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Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

Downsampling

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Aliasing

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...

Deconvolution

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...

Sampling Theorem

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Optimum recursive filtering of noisy two-dimensional data with sequential parameter identification.

Y H Yum¹, S B Park

¹Department of Electrical Sciences, Korea Advanced Institute of Science and Technology, Seoul, Korea.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This summary is machine-generated.

This study introduces a new recursive estimation algorithm for minimum mean-square error (MMSE) filtering of 2D data. The method significantly improves signal-to-noise ratio (SNR) in real image processing applications.

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Area of Science:

Signal Processing
Image Analysis
Recursive Estimation

Background:

Minimum Mean-Square Error (MMSE) filtering is crucial for signal and image processing.
Existing methods may face challenges with complex 2D data models.
Accurate parameter identification is essential for effective filtering.

Purpose of the Study:

To develop a novel 2D recursive estimation algorithm for MMSE filtering.
To formulate an asymmetric half-plane Autoregressive Moving Average (ARMA) model for 2D data.
To address sequential parameter identification from noisy 2D data.

Main Methods:

Utilized an asymmetric half-plane model for 2D data.
Employed stochastic approximation for sequential parameter identification.
Combined parameter identification and estimation algorithms for experimental validation.

Main Results:

The proposed algorithm effectively solves the optimum filtering problem for 2D data.
Demonstrated successful sequential parameter identification from noisy data.
Achieved considerable improvement in Signal-to-Noise Ratio (SNR) on real image data.

Conclusions:

The developed 2D recursive estimation algorithm offers significant advantages for MMSE filtering.
The integration of stochastic approximation enhances parameter identification accuracy.
The method provides a robust solution for enhancing image quality and data analysis.