Search

Respiratory ailments are a very serious health issue and can be life-threatening, especially for patients with COVID. Respiration rate (RR) is a very important vital health indicator for patients. Any abnormality in this metric indicates a deterioration in health. Hence, continuous monitoring of RR can act as an early indicator. Despite that, RR monitoring equipment is generally provided only to intensive care unit (ICU) patients. Recent studies have established the feasibility of using photoplethysmogram (PPG) signals to estimate RR. This paper proposes a deep-learning-based end-to-end solution for estimating RR directly from the PPG signal. The system was evaluated on two popular public datasets: VORTAL and BIDMC. A lightweight model, ConvMixer, outperformed all of the other deep neural networks. The model provided a root mean squared error (RMSE), mean absolute error (MAE), and correlation coefficient (R) of 1.75 breaths per minute (bpm), 1.27 bpm, and 0.92, respectively, for VORTAL, while these metrics were 1.20 bpm, 0.77 bpm, and 0.92, respectively, for BIDMC. The authors also showed how fine-tuning a small subset could increase the performance of the model in the case of an out-of-distribution dataset. In the fine-tuning experiments, the models produced an average R of 0.81. Hence, this lightweight model can be deployed to mobile devices for real-time monitoring of patients.

An intelligent insole system may monitor the individual's foot pressure and temperature in real-time from the comfort of their home, which can help capture foot problems in their earliest stages. Constant monitoring for foot complications is essential to avoid potentially devastating outcomes from common diseases such as diabetes mellitus. Inspired by those goals, the authors of this work propose a full design for a wearable insole that can detect both plantar pressure and temperature using off-the-shelf sensors. The design provides details of specific temperature and pressure sensors, circuit configuration for characterizing the sensors, and design considerations for creating a small system with suitable electronics. The procedure also details how, using a low-power communication protocol, data about the individuals' foot pressure and temperatures may be sent wirelessly to a centralized device for storage. This research may aid in the creation of an affordable, practical, and portable foot monitoring system for patients. The solution can be used for continuous, at-home monitoring of foot problems through pressure patterns and temperature differences between the two feet. The generated maps can be used for early detection of diabetic foot complication with the help of artificial intelligence.

Type 1 diabetes mellitus (T1DM) patients are a significant threat to chronic kidney disease (CKD) development during their life. However, there is always a high chance of delay in CKD detection because CKD can be asymptomatic, and T1DM patients bypass traditional CKD tests during their routine checkups. This study aims to develop and validate a prediction model and nomogram of CKD in T1DM patients using readily available routine checkup data for early CKD detection. This research utilized 1375 T1DM patients' sixteen years of longitudinal data from multi-center Epidemiology of Diabetes Interventions and Complications (EDIC) clinical trials conducted at 28 sites in the USA and Canada and considered 17 routinely available features. Three feature ranking algorithms, extreme gradient boosting (XGB), random forest (RF), and extremely randomized trees classifier (ERT), were applied to create three feature ranking lists, and logistic regression analyses were performed to develop CKD prediction models using these ranked feature lists to identify the best performing top-ranked features combination. Finally, the most significant features were selected to develop a multivariate logistic regression-based CKD prediction model for T1DM patients. This model was evaluated using sensitivity, specificity, accuracy, precision, and F1 score on train and test data. A nomogram of the final model was further generated for easy application in clinical practices. Hypertension, duration of diabetes, drinking habit, triglycerides, ACE inhibitors, low-density lipoprotein (LDL) cholesterol, age, and smoking habit were the top-8 features ranked by the XGB model and identified as the most important features for predicting CKD in T1DM patients. These eight features were selected to develop the final prediction model using multivariate logistic regression, which showed 90.04% and 88.59% accuracy in internal and test data validation. The proposed model showed excellent performance and can be used for CKD identification in T1DM patients during routine checkups.

A four-level double lambda closed atomic configuration is considered to study the polarization plane rotation of the probe beam through cold as well as thermal Rb[Formula: see text] atomic medium by varying the spontaneously generated coherence (SGC). Magnetic field and strong coupling field are applied to the atomic configuration. The light-matter interaction leads to enhanced the magneto-optical rotation. The intensity of the applied fields plays promising role in the generation and enhancement of birefringence. It ultimately enhances the polarization plane rotation of the probe beam in the Doppler medium. In the presence of both SGC and Doppler broadening effects, the optical rotation and transmission of the weak light beam are modified and controlled as well, which have potential applications in magnetometery and laser frequency stabilization., (© 2022. The Author(s).)

