Spectral density

SIGNAL (programming language)

Matched filter

Detector

Chebyshev filter

Algorithm

Statistics

Window (computing)

Signal-to-noise ratio (imaging)

Accounting

Operating system

Telecommunications

Selection (genetic algorithm)

Computer science

Filter (signal processing)

Binary Golay code

Adaptive filter

Business

Signal processing

Variance (accounting)

Database

Mathematics

Mathematical analysis

Artificial intelligence

Measure (data warehouse)

Programming language

Radar

Noise reduction

Mean squared error

Window function

Computer vision

IEEE Transactions on Instrumentation and Measurement

The Savitzky-Golay (SG) filtering is a widely used denoising method employed in different applications. The SG filter has two design parameters: the window length and the filter order. As the window length increases, the estimation variance is reduced, but at the same time, the bias error is increased. In this article, we obtain the optimal window length of an SG filter with an arbitrary order, based on minimizing the mean square error (mse), a well-known performance measure considering both the estimation bias and variance. To achieve the optimal window length, we propose an algorithm the performance of which is much better than the existing methods. In this article, we follow the viewpoint proposed by Persson and Strang and design the filter on the basis of the Chebyshev orthogonal polynomials.

Window Selection of the Savitzky–Golay Filters for Signal Recovery From Noisy Measurements