‫ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﻲ‬
‫ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﭼﻨﺪﺭﺳﺎﻧﻪﺍﻱ )‪(۴۰-۳۴۲‬‬
‫ﺩﺍﻧﺸﻜﺪﻩ ﻣﻬﻨﺪﺳﻲ ﻛﺎﻣﭙﻴﻮﺗﺮ‬
‫ﺗﺮﻡ ﺑﻬﺎﺭ ‪۱۳۸۶‬‬
‫ﺩﻛﺘﺮ ﺣﻤﻴﺪﺭﺿﺎ ﺭﺑﻴﻌﻲ‬
‫ﺗﻜﻠﻴﻒ ﺷﻤﺎﺭﻩ ‪ :۱‬ﺩﻳﺠﻴﺘﺎﻝ ﻛﺮﺩﻥ ﺻﻮﺕ ﻭ ﺗﺒﺪﻳﻞ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‬
‫‪ -١‬ﻣﻘﺪﻣﻪ‬
‫ﺩﺭ ﻳﻚ ﻣﻴﻜﺮﻭﻓﻮﻥ‪ ،‬ﺍﻣﻮﺍﺝ ﻓﺸﺎﺭ ﺻﺪﺍﻱ ﻓﻴﺰﻳﻜﻲ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺍﻟﻜﺘﺮﻳﻜﻲ ﻣﺘﻨﺎﻇﺮ ﺑﺎ ﺧﻮﺩ‪ ،‬ﺑﻪ ﻭﺳﻴﻠﻪ ﻣﺒﺪﻟﻬﺎﻱ ﺁﻛﻮﺳﺘﻴﻜﻲ ﻧﻈﻴﺮ ﻣﻴﻜﺮﻭﻓﻮﻥ ﻳﺎ‬
‫‪ Phonograph cartridge‬ﺗﺒﺪﻳﻞ ﻣﻲ ﺷﻮﻧﺪ‪ .‬ﺧﺮﻭﺟﻲ ﺍﻟﻜﺘﺮﻳﻜﻲ ﻣﺒﺪﻝ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺁﻧﺎﻟﻮﮒ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ ،‬ﺯﻳﺮﺍ ﺳﻴﮕﻨﺎﻝ ﺍﻟﻜﺘﺮﻳﻜﻲ‬
‫ﻣﺸﺎﺑﻪ ﺍﻟﮕﻮﻱ ﻓﺸﺎﺭ ﻣﻮﺝ ﺻﻮﺗﻲ ﺍﺳﺖ ﻛﻪ ﺁﻥ ﺭﺍ ﺑﻮﺟﻮﺩ ﺁﻭﺭﺩﻩ ﺍﺳﺖ‪ .‬ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺕ ﺑﻪ ﺻﻮﺭﺕ ﺍﻟﮕﻮﻫﺎﻱ ﻣﻮﺝ ﺩﻭﺑﻌﺪﻱ ﻣﻲ ﺑﺎﺷﻨﺪ ﻛﻪ‬
‫ﻣﺤﻮﺭ ‪ y‬ﻧﺸﺎﻥ ﺩﻫﻨﺪﺓ ﺷﺪﺕ ﻳﺎ ﺩﺍﻣﻨﻪ ﻭ ﻣﺤﻮﺭ ‪ x‬ﻧﺸﺎﻥ ﺩﻫﻨﺪﺓ ﻣﺴﻴﺮ ﺯﻣﺎﻥ ﻫﺴﺘﻨﺪ‪ ،‬ﺷﻜﻞ ‪ ،١‬ﺷﻜﻞ ﻣﻮﺝ ﺁﻧﺎﻟﻮﮒ ﺍﺯ ﻳﻚ ﺳﺮﻱ ﻣﻮﺟﻬﺎﻱ‬
‫ﺻﻮﺕ ﺍﺯ ﻳﻚ ‪ chime‬ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺍﻳﻦ ﺳﺮﻱ ﻣﻮﺟﻬﺎ ﺑﻪ ﻭﺳﻴﻠﻪ ﻣﻴﻜﺮﻭﻓﻮﻥ ﻭ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪﻩ ﺑﻪ ﻭﻟﺘﺎﮊ ﺁﻧﺎﻟﻮﮒ ﺑﺎ ﺣﺪﺍﻛﺜﺮ ