Frequency Domain Filtering Research Articles

Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.

Chromatic dispersion compensation in coherent transmission system using digital filters

We present a comparative analysis of three popular digital filters for chromatic dispersion compensation: a time-domain least mean square adaptive filter, a time-domain fiber dispersion finite impulse response filter, and a frequency-domain blind look-up filter. The filters are applied to equalize the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying transmission system. The characteristics of these filters are compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations, and their computational complexity. In addition, the phase noise tolerance of these filters is also analyzed.

Three-dimensional measurement method with orthogonal composite grating aided by fringe contrast and background calibration

A three dimensional (3-D) measurement method with orthogonal composite grating aided by fringe contrast and background calibration is proposed. Due to spectrum overlap, we find that the contrast and background of each deformed phase-shifting fringe demodulated from the captured composite fringe image is changed differently, which violates the principle that the contrast and background between any two deformed fringes must be uniform in the traditional 3-D measurement method with orthogonal composite grating, and therefore results in measurement error. We acquire the phase-shifting sinusoidal fringes from the composite fringe image captured on the reference plane, and the zero- and first-order spectra of the sinusoidal fringes can be obtained by filtering in the spatial frequency domain. Then the ratio contrast and background coefficients between the phase-shifting sinusoidal fringes can be calculated. When an object is measured, the contrast and background of the demodulated deformed fringes can be calibrated by these ratio coefficients. A new 3-D measurement mathematical model is set up to reconstruct the object. Experiments prove the new method can effectively restrain the effect of spectrum overlap, and can improve the measurement accuracy more than 1 time.

High quality multi-focus polychromatic composite image fusion algorithm based on filtering in frequency domain and synthesis in space domain

A novel multi-focus polychromatic image fusion algorithm based on filtering in the frequency domain using fast Fourier transform (FFT) and synthesis in the space domain (FFDSSD) is presented in this paper. First, the original multi-focus images are transformed into their frequency data by FFT for easy and accurate clarity determination. Then a Gaussian low-pass filter is used to filter the high frequency information corresponding to the image saliencies. After an inverse FFT, the filtered images are obtained. The deviation between the filtered images and the original ones, representing the clarity of the image, is used to select the pixels from the multi-focus images to reconstruct a completely focused image. These operations in space domain preserve the original information as much as possible and are relatively insensitive to misregistration scenarios with respect to transform domain methods. The polychromatic noise is well considered and successfully avoided while the information in different chromatic channels is preserved. A natural, nice-looking fused microscopic image for human visual evaluations is obtained in a dedicated experiment. The experimental results indicate that the proposed algorithm has a good performance in objective quality metrics and runtime efficiency.

Segmentation of multispectral high-resolution satellite imagery using log Gabor filters

Image segmentation has been recognized as a valuable approach that performs a region-based rather than a pixel-based analysis of high-resolution satellite imagery. A scheme for segmenting the multispectral IKONOS image based on frequency-domain filtering is presented. The frequency spectrum of typical landscape objects is analysed first. The spectrum curves are comparable in logarithmic coordinates rather than in Cartesian coordinates; therefore the Gabor filters are superseded by log Gabor filters to extract the multiscale texture features from panchromatic band. Edge features then are calculated from the pan-sharpened multispectral bands based on the vector field model. Finally, the texture-marked watershed segmentation algorithm is implemented and the segmentation accuracy is assessed. The experimental results show that the developed scheme generated an effective tool for automatic segmentation of multispectral high-resolution satellite imagery and suppressing the over-segmentation problem of watershed transform.

$F$–$k$ Filter Designs to Suppress Direct Waves for Bistatic Ground Penetrating Radar

