is proposed in this work for the classification of fault in the ball bearings. Applications of K-nearest neighbor (KNN) techniques are increasing, which redefines the state-of-the-art technology for defect diagnosis and classification. Vibration characteristics of deep groove ball bearing with different defects are studied in this paper. Experimentation is conducted at different loads and speeds with artificially created defects, and vibration data are processed using kurtosis to find frequency band of interest and amplitude demodulation (Envelope spectrum analysis). Bearing fault amplitudes are extracted from the filtered signal spectrum at bearing characteristic frequency. The decision of fault classification is made using a KNN machine learning classifier by training feature data. The training features are created using characteristics amplitude at different fault and bearing conditions. The results showed that the KNN's accuracies are 100% and 97.3% when applied to two different experimental databases. The quantitative results of the KNN classifier are applied as the guidance for investigating the type of defects of bearing. The KNN Classifier method proved to be an effective method to quantify defects and significantly improve classification efficiency.

Forming the Higher Derivatives of Characteristics of Non-Linear Elements

It was suggested to form higher derivatives, including the fourth one, characteristics of non-linear elements based on altering the synchronous, phase insensitive active band-stop filter to the needed harmonic component of the researched antiderivative of the characteristic of the examined element, which is proportional to the according derivative, which allows, if needed, to reestablish the missing phase component using a synchronous, sensitive to phase demodulating filter, which is agreed to the specially formed control signals, or to exclude it using a simple amplitude demodulator. The use of the proposed shaper of higher derivatives for the purpose of determining the primary parameters of various objects with nonlinear characteristics of antiderivatives makes it possible to substantially increase the accuracy of their measurements, bringing this process to the level of tenths of a percent, which is a very important result in the measurement technique, first of all, the Q-factor of radiotechnical elements, for example, varicaps, with a wide range of its change.

Application of two-dimensional warped discrete Fourier transform to nonlinear two-dimensional amplitude demodulation

This study introduces a novel nonlinear two-dimensional (2D) warped discrete Fourier transform (WDFT) amplitude demodulation method that allows higher-resolution measurements on specific two-dimensional regions of interest. The specific application in this study addresses the need for the nonlinear 2D amplitude demodulation of fringe-wave fields acquired by a deformed Mach–Zehnder interferometer. The proposed method exploits the properties based on which the WDFT can obtain frequency spectra sampled at non-equidistant intervals and the symmetry of the Fourier transform. As a result, this 2D-WDFT-based method can be used to nonlinearly demodulate the amplitude of the 2D interference fringe wave field to obtain a high-resolution localized fringe envelope. This study describes the proposed analysis procedure and its application using this 2D WDFT-based demodulation scheme. Experimental verification of the proposed approach was conducted with the use of deformed Mach–Zehnder interferometry. The successful experimental validation proves the efficiency of the proposed algorithm for amplitude demodulation with dense sampling points located in the central part of the envelope. To the best of the authors’ knowledge, this is the first investigational report on a 2D nonlinear envelope demodulator.

A novel concatenate feature fusion RCNN architecture for sEMG-based hand gesture recognition.

Hand gesture recognition tasks based on surface electromyography (sEMG) are vital in human-computer interaction, speech detection, robot control, and rehabilitation applications. However, existing models, whether traditional machine learnings (ML) or other state-of-the-arts, are limited in the number of movements. Targeting a large number of gesture classes, more data features such as temporal information should be persisted as much as possible. In the field of sEMG-based recognitions, the recurrent convolutional neural network (RCNN) is an advanced method due to the sequential characteristic of sEMG signals. However, the invariance of the pooling layer damages important temporal information. In the all convolutional neural network (ACNN), because of the feature-mixing convolution operation, a same output can be received from completely different inputs. This paper proposes a concatenate feature fusion (CFF) strategy and a novel concatenate feature fusion recurrent convolutional neural network (CFF-RCNN). In CFF-RCNN, a max-pooling layer and a 2-stride convolutional layer are concatenated together to replace the conventional simple dimensionality reduction layer. The featurewise pooling operation serves as a signal amplitude detector without using any parameter. The feature-mixing convolution operation calculates the contextual information. Complete evaluations are made on both the accuracy and convergence speed of the CFF-RCNN. Experiments are conducted using three sEMG benchmark databases named DB1, DB2 and DB4 from the NinaPro database. With more than 50 gestures, the classification accuracies of the CFF-RCNN are 88.87% on DB1, 99.51% on DB2, and 99.29% on DB4. These accuracies are the highest compared with reported accuracies of machine learnings and other state-of-the-art methods. To achieve accuracies of 86%, 99% and 98% for the RCNN, the training time are 2353.686 s, 816.173 s and 731.771 s, respectively. However, for the CFF-RCNN to reach the same accuracies, it needs only 1727.415 s, 542.245 s and 576.734 s, corresponding to a reduction of 26.61%, 33.56% and 21.19% in training time. We concluded that the CFF-RCNN is an improved method when classifying a large number of hand gestures. The CFF strategy significantly improved model performance with higher accuracy and faster convergence as compared to traditional RCNN.

