یک رویکرد جدید برای طراحی فیلتر هموارساز با استفاده از معادلات دیفرانسیل تاخیری

نوع مقاله : مقاله پژوهشی

نویسنده

گروه علوم کامپیوتر، دانشکده علوم پایه، دانشگاه دولتی فسا، فسا، ایران

چکیده

از میان روش های حذف نویز سیگنال، فیلترهای هموارساز smoothness priors یا quadratic variation regularization توجه بسیار زیادی را در دهه­ گذشته به خود جلب کرده است. در این روشها، سیگنال مطلوب با استفاده از یک روش بهینه سازی تخمین زده می­شود که در آن از مشتقات سیگنال به عنوان عامل جریمه کننده استفاده می­ شود. اما این روشها فقط برای تخمین سیگنالهای توانی (polynomial signals) مفید هستند. در نتیجه بازدهی آنها در تخمین سیگنالهای غیرتوانی کاهش می ­یابد. برای جبران این محدودیت، در این مقاله، یک رویکرد جدید برای طراحی فیلتر هموارساز پیشنهاد می­شود که بر پایه معادله دیفرانسیل تاخیری می­ باشد. در این رویکرد، به جای مشتقات سیگنال از معادله دیفرانسیل تاخیری به عنوان عامل جریمه کننده استفاده می ­شود. به عنوان نمونه، از معادله دیفرانسیل تاخیری مدل MA در طراحی فیلتر هموارساز استفاده می­شود. فیلتر هموارسازMA  پیشنهادی در حوزه فرکانس آنالیز شده و نشان داده می ­شود که این فیلتر برای مقادیرکوچک اندازه پنجره، یک رفتارخوب در باند­فرکانسی ­گذر و باند­فرکانسی توقف از خود نشان می­ دهد. به عنوان یک کاربرد عملی، فیلتر هموارساز پیشنهادی برای حذف نویز سیگنال­های قلبی به­ کار گرفته می­شود. این روش، روی داده ­های واقعی موجود در پایگاه دادهPhysioNet PTB  آزمایش ­شده است. نتایج حاصل نشان می ­دهد که روش پیشنهادی در مقایسه با روش­ های قبلی، بهتر عمل می­ کند. 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A New Approach based Delay Differential Equation to Smoothing Filter Design

نویسنده [English]

  • Arman Kheirati Roonizi
Faculty of Computer Science, Fasa University, Fasa, Iran
چکیده [English]

Among the techniques that are used for signal denoising, smoothing filters have received significant attention during the past. However, these methods are particularly suited for polynomial signal smoothing. Therefore, their performance is significantly decreased for signals that cannot be well modelled with a polynomial function. To overcome this limitation, in this paper, we propose a new approach to smoothing filter design, which is based on the delay differential equation model. In this approach, we propose to substitute the derivative of the signal with a DDE model of the signal. As an example, a delay differential equation of moving average (MA) model is used as penalty term in the optimization problem. The results indicate that a better solution can be found by appropriate balancing a trade-off between the MA model of the signal and the minimum mean square error. The proposed MA smoothing filter is analyzed in frequency domain. It is shown that the proposed MA smoothing filter displays good properties within its pass-band and stop-band bands for small values of window length. As an application, the proposed MA smoothing filter was used for electrocardiogram (ECG) signal denoising. We tested the method over data from the PhysioNet PTB database. The results show that the proposed MA smoothing filter outperforms the original smoothness priors or QV regularization.

کلیدواژه‌ها [English]

  • Delay differential equation
  • Smoothing filter design
  • Estimation
  • Moving average
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