Two design methods of a filter in a frequency-spatial frequency (f-k) domain have been developed for bistatic ground penetrating radar. The proposed methods suppress the direct wave, which causes significant artifacts in radar images, and are evaluated by laboratory measurements. Because the geometric positions of a transmitting antenna and a receiving antenna are not fixed, the suppression of a direct wave is an important issue. Then, we propose an f-k filtering approach for the solution, and present two methods to design the f-k filter. Both methods use a difference of an apparent horizontal velocity between a direct wave and a reflection from a target, and work automatically from position information of a transmitting antenna and a receiving antenna. One method is to mask an f-k spectrum in a region where a spectrum of the direct wave is distributed. The region is defined from the maximum and the minimum apparent horizontal velocity of the direct wave, which are calculated from the location of the transmitting antenna and the scanning area of the receiver. As for the other method, the most essential point is applying a time shift to eliminate a difference of an arrival time of a direct wave, where the time shift is calculated beforehand from the location of the transmitting antenna and the receiving antenna. Then, an apparent horizontal velocity of the direct wave becomes infinitely large due to the time shift. Thus, the f-k spectrum of the direct wave concentrates around a frequency axis because its slope is infinitely large. Then, a filter to reject the dc component in the spatial frequency direction is applied. Both methods are applied to an experimental data set which is acquired by a bistatic radar measurement to detect a buried landmine model with a depth of 10 cm. In addition, it is confirmed that they can suppress the undesired fluctuation of the images nearly one-tenth and help the reliable detection of a buried object.

On widely linear Wiener and tradeoff filters for noise reduction

Noise reduction is often formulated as a linear filtering problem in the frequency domain. With this formulation, the core issue of noise reduction becomes how to design an optimal frequency-domain filter that can significantly suppress noise without introducing perceptually noticeable speech distortion. While higher-order information can be used, most existing approaches use only second-order statistics to design the noise-reduction filter because they are relatively easier to estimate and are more reliable. When we transform non-stationary speech signals into the frequency domain and work with the short-time discrete Fourier transform coefficients, there are two types of second-order statistics, i.e., the variance and the so-called pseudo-variance due to the noncircularity of the signal. So far, only the variance information has been exploited in designing different noise-reduction filters while the pseudo-variance has been neglected. In this paper, we attempt to shed some light on how to use noncircularity in the context of noise reduction. We will discuss the design of optimal and suboptimal noise reduction filters using both the variance and pseudo-variance and answer the basic question whether noncircularity can be used to improve the noise-reduction performance.

Accelerated Calculation of Gabor Features in Spatial Domain

A lot of computer vision tasks are tried to solve by using Gabor features that proved to be very effective feature descriptors. One of the main drawbacks of using Gabor features in real-time practical applications is computational heaviness. Convolution with Gabor filters in frequency domain generates responses of Gabor features at each position in the image and is time consuming operation when Gabor feature consists of tens of Gabor filters. In this article, we introduce the concept of calculating Gabor features at regular grid in the image and show how this together with a generalized separability, symmetry and anti-symmetry of Gabor filter can be exploited to calculate Gabor features in spatial domain even faster than in frequency domain. Ill. 6, bibl.20 (in English; abstracts in English, Russian and Lithuanian).

Cleaning-up dirty isotachopherograms in time and frequency domain

In chromatography and electrophoresis S/N is increased by time or frequency domain filtering, multiple injections or sample stacking (in case of CZE). Bottom line is noise reduction without peak distortion. Isotachophoresis (ITP) using conductivity detection is also relevant because of its entirely different information content and the importance in CZE stacking. Several time- and frequency domain filters (Fourier & Walsh transform) were compared. Results were:•Time domain filters can be equally applied to either integral or differential signal;•Fourier and Walsh transforms are likewise suitable, whereas Walsh better preserves sharp boundaries;•Disturbance by detector transfer function can only be partly un-done with de-convolution; conditions are critical.

An efficient statistics-based method for the automated detection of sperm whale clicks

In this paper, we present a new method for the automated detection of sperm whale regular clicks and creaks based on statistical computations. In the first stage, a spectrogram is computed from the input waveform, followed by a noise normalisation process. A frequency domain filter is then applied, and the energy accumulated in each time frame is calculated. Two-second time-windows are then classified as containing either regular clicks, creaks, or noise based on statistical parameters using a neural network classifier. Finally, previously obtained statistical parameters are used to implement an energy-based detection criterion for the classified time-windows. Individual regular clicks and creaks are isolated by linking contiguous detected time frames. The proposed method was tested on five recordings of sperm whale sounds. Comparison of the detection performances to hand-labelled regular clicks and creaks revealed that this method outperforms two recently reported waveform-based methods when working with the same recordings files. An average percentage of detection of 86.97% was attained for the set of files. This method consumes also little computation time.