Diabetes mellitus (DM) is one of the most prevalent diseases in the world, and is correlated to a high index of mortality. One of its major complications is diabetic foot, leading to plantar ulcers, amputation, and death. Several studies report that a thermogram helps to detect changes in the plantar temperature of the foot, which may lead to a higher risk of ulceration. However, in diabetic patients, the distribution of plantar temperature does not follow a standard pattern, thereby making it difficult to quantify the changes. The abnormal temperature distribution in infrared (IR) foot thermogram images can be used for the early detection of diabetic foot before ulceration to avoid complications. There is no machine learning-based technique reported in the literature to classify these thermograms based on the severity of diabetic foot complications. This paper uses an available labeled diabetic thermogram dataset and uses the k-mean clustering technique to cluster the severity risk of diabetic foot ulcers using an unsupervised approach. Using the plantar foot temperature, the new clustered dataset is verified by expert medical doctors in terms of risk for the development of foot ulcers. The newly labeled dataset is then investigated in terms of robustness to be classified by any machine learning network. Classical machine learning algorithms with feature engineering and a convolutional neural network (CNN) with image-enhancement techniques are investigated to provide the best-performing network in classifying thermograms based on severity. It is found that the popular VGG 19 CNN model shows an accuracy, precision, sensitivity, F1-score, and specificity of 95.08%, 95.08%, 95.09%, 95.08%, and 97.2%, respectively, in the stratification of severity. A stacking classifier is proposed using extracted features of the thermogram, which is created using the trained gradient boost classifier, XGBoost classifier, and random forest classifier. This provides a comparable performance of 94.47%, 94.45%, 94.47%, 94.43%, and 93.25% for accuracy, precision, sensitivity, F1-score, and specificity, respectively.

Diabetic neuropathy (DN) is one of the prevalent forms of neuropathy that involves alterations in biomechanical changes in the human gait. Diabetic foot ulceration (DFU) is one of the pervasive types of complications that arise due to DN. In the literature, for the last 50 years, researchers have been trying to observe the biomechanical changes due to DN and DFU by studying muscle electromyography (EMG) and ground reaction forces (GRF). However, the literature is contradictory. In such a scenario, we propose using Machine learning techniques to identify DN and DFU patients by using EMG and GRF data. We collected a dataset from the literature which involves three patient groups: Control (n = 6), DN (n = 6), and previous history of DFU (n = 9) and collected three lower limb muscles EMG (tibialis anterior (TA), vastus lateralis (VL), gastrocnemius lateralis (GL)), and three GRF components (GRFx, GRFy, and GRFz). Raw EMG and GRF signals were preprocessed, and different feature extraction techniques were applied to extract the best features from the signals. The extracted feature list was ranked using four different feature ranking techniques, and highly correlated features were removed. In this study, we considered different combinations of muscles and GRF components to find the best performing feature list for the identification of DN and DFU. We trained eight different conventional ML models: Discriminant analysis classifier (DAC), Ensemble classification model (ECM), Kernel classification model (KCM), k-nearest neighbor model (KNN), Linear classification model (LCM), Naive Bayes classifier (NBC), Support vector machine classifier (SVM), and Binary decision classification tree (BDC), to find the best-performing algorithm and optimized that model. We trained the optimized the ML algorithm for different combinations of muscles and GRF component features, and the performance matrix was evaluated. Our study found the KNN algorithm performed well in identifying DN and DFU, and we optimized it before training. We found the best accuracy of 96.18% for EMG analysis using the top 22 features from the chi-square feature ranking technique for features from GL and VL muscles combined. In the GRF analysis, the model showed 98.68% accuracy using the top 7 features from the Feature selection using neighborhood component analysis for the feature combinations from the GRFx-GRFz signal. In conclusion, our study has shown a potential solution for ML application in DN and DFU patient identification using EMG and GRF parameters. With careful signal preprocessing with strategic feature extraction from the biomechanical parameters, optimization of the ML model can provide a potential solution in the diagnosis and stratification of DN and DFU patients from the EMG and GRF signals.

