A class of Wiener filters useful in PLL APPLICATIONS.
Wiener filters in phase locked loop design, noting tracking function for orbital trajectory, derivation of optimum filter and noise bandwidth
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Wiener filters in phase locked loop design, noting tracking function for orbital trajectory, derivation of optimum filter and noise bandwidth
The effectivity of multichannel Wiener filters to improve images obtained with passive microwave systems was investigated by applying Wiener filters to passive microwave images of first-year sea ice. Four major parameters which define the filter were varied: the lag or pixel offset between the original and the desired scenes, filter length, the number of lines in the filter, and the weight applied to the empirical correlation functions. The effect of each variable on the image quality was assessed by visually comparing the results. It was found that the application of multichannel Wiener theory to passive microwave images of first-year sea ice resulted in visually sharper images with enhanced textural features and less high-frequency noise. However, Wiener filters induced a slight blocky grain to the image and could produce a type of ringing along scan lines traversing sharp intensity contrasts.
Synthetic aperture radar (SAR) images are degraded by speckle. A multiplicative speckle noise model for SAR images is presented. Using this model, a Wiener filter is derived by minimizing the mean-squared error using the known speckle statistics. Implementation of the Wiener filter is discussed and experimental results are presented. Finally, possible improvements to this method are explored.
A novel approach to the reduction of scattered, interfering signals that corrupt measurements of the signal backscattered from radar targets of interest is being developed. It is being explored with sphere measurements in an indoor microwave radar range. This method is based on the concept of Wiener filtering (which minimizes the difference between the signal plus noise and the desired signal in the time domain). In contrast to the traditional Wiener filter, in which the time domain error between two sequences are minimized, the approach reported uses the frequency domain phasor amplitudes of a swept frequency signal. It minimizes the difference (least-mean-square-magnitude) between the signal-plus-noise and the signal complex phasors, across the entire spectrum.
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In this paper, a technique is developed to improve the image quality of an object in three-dimensional reconstruction by a weighted average of successive overlapping two-dimensional sections of the object. It is demonstrated that the signal-to-noise ratio of a two-dimensional picture can be improved by roughly a factor of 2 for typical X-ray beam shapes.
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We derive an optimal linear filter to suppress the noise from the cosmic background explorer satellite (COBE) Differential Microwave Radiometer (DMR) sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within 20 deg of the Galactic plane from the data. We are able to identify particular hot and cold spots in the filtered maps at a level 2 to 3 times the noise level. We use the formalism of constrained realizations of Gaussian random fields to assess the uncertainty in the filtered sky maps. In addition to improving the signal-to-noise ratio of the map as a whole, these techniques allow us to recover some information about the cosmic microwave background anisotropy in the missing Galactic plane region. From these maps we are able to determine which hot and cold spots in the data are statistically significant, and which may have been produced by noise. In addition, the filtered maps can be used for comparison with other experiments on similar angular scales.
Approximations to wiener optimum filters and predictors
The Wiener filter is formulated as a function of the basic image-gathering and image-reconstruction constraints, thereby providing a method for minimizing the mean-squared error between the (continuous-input) radiance field and its restored (continuous-output) representation. This formulation of the Wiener filter is further extended to the Wiener-characteristic filter, which provides a method for explicitly specifying the desired representation. Two specific examples of Wiener filters are presented.
An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels. The algorithm is based on a comprehensive, end-to-end imaging system model that accounts for the important components of the imaging process: the statistics of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and display reconstruction. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernel values that restore the image with maximum fidelity, that is, the kernel minimizes the expected mean-square restoration error. The algorithm is consistent with the derivation of the spatially unconstrained Wiener filter, but leads to a small, spatially constrained kernel that, unlike the unconstrained filter, can be efficiently implemented by convolution. Simulation experiments demonstrate that for a wide range of imaging systems these small kernels can restore images with fidelity comparable to images restored with the unconstrained Wiener filter.