Performance of Time Domain Migration Influenced by Non-Ideal UWB Antennas

The antennas in ultrawideband (UWB) systems act as filters in both frequency domain and the spatial domain. This means that the antenna influence on a received signal varies with the wave incidence angle. This is particulary important for imaging systems, which make use of the time information of the received signals. However, since the incidence angles of the signals are not <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> known it is difficult to remove this effect from the measured data. To assess the antenna impact on the performance of the imaging system, in this work, simulated scattered signals are used as input for time domain migration algorithm. Then the image features like position errors, shape of the target image, resolution and coverage of an imaging system are extracted and compared for different real UWB antennas.

Iterative Detection of Multicode DS-CDMA Signals With Strong Nonlinear Distortion Effects

Whenever a direct-sequence code-division multiple-access (DS-CDMA) signal is the sum of several components associated with different spreading codes [e.g., the DS-CDMA signal to be transmitted by the base station (BS) in the downlink or any multicode DS-CDMA signal], it has high envelope fluctuations and a high peak-to-mean envelope power ratio (PMEPR), setting strong linearity requirements for the power amplifiers. For this reason, it is desirable to reduce the envelope fluctuations of the transmitted signals. The use of clipping techniques combined with frequency-domain filtering was shown to be an effective way of reducing the envelope fluctuations (and, inherently, the PMEPR) of DS-CDMA signals, while maintaining the spectral occupation of the corresponding conventional DS-CDMA signals. To avoid PMEPR regrowth effects, the clipping and filtering operations can be repeated several times. However, the performance degradation due to nonlinear distortion effects on the transmitted signals can be relatively high, particularly when a very low PMEPR is intended (e.g., when a low clipping level and several iterations are adopted). This can particularly be serious if different powers are assigned to different spreading codes. To avoid significant performance degradation in these situations, we consider an improved receiver where there is an iterative estimation and cancellation of nonlinear distortion effects. Our performance results show that the proposed receiver allows significant performance improvements after just a few iterations, even when we have strong nonlinear distortion effects.

Fabric defects detection based on frequency domain filtering

According to the spectrum of fabric texture and defects, a new method for defect detection was presented. Firstly, on the basis of the fabric texture classification, a spectrum image was derived from the Fast Fourier Transform (FFT). Then, the frequency filter was designed to remove normal texture information, and the acquired reconstruction images were segmented into many sub-windows, in which variances were calculated as characteristics. Lastly, the characteristics were compared with the standard threshold to determine whether there were defects. Experimental results show that this method is valid, and the detection average accuracy is over 90%.

Cross-Validation Estimation for Frequency-Dependent I/Q Imbalance in MIMO-OFDM Receivers

The effects of variation in RF, such as I/Q imbalance and filter mismatch, are extremely important for OFDM wireless accesses. This work presents a low-computational estimation of I/Q imbalances with filter mismatches to improve performance in MIMO-OFDM receivers. For N × N MIMO-OFDM systems, the proposed cross-validation estimation is such that, only N + 1 preambles are required to extract the mismatches of filters, gains and phases. With the estimated parameters, frequency-domain filters are exploited to correct frequency-dependent I/Q imbalances. Through performance evaluation of a 2 × 2 MIMO-OFDM system, with ideal channel estimations this study incurs a SNR loss of 1–1.2 dB to maintain a 10% PER at 1-dB gain error, 10°-phase error and the worst 180°-filter mismatch. In addition, this algorithm is well-matched to IEEE 802.11n and new specifications discussed in IEEE 802.11 VHT study group.

Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet Transforms

The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Q-factor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Q-factors (desirable for processing oscillatory signals) or the same low Q-factor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible 'constant-Q' discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2(R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the time-frequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform's redundancy and the flexibility allowed by frequency-domain filter design.