The electroencephalogram (EEG) and functional near-infrared spectroscopy (fNIRS) signals, highly non-stationary in nature, greatly suffers from motion artifacts while recorded using wearable sensors. Since successful detection of various neurological and neuromuscular disorders is greatly dependent upon clean EEG and fNIRS signals, it is a matter of utmost importance to remove/reduce motion artifacts from EEG and fNIRS signals using reliable and robust methods. In this regard, this paper proposes two robust methods: (i) Wavelet packet decomposition (WPD) and (ii) WPD in combination with canonical correlation analysis (WPD-CCA), for motion artifact correction from single-channel EEG and fNIRS signals. The efficacy of these proposed techniques is tested using a benchmark dataset and the performance of the proposed methods is measured using two well-established performance matrices: (i) difference in the signal to noise ratio ( ) and (ii) percentage reduction in motion artifacts ( ). The proposed WPD-based single-stage motion artifacts correction technique produces the highest average (29.44 dB) when db2 wavelet packet is incorporated whereas the greatest average (53.48%) is obtained using db1 wavelet packet for all the available 23 EEG recordings. Our proposed two-stage motion artifacts correction technique, i.e., the WPD-CCA method utilizing db1 wavelet packet has shown the best denoising performance producing an average and values of 30.76 dB and 59.51%, respectively, for all the EEG recordings. On the other hand, for the available 16 fNIRS recordings, the two-stage motion artifacts removal technique, i.e., WPD-CCA has produced the best average (16.55 dB, utilizing db1 wavelet packet) and largest average (41.40%, using fk8 wavelet packet). The highest average and using single-stage artifacts removal techniques (WPD) are found as 16.11 dB and 26.40%, respectively, for all the fNIRS signals using fk4 wavelet packet. In both EEG and fNIRS modalities, the percentage reduction in motion artifacts increases by 11.28% and 56.82%, respectively when two-stage WPD-CCA techniques are employed in comparison with the single-stage WPD method. In addition, the average also increases when WPD-CCA techniques are used instead of single-stage WPD for both EEG and fNIRS signals. The increment in both and values is a clear indication that two-stage WPD-CCA performs relatively better compared to single-stage WPD. The results reported using the proposed methods outperform most of the existing state-of-the-art techniques.

In this paper, we report on the synthesis-via the wet chemical precipitation route method-and thin film characteristics of inorganic semiconductor, cuprous oxide (Cu 2 O) nanoparticles, for their potential application in enhancing the humidity-sensing properties of semiconducting polymer poly(9,9-dioctylfluorene) (F8). For morphological analysis of the synthesized Cu 2 O nanoparticles, transmission electron microscope (TEM) and scanning electron microscope (SEM) micrographs are studied to investigate the texture, distribution, shape, and sizes of Cu 2 O crystallites. The TEM image of the Cu 2 O nanoparticles exhibits somewhat non-uniform distribution with almost uniform shape and size having an average particle size of ≈24 ± 2 nm. Fourier transformed infrared (FTIR) and X-ray diffraction (XRD) spectra are studied to validate the formation of Cu 2 O nanoparticles. Additionally, atomic force microscopy (AFM) is performed to analyze the surface morphology of polymer-inorganic (F8-Cu 2 O) nanocomposites thin film to see the grain sizes, mosaics, and average surface roughness. In order to study the enhancement in sensing properties of F8, a hybrid organic-inorganic (F8-Cu 2 O) surface-type humidity sensor Ag/F8-Cu 2 O/Ag is fabricated by employing F8 polymer as an active matrix layer and Cu 2 O nanoparticles as a dopant. The Ag/F8-Cu 2 O/Ag device is prepared by spin coating a 10:1 wt% solution of F8-Cu 2 O nanocomposite on pre-patterned silver (Ag) electrodes on glass. The inter-electrode gap (≈5 μm) between Ag is developed by photolithography. To study humidity sensing, the Ag/F8-Cu 2 O/Ag device is characterized by measuring its capacitance (C) as a function of relative humidity (%RH) at two different frequencies (120 Hz and 1 kHz). The device exhibits a broad humidity sensing range (27-86%RH) with shorter response time and recovery time, i.e., 9 s and 8 s, respectively. The present results show significant enhancement in the humidity-sensing properties as compared to our previously reported results of Ag/F8/Ag sensor wherein the humidity sensing range was 45-78%RH with 15 s and 7 s response and recovery times, respectively. The improvement in the humidity-sensing properties is attributed to the potential use of Cu 2 O nanoparticles, which change the hydrophobicity, surface to volume ratio of Cu 2 O nanoparticles, as well as modification in electron polarizability and polarity of the F8 matrix layer.

