FFT-based Spectrum Research Articles

Novel filter bank-based cooperative spectrum sensing under practical challenges for beyond 5G cognitive radios

Cognitive radio (CR) technology with dynamic spectrum management capabilities is widely advocated for utilizing effectively the unused spectrum resources. The main idea behind CR technology is to trigger secondary communications to utilize the unused spectral resources. However, CR technology heavily relies on spectrum sensing techniques which are applied to estimate the presence of primary user (PU) signals. This paper firstly focuses on novel analysis filter bank (AFB) and FFT-based cooperative spectrum sensing (CSS) techniques as conceptually and computationally simplified CSS methods based on subband energies to detect the spectral holes in the interesting part of the radio spectrum. To counteract the practical wireless channel effects, collaborative subband-based approaches of PU signal sensing are studied. CSS has the capability to relax the problems of both hidden nodes and fading multipath channels. FFT- and AFB-based receiver side sensing methods are applied for OFDM waveform and filter bank-based multicarrier (FBMC) waveform, respectively, the latter one as a candidate beyond-OFDM/beyond-5G scheme. Subband energies are then applied for enhanced energy detection (ED)-based CSS methods that are proposed in the context of wideband, multimode sensing. Our first case study focuses on sensing potential spectral gaps close to relatively strong primary users, considering also the effects of spectral regrowth due to power amplifier nonlinearities. The study shows that AFB-based CSS with FBMC waveform is able to improve the performance significantly. Our second case study considers a novel maximum–minimum energy detector (Max–Min ED)-based CSS. The proposed method is expected to effectively overcome the issue of noise uncertainty (NU) with remarkably lower implementation complexity compared to the existing methods. The developed algorithm with reduced complexity, enhanced detection performance, and improved reliability is presented as an attractive solution to counteract the practical wireless channel effects under low SNR. Closed-form analytic expressions are derived for the threshold and false alarm and detection probabilities considering frequency selective scenarios under NU. The validity of the novel expressions is justified through comparisons with respective results from computer simulations.

A flexible numerical calculation method of angular spectrum based on matrix product.

Fast Fourier transform (FFT) is the most commonly used mathematical method in numerical calculation, and the FFT-based angular spectrum method (ASM) is also used widely in diffraction calculation. However, the frequency and spatial sampling rules in FFT limit the effective propagation distance and the observation window range of ASM. A novel method for calculating the angular spectrum based on the matrix product is proposed in this Letter. This method realizes the fast calculation of discrete Fourier transform (DFT) based on the matrix product, in which the sampling matrix is orthogonally decomposed into two vectors. Instead of FFT, angular spectrum diffraction calculation is carried out based on the matrix product, which is named the matrix product ASM. The method in this Letter uses a simple mathematical transformation to achieve maximum compression of the sampling interval in the frequency domain, which significantly increases the effective propagation distance of the angular spectrum. Additionally, the size of the observation window can be enlarged to obtain a wider calculation range by changing the spatial sampling of the output plane.

Spectrum shaping using NC‐OFDM for cognitive radio applications

Cognitive radio (CR) is an innovative technology that supports dynamic spectrum access to utilise the spectrum more efficiently in an opportunistic manner without interfering with the licensed users. Multi-carrier modulation techniques such as orthogonal frequency division multiplexing (OFDM) is identified as one of the suitable candidates for the design of CR systems. To provide high data rates while avoiding interference with licensed users, a variant of OFDM called non-contiguous OFDM (NC-OFDM) is used in CR. NC-OFDM is useful for dynamic shaping of spectrum based on the channel impairments, interference and jamming threats. In this work, the customised NC-OFDM transceiver link is simulated and compared with the customised OFDM link in the MATLAB environment. It is implemented in Zynq-7000 System-on-Chip (SoC) 7Z020 with radio-frequency front-end board, AD-FMCOMMS3-EBZ Software Defined Radio platform. Implementation of this link is carried out on Spartan-3A FPGA and compared the hardware resource utilisation with Zynq platform. It is observed that the Zynq platform utilises less hardware resources for the implementation. The transmitter spectrum, spectrum after de-activating unwanted sub-carriers, the spectrum shaping using raised cosine filtering, spectrum sensing using the correlation of known pattern and FFT-based spectrum sensing are also simulated in the MATLAB.

