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انجام پروژه های مهندسی برق - جداسازی نویز از سیگنال با استفاده از تحلیل مولفه های اصلی یا PCA
جداسازی نویز از سیگنال با استفاده از تحلیل مولفه های اصلی یا PCA
چهارشنبه 23 دی 1394 ساعت 02:42 ب.ظ | نوشته ‌شده به دست رسول نیک بخت | ( نظرات )
[1] یک روش آماری است که با اعمال یک تبدیل متعامد به مجموعه از متغیرهای وابسته،  آن‌ها را به متغیرهای غیر وابسته خطی یا همان مؤلفه‌های اصلی تبدیل می‌کند.
جهت استفاده از این روش آماری ابتدا ماتریس کواریانس داده های موجود را تشکیل داده و سپس با محاسبه مقادیر ویژه این ماتریس و بردار های ویژه متناسب با آن،  تحلیل PCA را انجام می دهیم.
اگر توزیع مولفه های نویز در دسترس باشد (به عنوان مثال دارای توزیع گوسی باشند) و یا در حالت کلی تر مولفه های نویز مستقل از هم باشد می توان با استفاده از نتایج حاصل از Random Matrix theory مولفه های اصلی مربوط به نویز را از مولفه های اصلی مربوط به نویز جدا کرد.
شبیه سازی Matlab:



[1] Principal component analysis

به عنوان مثال در شکل زیر نویز گوسی موجود در یک سیگنال پهن باند به کمک تشکیل ماتریس کواریانس و تحلیل PCA جداسازی شده و تابع چگالی طیفی توان مقایسه ای رسم شده است.

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مرتبط با: Random Matrix Theory , Denoising ,


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