Diabetes mellitus (DM) can lead to plantar ulcers, amputation and death. Plantar foot thermogram images acquired using an infrared camera have been shown to detect changes in temperature distribution associated with a higher risk of foot ulceration. Machine learning approaches applied to such infrared images may have utility in the early diagnosis of diabetic foot complications. In this work, a publicly available dataset was categorized into different classes, which were corroborated by domain experts, based on a temperature distribution parameter-the thermal change index (TCI). We then explored different machine-learning approaches for classifying thermograms of the TCI-labeled dataset. Classical machine learning algorithms with feature engineering and the convolutional neural network (CNN) with image enhancement techniques were extensively investigated to identify the best performing network for classifying thermograms. The multilayer perceptron (MLP) classifier along with the features extracted from thermogram images showed an accuracy of 90.1% in multi-class classification, which outperformed the literature-reported performance metrics on this dataset.

Precision crop safety relies on automated systems for detecting and classifying plants. This work proposes the detection and classification of nine species of plants of the PlantVillage dataset using the proposed developed compact convolutional neural networks and AlexNet with transfer learning. The models are trained using plant leaf data with different data augmentations. The data augmentation shows a significant improvement in classification accuracy. The proposed models are also used for the classification of 32 classes of the Flavia dataset. The proposed developed N1 model has a classification accuracy of 99.45%, N2 model has a classification accuracy of 99.65%, N3 model has a classification accuracy of 99.55%, and AlexNet has a classification accuracy of 99.73% for the PlantVillage dataset. In comparison to AlexNet, the proposed models are compact and need less training time. The proposed N1 model takes 34.58%, the proposed N2 model takes 18.25%, and the N3 model takes 20.23% less training time than AlexNet. The N1 model and N3 models are size 14.8 MB making it 92.67% compact, and the N2 model is 29.7 MB which makes it 85.29% compact as compared to AlexNet. The proposed models are giving good accuracy in classifying plant leaf, as well as diseases in tomato plant leaves.

Epileptic seizures are temporary episodes of convulsions, where approximately 70 percent of the diagnosed population can successfully manage their condition with proper medication and lead a normal life. Over 50 million people worldwide are affected by some form of epileptic seizures, and their accurate detection can help millions in the proper management of this condition. Increasing research in machine learning has made a great impact on biomedical signal processing and especially in electroencephalogram (EEG) data analysis. The availability of various feature extraction techniques and classification methods makes it difficult to choose the most suitable combination for resource-efficient and correct detection. This paper intends to review the relevant studies of wavelet and empirical mode decomposition-based feature extraction techniques used for seizure detection in epileptic EEG data. The articles were chosen for review based on their Journal Citation Report, feature selection methods, and classifiers used. The high-dimensional EEG data falls under the category of '3N' biosignals-nonstationary, nonlinear, and noisy; hence, two popular classifiers, namely random forest and support vector machine, were taken for review, as they are capable of handling high-dimensional data and have a low risk of over-fitting. The main metrics used are sensitivity, specificity, and accuracy; hence, some papers reviewed were excluded due to insufficient metrics. To evaluate the overall performances of the reviewed papers, a simple mean value of all metrics was used. This review indicates that the system that used a Stockwell transform wavelet variant as a feature extractor and SVM classifiers led to a potentially better result.

