An Error Analysis for the Sampling of Periodic Signals
نویسندگان
چکیده
|We analyze the representation of periodic signals in a scaling function basis. This representation is suÆciently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form expression for the approximation error in the scaling function representation. The error formula takes the simple form of a Parseval like sum, weighted by an appropriate error kernel. This formula may be useful in choosing the right representation for a class of signals. We also experimentally verify the theory in the particular case of description of closed curves.
منابع مشابه
A unified theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions
The article introduces cyclic dilation groups and finite affine groups for prime integers, and as an application of this theory it presents a unified group theoretical approach for the cyclic wavelet transform (CWT) of prime dimensional periodic signals.
متن کاملSampling of periodic signals: a quantitative error analysis
We present an exact expression for the 2 error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines , and bandlimited signal expansions. The formula takes the simple form of a Parseval’s-like relation, where the Fourier c...
متن کاملA Novel Sampling Approach in GNSS-RO Receivers with Open Loop Tracking Method
Propagation of radio occultation (RO) signals through the lower troposphere results in high phase acceleration and low signal to noise ratio signal. The excess Doppler estimation accuracy in lower troposphere is very important in receiving RO signals which can be estimated by sliding window spectral analysis. To do this, various frequency estimation methods such as MUSIC and ESPRIT can be adopt...
متن کاملOptimized Seizure Detection Algorithm: A Fast Approach for Onset of Epileptic in EEG Signals Using GT Discriminant Analysis and K-NN Classifier
Background: Epilepsy is a severe disorder of the central nervous system that predisposes the person to recurrent seizures. Fifty million people worldwide suffer from epilepsy; after Alzheimer’s and stroke, it is the third widespread nervous disorder.Objective: In this paper, an algorithm to detect the onset of epileptic seizures based on the analysis of brain electrical signals (EEG) has b...
متن کاملAdaptive Optimum Notch Filter for Periodic Noise Reduction in Digital Images
Periodic noises are unwished and spurious signals that create repetitive pattern on images and decreased the visual quality. Firstly, this paper investigates various methods for reducing the effects of the periodic noise in digital images. Then an adaptive optimum notch filter is proposed. In the proposed method, the regions of noise frequencies are determined by analyzing the spectral of noisy...
متن کامل