Article

Replikasi Signal dengan Menggunakan Metode Bootstrap

01/2008; DOI: 10.9744/jte.7.2.97-100
Source: OAI

ABSTRACT Signal can be modeled as a periodic or a nonperiodic stochastic process. Therefore to replicate a signal, we should keep the original character of the signal as well as the random character in it. One of plausible methods for doing such kind of job is bootstrap. However, we should modify the boostrap to accomodate the dependency in the series and their periodicities. As the pre bootraping we need to detect the existence of periodicities in the series. Two methods are given for detecting the existence of periodicities, i.e. the Fisher classical statistic, and the Chiu statistic. At the end we give an illustration. We used simulated data for testing and replicating a signal. Abstract in Bahasa Indonesia : Signal dapat dimodelkan sebagai proses stokastik yang berperiode ataupun tidak berperiode. Untuk itu dalam mereplikasi sebuah signal, kita harus tetap menjaga karakter asli dari signal dan juga sifat keacakannya. Salah satu metode yang mungkin untuk dilakukan adalah bootstrap. Namun demikian, kita harus memodifikasi metode bootrap ini untuk mengakomodasi sifat ketergantungan dari series beserta periodisitasnya. Sebagai langkah awal dalam bootstrap ini diperlukan uji ada tidaknya periodisitas dalam signal. Diberikan dua metode untuk mendeteksi periodisitas, yaitu Fisher statistik dan Chiu statistik dan sebuah ilustrasi dengan menggunakan data simulasi untuk menguji dan mereplikasi sebuah signal. Kata kunci: bootstrap, periodogram, fisher statistic

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    ABSTRACT: In this expository article, we give an introduction into the basics of bootstrap tests in gen- eral. We discuss the residual-based and the wild bootstrap for regression models suitable for applications in signal and image analysis. As an illustration of the general idea, we consider a particular test for detecting differences between two noisy signals or images which also works for noise with variable variance. The test statistic is essentially the integrated squared differ- ence between the signals after denoising them by local smoothing. Determining its quantile, which marks the boundary between accepting and rejecting the hypothesis of equal signals, is hardly possible by standard asymptotic methods whereas the bootstrap works well. Applied to the rows and columns of images, the resulting algorithm not only allows for the detection of defects but also for the characterization of their location and shape in surface inspection problems. AMS 2000 subject classifications. Primary: 62G09, 62P30 secondary: 62G08, 62M40.

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