Chronic kidney disease (CKD) is one of the severe side effects of type 1 diabetes mellitus (T1DM). However, the detection and diagnosis of CKD are often delayed because of its asymptomatic nature. In addition, patients often tend to bypass the traditional urine protein (urinary albumin)-based CKD detection test. Even though disease detection using machine learning (ML) is a well-established field of study, it is rarely used to diagnose CKD in T1DM patients. This research aimed to employ and evaluate several ML algorithms to develop models to quickly predict CKD in patients with T1DM using easily available routine checkup data. This study analyzed 16 years of data of 1375 T1DM patients, obtained from the Epidemiology of Diabetes Interventions and Complications (EDIC) clinical trials directed by the National Institute of Diabetes, Digestive, and Kidney Diseases, USA. Three data imputation techniques (RF, KNN, and MICE) and the SMOTETomek resampling technique were used to preprocess the primary dataset. Ten ML algorithms including logistic regression (LR), k-nearest neighbor (KNN), Gaussian naïve Bayes (GNB), support vector machine (SVM), stochastic gradient descent (SGD), decision tree (DT), gradient boosting (GB), random forest (RF), extreme gradient boosting (XGB), and light gradient-boosted machine (LightGBM) were applied to developed prediction models. Each model included 19 demographic, medical history, behavioral, and biochemical features, and every feature's effect was ranked using three feature ranking techniques (XGB, RF, and Extra Tree). Lastly, each model's ROC, sensitivity (recall), specificity, accuracy, precision, and F-1 score were estimated to find the best-performing model. The RF classifier model exhibited the best performance with 0.96 (±0.01) accuracy, 0.98 (±0.01) sensitivity, and 0.93 (±0.02) specificity. LightGBM performed second best and was quite close to RF with 0.95 (±0.06) accuracy. In addition to these two models, KNN, SVM, DT, GB, and XGB models also achieved more than 90% accuracy.

Surface plasmon (SP)-induced spectral hole burning (SHB) at the silver-dielectric interface is investigated theoretically. We notice a typical lamb dip at a selective frequency, which abruptly reduces the absorption spectrum of the surface plasmons polaritons (SPP). Introducing the spontaneous generated coherence (SGC) in the atomic medium, the slope of dispersion becomes normal. Additionally, slow SPP propagation is also noticed at the interface. The spectral hole burning dip is enhanced with the SGC effect and can be modified and controlled with the frequency and intensity of the driving fields. The SPP propagation length at the hole-burning region is greatly enhanced under the effect of SGC. A propagation length of the order of 600 µm is achieved for the modes, which is a remarkable result. The enhancement of plasmon hole burning under SGC will find significant applications in sensing technology, optical communication, optical tweezers and nano-photonics.

This research proposes a three-phase six-level multilevel inverter depending on twelve-switch three-phase Bridge and multilevel DC-link. The proposed architecture increases the number of voltage levels with less power components than conventional inverters such as the flying capacitor, cascaded H-bridge, diode-clamped and other recently established multilevel inverter topologies. The multilevel DC-link circuit is constructed by connecting three distinct DC voltage supplies, such as single DC supply, half-bridge and full-bridge cells. The purpose of both full-bridge and half-bridge cells is to provide a variable DC voltage with a common voltage step to the three-phase bridge's mid-point. A vector modulation technique is also employed to achieve the desired output voltage waveforms. The proposed inverter can operate as a six-level or two-level inverter, depending on the magnitude of the modulation indexes. To guarantee the feasibility of the proposed configuration, the proposed inverter's prototype is developed, and the experimental results are provided. The proposed inverter showed good performance with high efficiency of 97.59% following the IEEE 1547 standard. The current harmonics of the proposed inverter was also minimized to only 5.8%.

Despite the availability of various clinical trials that used different diagnostic methods to identify diabetic sensorimotor polyneuropathy (DSPN), no reliable studies that prove the associations among diagnostic parameters from two different methods are available. Statistically significant diagnostic parameters from various methods can help determine if two different methods can be incorporated together for diagnosing DSPN. In this study, a systematic review, meta-analysis, and trial sequential analysis (TSA) were performed to determine the associations among the different parameters from the most commonly used electrophysiological screening methods in clinical research for DSPN, namely, nerve conduction study (NCS), corneal confocal microscopy (CCM), and electromyography (EMG), for different experimental groups. Electronic databases (e.g., Web of Science, PubMed, and Google Scholar) were searched systematically for articles reporting different screening tools for diabetic peripheral neuropathy. A total of 22 studies involving 2394 participants (801 patients with DSPN, 702 controls, and 891 non-DSPN patients) were reviewed systematically. Meta-analysis was performed to determine statistical significance of difference among four NCS parameters, i.e., peroneal motor nerve conduction velocity, peroneal motor nerve amplitude, sural sensory nerve conduction velocity, and sural sensory nerve amplitude (all p < 0.001); among three CCM parameters, including nerve fiber density, nerve branch density, and nerve fiber length (all p < 0.001); and among four EMG parameters, namely, time to peak occurrence (from 0 to 100% of the stance phase) of four lower limb muscles, including the vastus lateralis (p < 0.001), tibialis anterior (p = 0.63), lateral gastrocnemius (p = 0.01), and gastrocnemius medialis (p = 0.004), and the vibration perception threshold (p < 0.001). Moreover, TSA was conducted to estimate the robustness of the meta-analysis. Most of the parameters showed statistical significance between each other, whereas some were statistically nonsignificant. This meta-analysis and TSA concluded that studies including NCS and CCM parameters were conclusive and robust. However, the included studies on EMG were inconclusive, and additional clinical trials are required.