The Noise Generation in One-Frequency IMPATT Diode Oscillator of Millimeter Wave Range on the Effect of Low-Frequency Harmonic Oscillation

The investigation of effect of the low-frequency harmonic oscillation on the nourishment circuit of the 7 mm wave region IMPATT diode oscillator was continued. In first time it was shown, that excitement of noise and the maximum height-frequency noise spectrum extension at a low-frequency oscillation amplitude increasing are connected with a transitory decreasing of the diode current lower the start current of height-frequency generation in the IMPATT diode oscillator. Keywords: effect, low-frequency harmonic oscillation, IMPATT diode oscillator, 7mm wave range, spectrum, amplitude detector.

Micromagnetic simulation of a majority&amp;quot; logic gate based on the interference of spin waves' caustics

Using micromagnetic simulations, we show the possibility to build spin logic devices based on films of yttrium iron garnet and permalloy where energy channeling of spin waves is achieved due to excitation of focused and narrow-directed wave beams by used antennas. We studied the methods to construct a &amp;quot;majority&amp;quot; logic gate based on the interference of caustics of spin waves excited by the rectilinear transducers directed at an angle to the in-plane magnetic field. We propose an approach when adding a reference signal with fixed initial phase to three information signals allows to use an amplitude detector at the output of the device to built a truth table. The possibility to scale the device on the example of its work in the range of spin waves with micron and submicron wavelengths is demonstrated. Keywords: spin waves, magnetic field, ferromagnetic films, permalloy.

The Generalized Lyapunov Demodulator: High-Bandwidth, Low-Noise Amplitude and Phase Estimation

Effective demodulation of amplitude and phase is a requirement in a wide array of applications. Recent efforts have increased the demodulation performance, in particular, the Lyapunov demodulator allows bandwidths up to the carrier frequency of the signal. However, being inherently restricted to first-order filtering of the input signal, it is highly sensitive to frequency components outside its passband region. This makes it unsuitable for certain applications such as multifrequency atomic force microscopy (AFM). In this article, the structure of the Lyapunov demodulator is transformed to an equivalent form and generalized by exploiting the internal model principle. The resulting generalized Lyapunov demodulator structure allows for arbitrary filtering order and is easy to implement, requiring only a bandpass filter, a single integrator, and two nonlinear transformations. The generalized Lyapunov demodulator is implemented experimentally on a field-programmable gate array (FPGA). Then it is used for imaging in an AFM and benchmarked against the standard Lyapunov demodulator and the widely used lock-in amplifier. The lock-in amplifier achieves great noise attenuation capabilities and off-mode rejection at low bandwidths, whereas the standard Lyapunov demodulator is shown to be effective at high bandwidths. We demonstrate that the proposed demodulator combines the best from the two state-of-the-art demodulators, demonstrating high bandwidths, large off-mode rejection, and excellent noise attenuation simultaneously.

Микромагнитное моделирование логического ключа большинства" на основе интерференции каустик спиновых волн

Using micromagnetic simulations, we show the possibility to build spin logic devices based on films of yttrium iron garnet and permalloy where energy channeling of spin waves is achieved due to excitation of focused and narrow-directed wave beams with used antennas. We studied the methods to construct a majority logic gate based on the interference of caustics of spin waves excited with the rectilinear transducers directed at an angle to the in-plane magnetic field. We propose the approach that allows using of amplitude detector to build a truth table and that consists in adding a reference signal with the fixed initial phase to three information signals. The possibility to scale the device on the example of its work in the range of spin waves with micron and submicron wavelengths is demonstrated.

Alternative Autocorrelation Function for Radio Pulse Processing

The idea of improving the methods of processing the received radio signals under intense noise used in radio communication and radar systems is considered. A method for receiving radio pulses using their autocorrelation functions ACF is presented. It makes it possible to determine the presence of a periodic signal in a mixture with intense noise, the value of the carrier frequency of the radio pulse and the value of its average amplitude. However, to calculate the ACF, many multiplication operations are required, which take much longer than addition operations. It is proposed to use a function similar to the ACF, which by its properties makes it possible to determine the carrier frequency of the radio pulse, the value of its average amplitude, the value of the average amplitude of the noise that distorts the radio pulse. When calculating such a function, the multiplication operations that are in the ACF expression are replaced by the addition operations. However, to obtain such a function, it is not necessary to have signals with a time shift, as in calculating the ACF, but the exact value of the sum of their amplitudes. In this work, this function is called the alternative autocorrelation function AAKF. Shown are the ACF and AAKF images for a radio pulse of long duration, for additive noise, and also for a mixture of a radio pulse and noise. The main properties of the AAKF mixture of a radio pulse and noise relative to the ACF are considered. The forms of AAKF and ACF are different, but their periods are the same. It is shown that a device that allows one to obtain the exact value of signal amplitudes can be constructed according to the scheme of a two-channel "ideal" peak amplitude detector, which is proposed in this work. The possibility of obtaining a periodic AAKF of a mixture of a radio pulse and noise is very briefly considered. It is shown that with the help of periodic AAKF further processing of radio pulses can be done, with additional suppression of the influence of noise. In this case, the shape of the envelope of the periodic AAKF is rectangular. This approach is better suited for processing rectangular radio bursts. To solve this problem, you can use bandpass filtering of periodic AAKF and the operation of inverting the results of calculations. It is emphasized that the considered method for calculating the parameters of the useful signal and noise can be implemented on a modern element base when transferring a signal to an intermediate frequency, but this requires a large time delay in obtaining the results.