Removing Noise from Noisy Signal Data within Principal Component Analysis Framework

Abstract

The separation of noise from data represents one of the fundamental problems in signal processing. Principal component analysis (PCA) is a multivariate statistical technique that is employed in all scientific disciplines for the identification of patterns in data and the compression of data by reducing the size without significant loss of information. This paper concerns the removal of noise from noisy sinusoidal data using PCA. The aim is to achieve this by focusing on the separation of noise from signal data without estimating the parameters of sinusoidal signals. To this end, a code was developed in the Mathematica programming language, with modifications of its algorithm then being assessed on data derived from a number of noisy signals. The effectiveness of PCA was assessed by using the mean square error (MSE) values in relation to the variation in signal-to-noise ratio (SNR). The simulation results obtained demonstrate the effectiveness of PCA in removing noise from noisy sinusoidal signals.

Keywords

• Principal component analysis
• sinusoidal
• dimension reduction
• optimization

Temel Bileşenler Analizi Çerçevesinde Gürültülü Sinyal Verilerinden Gürültünün Giderilmesi

Abstract

Gürültünün verilerden ayrılması, sinyal işlemenin temel problemlerinden birini temsil etmektedir. Temel bileşen analizi (PCA), verilerdeki örüntülerin tanımlanması ve önemli bilgi kaybı olmadan boyutun küçültülerek verilerin sıkıştırılması için tüm bilimsel disiplinlerde kullanılan çok değişkenli bir istatistiksel tekniktir. Bu makale, PCA kullanarak gürültülü sinüzoidal verilerden gürültünün giderilmesi ile ilgilenmektedir. Amaç, sinüzoidal sinyallerin parametrelerini tahmin etmeden sinyal verilerinden gürültünün ayrılmasına odaklanarak bunu başarmaktır. Bunun için, Mathematica programlama dilinde bir kod geliştirilmiş ve algoritmasının modifikasyonları daha sonra bir dizi gürültülü sinyalden elde edilen veriler üzerinde değerlendirilmiştir. PCA'nın etkinliği, sinyal-gürültü oranındaki (SNR) değişime bağlı olarak ortalama kare hata (MSE) değerleri kullanılarak değerlendirilmiştir. Elde edilen simülasyon sonuçları, PCA'nın gürültülü sinüzoidal sinyallerdeki gürültüyü gidermedeki etkinliğini göstermektedir.

Keywords

• Temel bileşenler analizi
• sinüzoidal
• boyut azaltma
• optimizasyon

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