This paper reports the potential application of cadmium selenide (CdSe) quantum dots (QDs) in improving the microelectronic characteristics of Schottky barrier diode (SBD) prepared from a semiconducting material poly-(9,9-dioctylfluorene) (F8). Two SBDs, Ag/F8/P3HT/ITO and Ag/F8-CdSe QDs/P3HT/ITO, are fabricated by spin coating a 10 wt% solution of F8 in chloroform and 10:1 wt% solution of F8:CdSe QDs, respectively, on a pre-deposited poly(3-hexylthiophene) (P3HT) on indium tin oxide (ITO) substrate. To study the electronic properties of the fabricated devices, current-voltage (I-V) measurements are carried out at 25 °C in dark conditions. The I-V curves of Ag/F8/P3HT/ITO and Ag/F8-CdSe QDs/P3HT/ITO SBDs demonstrate asymmetrical behavior with forward bias current rectification ratio (RR) of 7.42 ± 0.02 and 142 ± 0.02, respectively, at ± 3.5 V which confirm the formation of depletion region. Other key parameters which govern microelectronic properties of the fabricated devices such as charge carrier mobility (µ), barrier height (ϕ b ), series resistance (R s ) and quality factor (n) are extracted from their corresponding I-V characteristics. Norde's and Cheung functions are also applied to characterize the devices to study consistency in various parameters. Significant improvement is found in the values of R s , n, and RR by 3, 1.7, and 19 times, respectively, for Ag/F8-CdSe QDs/P3HT/ITO SBD as compared to Ag/F8/P3HT/ITO. This enhancement is due to the incorporation of CdSe QDs having 3-dimensional quantum confinement and large surface-to-volume area. Poole-Frenkle and Richardson-Schottky conduction mechanisms are also discussed for both of the devices. Morphology, optical bandgap (1.88 ± 0.5 eV) and photoluminescence (PL) spectrum of CdSe QDs with a peak intensity at 556 nm are also reported and discussed.

This paper presents a new practical QPSK receiver that uses digitized samples of incoming QPSK analog signal to determine the phase of the QPSK symbol. The proposed technique is more robust to phase noise and consumes up to 89.6% less power for signal detection in demodulation operation. On the contrary, the conventional QPSK demodulation process where it uses coherent detection technique requires the exact incoming signal frequency; thus, any variation in the frequency of the local oscillator or incoming signal will cause phase noise. A software simulation of the proposed design was successfully carried out using MATLAB Simulink software platform. In the conventional system, at least 10 dB signal to noise ratio (SNR) is required to achieve the bit error rate (BER) of 10(-6), whereas, in the proposed technique, the same BER value can be achieved with only 5 dB SNR. Since some of the power consuming elements such as voltage control oscillator (VCO), mixer, and low pass filter (LPF) are no longer needed, the proposed QPSK demodulator will consume almost 68.8% to 99.6% less operational power compared to conventional QPSK demodulator.

The design and implementation of a high-speed direct digital frequency synthesizer are presented. A modified Brent-Kung parallel adder is combined with pipelining technique to improve the speed of the system. A gated clock technique is proposed to reduce the number of registers in the phase accumulator design. The quarter wave symmetry technique is used to store only one quarter of the sine wave. The ROM lookup table (LUT) is partitioned into three 4-bit sub-ROMs based on angular decomposition technique and trigonometric identity. Exploiting the advantages of sine-cosine symmetrical attributes together with XOR logic gates, one sub-ROM block can be removed from the design. These techniques, compressed the ROM into 368 bits. The ROM compressed ratio is 534.2:1, with only two adders, two multipliers, and XOR-gates with high frequency resolution of 0.029 Hz. These techniques make the direct digital frequency synthesizer an attractive candidate for wireless communication applications.