Robust low-complexity joint space–time–frequency channel estimation with transmit diversity in mobile wireless channels

In this paper, a robust low-complexity joint space–time–frequency channel estimation with transmit diversity in mobile wireless channels is proposed. Based on the orthogonal frequency division multiplexing (OFDM), the previously known training sequences are firstly blocked, space–frequency complex orthogonally encoded, up-converted and transmitted with diversity in the transmitter. In the receive end, each subchannel frequency response is estimated directly through the inverse pilot space–frequency complex orthogonally decoding. Wiener filtering and interpolating with the time- and frequency-domain correlations of the frequency response of the mobile wireless channels, low-complexity joint space–time–frequency channel estimator is finally constructed. In our proposed scheme, the high-level large-scale matrix inverse operations in traditional multiple input multiple output (MIMO) channel estimations are avoided. Separate and independent channel estimation corresponding to each pair of transmit and receive antennas in the MIMO space–frequency block coding system is achieved with transmit diversity, which can be used to significantly reduce the computation complexity with no degradation in system performance. Moreover, to successfully decoding the known pilot subblock coding matrix, it is only required that the fading channel keep approximately constant in each space–frequency coding subblock during one OFDM symbol block period. Making full use of the best time- and frequency-domain filtering, it makes our proposed scheme even more robust and accurate to estimate and track the channels with rapid time-varying dispersive fading. Numerical results are provided to validate the performance of our proposed channel estimators with diversity in mobile wireless channels.

Three filters for visualization of phase objects with large variations of phase gradients

We propose three amplitude filters for visualization of phase objects. They interact with the spectra of pure-phase objects in the frequency plane and are based on tangent and error functions as well as antisymmetric combination of square roots. The error function is a normalized form of the Gaussian function. The antisymmetric square-root filter is composed of two square-root filters to widen its spatial frequency spectral range. Their advantage over other known amplitude frequency-domain filters, such as linear or square-root graded ones, is that they allow high-contrast visualization of objects with large variations of phase gradients.

Enhanced Speech Features by Single-Channel Joint Compensation of Noise and Reverberation

For a natural verbal communication between humans and machines, automatic speech recognition, which works reasonably well on recordings captured with mid- or far-field microphones, is essential. While a lot of research and development are devoted to address one of the two distortions frequently encountered in mid- and far-field sound pickup, namely noise or reverberation, less effort has been undertaken to jointly combat both kinds of distortions. In our view, however, this is essential to further reduce the demolishing effect by moving the microphone away from the speaker's mouth because in real environments both kinds of distortions are present. In this paper, we propose a first step into this direction by integrating an estimate of the reverberation energy derived by an auxiliary model based on multistep linear prediction, into a framework, which, so far tracks and removes nonstationary additive distortion by particle filters in a low-dimension logarithmic power frequency domain. On actual recordings with different speaker-to-microphone distances, we observe that combating, in the feature space, either nonstationary noise or reverberation alone, on a single channel, is already able to improve speech recognition performance before and after acoustic model adaptation. Furthermore, we observe that a simple concatenation of techniques addressing either additive noise or reverberation can further improve the accuracy in some cases. Last but not least, we demonstrate that the joint estimation and removal of both kinds of distortions, as proposed in this publication, further improve the accuracy of the text output.

An effective and robust fingerprint enhancement by adaptive filtering in frequency domain

Extensive research of automatic fingerprint identification system (AFIS), although started in the early 1960s, has not yet give the answer to reliable fingerprint recognition problem. A critical step for AFIS accuracy is reliable extraction of features (mostly minutiae) from the input fingerprint image. However, the effectiveness of a feature extraction relies heavily on the quality of the input fingerprint images. This leads to the incorporation of a fingerprint enhancement module in fingerprint recognition system to make the system robust with respect to the quality of input fingerprint images. In this paper we propose an adaptive filtering in frequency domain in order to enhance fingerprint image. Two different directional filters are proposed and results are compared. .

Spectral Extraction Algorithm for LAMOST Two-dimensional Fiber-spectroscopic Images

This paper describes the method of spectral extraction to be used for the data processing of LAMOST's two-dimensional fiber-spectroscopic images. The effect of the selection of sampling points on the result of spectral extraction is analyzed. Based on the characteristics of Gaussian distribution functions and some experiments, the selection range of sampling points is defined, and the problem that some negative flux values appear in the result of spectral extraction is resolved. In addition, aiming at the problem that rather large errors exist in the result of spectral extraction under strong noise background, an improved extraction method based on the frequency-domain filtering is proposed. By using the FFT and low-pass filter, the sharp noises affecting the real fiber profiles are removed at first, before the normal spectral extraction is performed. Experiments and tests are made by using the simulative data provided by the data processing system of the LAMOST telescope, and the results indicate that the improved extraction method is feasible and effective.