A deconvolution method is presented for estimating input data from measured output data and a model of the dynamic process involved. The method uses an optimal Wiener filter for separating the measured data into signal and noise components, and a high-accuracy Fourier transform for inverting the model dynamics in the frequency domain. The method is an extension of optimal Fourier smoothing, and uses a technique to enhance the contrast between the signal and noise spectra in designing the Wiener filter. The deconvolution method was applied to simulation and flight test data for the purposes of removing unwanted distortions introduced by signal-conditioning filters and sensor dynamics, and for reconstructing turbulence inputs from measured sensor data. Results indicated hat the method performs well given good signal-to-noise levels and accurate models of the dynamic process.
been proposed for receiving weak single- channel phase-modulated radio signals bearing low-rate-turbo-coded binary data. Originally intended for use in receiving telemetry signals from distant spacecraft, the proposed receiver/ decoders may also provide enhanced reception in mobile radiotelephone systems. A radio signal of the type to which the proposal applies comprises a residual carrier signal and a phase-modulated data signal. The residual carrier signal is needed as a phase reference for demodulation as a prerequisite to decoding. Low-rate turbo codes afford high coding gains and thereby enable the extraction of data from arriving radio signals that might otherwise be too weak. In the case of a conventional receiver, if the signal-to-noise ratio (specifically, the symbol energy to one-sided noise power spectral density) of the arriving signal is below approximately 0 dB, then there may not be enough energy per symbol to enable the receiver to recover properly the carrier phase. One could solve the problem at the transmitter by diverting some power from the data signal to the residual carrier. A better solution . a coupled receiver/decoder according to the proposal . could reduce the needed amount of residual carrier power. In all that follows, it is to be understood that all processing would be digital and the incoming signals to be processed would be, more precisely, outputs of analog-to-digital converters that preprocess the residual carrier and data signals at a rate of multiple samples per symbol. The upper part of the figure depicts a conventional receiving system, in which the receiver and decoder are uncoupled, and which is also called a non-data-aided system because output data from the decoder are not used in the receiver to aid in recovering the carrier phase. The receiver tracks the carrier phase from the residual carrier signal and uses the carrier phase to wipe phase noise off the data signal. The receiver typically includes a phase-locked loop (PLL) or Costas loop that requires no delay or perhaps a single sample delay. The lower part of the figure depicts a basic coupled receiver/decoder . a data-aided system that would implement an iterative receiving/decoding process. The receiver would include a PLL or a Wiener filter that, to the extent possible, would track the residual carrier signal, wipe phase noise off the data signal, then send the result to the turbo decoder. Recovery of timing could be effected by, for example, a digital transition tracking loop (DTTL) or other, similar loop. The first iteration of turbo decoding would yield soft data symbols, which would be sent back to the receiver for use in softly wiping off the data signal in an effort to recover the residual carrier signal. The wiped signal would contain a relatively large carrier-phase component that could be tracked by use of a second Wiener filter.
A spatial domain adaptive Wiener filter for smoothing radar images corrupted by multiplicative noise is presented. The filter is optimum in a minimum mean squared error sense, computationally efficient, and preserves edges in the image better than other filters. The proposed algorithm can also be used for processing optical images with illumination variations that have a multiplicative effect.
Wiener filtering theory for stationary ergodic inputs with known spectral densities and optimal control transfer functions of random-input nonlinear saturating systems with random unwanted disturbances
In many aerodynamic measurement applications, the ability to make time-accurate measurements with pressure scanners provides practical advantages over making the same measurements directly using flush-mounted transducers. The pneumatic distortion due to the tubing between the sensing module and surface port limits the usefulness of such measurements to averaged, steady data only. This issue has restricted the application of pressure scanners for unsteady pressure measurements in wind tunnel and flight-testing applications. The Wiener-filtered inverse system response model has been proven to be effective in reconstructing complex unsteady pressure signals acquired remotely using pressure scanners. In this work, the feasibility of using pressure scanning systems for time-resolved pressure measurements in the NASA Langley 14- by 22-Foot Subsonic Wind Tunnel was evaluated. Results demonstrated good agreement between the reference transducers and reconstructed pressure scanner measurements up to frequencies of approximately 500 Hz.