Embedded FFT with dsPIC30F4013

FFT-based digital spectral analyzer has become more and more widely used as a result of the development of Digital Signal Processing (DSP) techniques. Modern Analog-to-Digital Converters (ADC) and processors have made it possible to make fast measurements with a limited number of hardware. In this paper, a design of a simple low-cost FFT-based digital spectrum analyzer was presented. The author discusses the design of each components of the system in qualitatively and quantitatively. The report presents the whole system design in detail which contains filter design, micro-controller design and UART transmission design. Some satisfying measurement result of the system were presented in the paper. The system can provide fast measurement with good accuracy. But the measured result has a limited range and resolution of the display is not very high. At last, the advantages and disadvantages of the system was discussed which is considered as guidelines for further work.

One-chip analog circuits for a new type of plasma wave receiver on board space missions

Abstract. Plasma waves are important observational targets for scientific missions investigating space plasma phenomena. Conventional fast Fourier transform (FFT)-based spectrum plasma wave receivers have the disadvantages of a large size and a narrow dynamic range. This paper proposes a new type of FFT-based spectrum plasma wave receiver that overcomes the disadvantages of conventional receivers. The receiver measures and calculates the whole spectrum by dividing the observation frequency range into three bands: bands 1, 2, and 3, which span 1 Hz to 1 kHz, 1 to 10 kHz, and 10 to 100 kHz, respectively. To reduce the size of the receiver, its analog section was realized using application-specific integrated circuit (ASIC) technology, and an ASIC chip was successfully developed. The dimensions of the analog circuits were 4.21 mm × 1.16 mm. To confirm the performance of the ASIC, a test system for the receiver was developed using the ASIC, an analog-to-digital converter, and a personal computer. The frequency resolutions for bands 1, 2, and 3 were 3.2, 32, and 320 Hz, respectively, and the average time resolution was 384 ms. These frequency and time resolutions are superior to those of conventional FFT-based receivers.

FFT-Based Spectrum Analysis in the Case of Data Loss

The significance of measurement data transfer over unreliable channel has emerged in the last decade, due to the spread of sensor networks and the idea of Internet of things. This paper investigates the behavior of the fast Fourier transform (FFT)-based power spectral density (PSD) estimation in the case of data loss. There are different methods available to estimate the PSD, but the hegemony of the FFT is beyond dispute, especially in real-time applications. This paper investigates the behavior of the PSD estimator in the case of different data loss models, and then offers some simple solutions on how the data loss can be handled in PSD estimation, when only moderate computing resources are available. The efficiency of the proposed method is demonstrated by the simulation and measurement results.

Electromagnetic attenuation of eight earthquakes registered in Mexico using FFT-based spectrum and t-test statistical analysis for ULF Q-R ratios signals

A method to improve the detection of seismo-magnetic signals is presented herein. Eight events registered for periods of 24 hours with seismic activity were analyzed and compared with non-seismic periods of the same duration. The distance between the earthquakes (EQs) and the ultra-low frequency detector is of ρ = (1.8) 100.45M, where M is the magnitude of the EQ reported by the Seismological National Service of Mexico, in a period of three years. An improved fast Fourier transform analysis in the form of the ratio of the vertical magnetic field component to the horizontal one (Q = Bz/Bx) has been developed. There are important differences between the frequencies obtained during the days of seismic activity compared with those with no seismic activity.

Brain’s alpha activity is highly reduced in euthymic bipolar disorder patients

Brain's alpha activity and alpha responses belong to major electrical signals that are related to sensory/cognitive signal processing. The present study aims to analyze the spontaneous alpha activity and visual evoked alpha response in drug free euthymic bipolar patients. Eighteen DSM-IV euthymic bipolar patients (bipolar I n=15, bipolar II n=3) and 18 healthy controls were enrolled in the study. Patients needed to be euthymic at least for 4weeks and psychotrop free for at least 2weeks. Spontaneous EEG (4min eyes closed, 4min eyes open) and evoked alpha response upon application of simple visual stimuli were analyzed. EEG was recorded at 30 positions. The digital FFT-based power spectrum analysis was performed for spontaneous eyes closed and eyes open conditions and the response power spectrum was also analyzed for simple visual stimuli. In the analysis of spontaneous EEG, the ANOVA on alpha responses revealed significant results for groups (F(1,34)=8.703; P<0.007). Post-hoc comparisons showed that spontaneous EEG alpha power of healthy subjects was significantly higher than the spontaneous EEG alpha power of euthymic patients. Furthermore, visual evoked alpha power of healthy subjects was significantly higher than visual evoked alpha power of euthymic patients (F(1,34)=4.981; P<0.04). Decreased alpha activity in spontaneous EEG is an important pathological EEG finding in euthymic bipolar patients. Together with an evident decrease in evoked alpha responses, the findings may lead to a new pathway in search of biological correlates of cognitive impairment in bipolar disorder.

