Related Experiment Video
Updated: Jul 7, 2026
11:54
Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles
Published on: March 13, 2017
Signal recovery by best feasible approximation
1Dept. of Electr. Eng., City Univ. of New York, NY.
Summary
New algorithms project signals onto set intersections for best feasible approximation. This advances signal recovery by finding the closest signal to a reference, improving upon existing feasibility methods with minimal added complexity.
Area of Science:
- Signal Processing
- Optimization Theory
- Set Theory
Background:
- Set theoretical signal recovery aims to find a signal within the intersection of sets representing available information.
- Existing feasibility algorithms like POCS do not find the best approximation of a reference signal.
Purpose of the Study:
- To introduce and apply novel methods for projecting a point onto the intersection of closed, convex sets.
- To enable signal recovery through best feasible approximation of a reference signal.
Main Methods:
- Development of algorithms for projecting a point onto the intersection of closed and convex sets in a Hilbert space.
- Application of these projection methods to signal recovery problems.
Main Results:
- The introduced algorithms effectively compute the projection of a reference signal onto the intersection of sets.
- These methods provide the best feasible approximation of the reference signal.
Conclusions:
- The new projection algorithms enhance signal recovery by finding the closest feasible signal to a reference.
- These methods offer a significant improvement over existing techniques with minimal computational overhead.
Related Concept Videos
01:18Aliasing
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...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
01:10Reconstruction 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...
01:15Sampling 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.
01:22Upsampling
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...
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.