Comparison and verification of numerical reconstruction methods in digital holography

The expressions for the reconstructed field from the sample of the diffracted wave, which is produced by illuminating an object, are found by use of different diffraction integrals in the digital holography. The numerical reconstruction methods that truncate and sample this field are compared in overlapping quality, accuracy, pixel resolution, computation window, and speed. The fast Fourier transform (FFT)-based direct integration method for the Fresnel integral and the modified FFT-based direct integration method for the Rayleigh-Sommerfeld integral have similar overlapping quality and can flexibly control pixel resolution and computation window size. Meanwhile, the FFT-based angular spectrum method is superior to the FFT-based convolution method in accuracy and speed. The experimental results are presented to verify these consequences.

Post-processing of auditory steady-state responses to correct spectral leakage

Auditory steady-state responses (ASSRs) are electrical manifestations of brain due to high rate sound stimulation. These evoked responses can be used to assess the hearing capabilities of a subject in an objective, automatic fashion. Usually, the detection protocol is accomplished by frequency-domain techniques, such as magnitude-squared coherence, whose estimation is based on the fast Fourier transform (FFT) of several data segments. In practice, the FFT-based spectrum may spread out the energy of a given frequency to its side bins and this escape of energy in the spectrum is called spectral leakage. The distortion of the spectrum due to leakage may severely compromise statistical significance of objective detection. This work presents an offline, a posteriori method for spectral leakage minimization in the frequency-domain analysis of ASSRs using coherent sampling criterion and interpolation in time. The technique was applied to the local field potentials of 10 Wistar rats and the results, together with those from simulated data, indicate that a leakage-free analysis of ASSRs is possible for any dataset if the methods showed in this paper were followed.

A Noise-Robust FFT-Based Auditory Spectrum With Application in Audio Classification

In this paper, we investigate the noise robustness of Wang and Shamma's early auditory (EA) model for the calculation of an auditory spectrum in audio classification applications. First, a stochastic analysis is conducted wherein an approximate expression of the auditory spectrum is derived to justify the noise-suppression property of the EA model. Second, we present an efficient fast Fourier transform (FFT)-based implementation for the calculation of a noise-robust auditory spectrum, which allows flexibility in the extraction of audio features. To evaluate the performance of the proposed FFT-based auditory spectrum, a set of speech/music/noise classification tasks is carried out wherein a support vector machine (SVM) algorithm and a decision tree learning algorithm (C4.5) are used as the classifiers. Features used for classification include conventional Mel-frequency cepstral coefficients (MFCCs), MFCC-like features obtained from the original auditory spectrum (i.e., based on the EA model) and the proposed FFT-based auditory spectrum, as well as spectral features (spectral centroid, bandwidth, etc.) computed from the latter. Compared to the conventional MFCC features, both the MFCC-like and spectral features derived from the proposed FFT-based auditory spectrum show more robust performance in noisy test cases. Test results also indicate that, using the new MFCC-like features, the performance of the proposed FFT-based auditory spectrum is slightly better than that of the original auditory spectrum, while its computational complexity is reduced by an order of magnitude.

Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.

Synthetic instruments extract masked signal parameters

We have reviewed the signal conditioning required to obtain high-quality spectral measurements with an FFT-based spectrum analyzer. The conditioning includes data windowing and extended length. Folded windows are required at the input to the transform, and significant ensemble averaging of power spectrum and cross power spectrum at the output of the FFT is needed. We also commented on the effect of cross coupling between signal and noise terms on the variance of the spectral output terms when the signal contains both spectral lines and additive noise. Finally, we presented techniques based on cross spectra. In particular, the normalized cross spectra known as the coherence function was shown as a technique to separate spectral components traceable to the input signal from those not traceable to the input signal.

Spectrum Estimation by Noise-Compensated Data Extrapolation

High-resolution spectrum estimation techniques have been extensively studied in recent publications. Knowledge of the noise variance is vital for spectrum estimation from noise-corrupted observations. This paper presents the use of noise compensation and data extrapolation for spectrum estimation. We assume that the observed data sequence can be represented by a set of autoregressive parameters. A recently proposed iterative algorithm is then used for noise variance estimation while autoregressive parameters are used for data extrapolation. We also present analytical results to show the exponential decay characteristics of the extrapolated samples and the frequency domain smoothing effect of data extrapolation. Some statistical results are also derived. The proposed noise-compensated data extrapolation approach is applied to both the autoregressive and FFT-based spectrum estimation methods. Finally, simulation results show the superiority of the method in terms of bias reduction and resolution improvement for sinusoids buried in noise.

The SERENDIP SETI project: new instrumentation for SETI and results of recent observations

Over the past 30 years research into the existence of extraterrestrial life has focused on attempts to detect stable narrowband radio signals emitted in the microwave portion of the radio frequency (RF) spectrum. The SERENDIP SETI group is currently conducting search operations on the world’s largest radio telescope at the Arecibo Observatory in Puerto Rico. The third generation SERENDIP system, SERENDIP III, is a 4 million channel FFT-based spectrum analyzer with 0.6 Hz frequency resolution. In this paper, we will discuss the results of our recent 3.5 year sky survey. SERENDIP looked at 95% of the sky visible from Arecibo in the 424–436 MHz range, analyzed 10 14 spectral bins, and logged information on over 2.5×10 8 signals. The fourth generation SERENDIP system expands on the SERENDIP III design. SERENDIP IV computes 2×10 11 operations each second, providing spectral analysis on 160 million channels in 1.7 s. We will discuss the design and use of the SERENDIP IV system and future observing plans.

Analysis of rat EEG using autoregressive power spectra

The main objective of this paper is to make the auto regressive (AR) power spectrum estimation method accessible to electrophysiologists and present some typical applications. The AR method is explained, choices of various parameters are explored and examples from the analysis of rat hippocampal EEG are given. We also provide the pseudocode for the computation of the AR coefficients and the AR spectrum. We compare the results from the AR method to the FFT-based power spectrum method and demonstrate the superiority of the AR method. We also show the differences in the spectra of the EEG of alcohol-preferring (P) and non-preferring (NP) rats in the baseline condition when no alcohol is infused. We found a statistically significant difference in peak theta frequency which was at 6.96 Hz for the P rats and at 7.74 Hz for the NP rats. There were also other observable differences in the shape of the spectra of the EEG of the P and NP rats.

The effects of sample duration and timing on speaker identification accuracy by means of long-term spectra

The purpose of this research was to examine the effects of speech sample duration on speaker identification accuracy when an FFT-based Long-Term Spectrum (LTS) analysis approach was utilized. A secondary goal was to assess the usefulness of FFT-LTS when non-contemporary speech samples were used. Two separate experiments were performed. Results for Experiment 1 revealed identification accuracy of 92–100% for text-independent, contemporary speech samples of 20 s and 10 s duration. Five-second contemporary samples resulted in accuracy rates of 28–96%. Statistical analysis revealed that the specific text of the test sample was significantly related to accuracy rate; thus, this procedure could not be considered “text-independent” at the 5 s duration. Preliminary phonemic analysis did not reveal a phonetically-based explanation for this text-related difference in accuracy results at 5 s. Results of Experiment 2 indicated that for non-contemporary samples with similar text, the identification accuracy of the LTS vector was significantly reduced (52–72% correct). It was concluded that the LTS approach may be most useful as one element in a multi-vector speaker recognition/identification profile.

Coefficient Quantization Error in FFT-Based Spectrum Analysis

In every DFT-based spectrum analysis -especially when fixed-point number representation and arithmetics are used- quantization error will arise due to finite word length. The three main error sources: input data quantization, the use of quantized sin/cos coefficients and the effects of finite word length arithmetics are usually analysed by means of satistical methods; the effects of quantization are modelled by independent additive noise. Ihe nature of coefficient quantization is nonstatistical. The same inexact values are used repeatedly in the computation of one spectrum line, so statistical method gives only rough approximation of this error. This paper presents a more accurate analysis of coefficient quantization error. A deterministic error analysis is presented; the results show that the effect of coefficient error can be modelled by windowing the input signal. Special window functions describing the biasing effect ot coefficient quantization and the mean-squared error of the output frequency lines of given F FT algorithms are determined. An upper bound of the output noise-to-signal ratio is given, which is much less than the bound determined using deterministic worst case analysis.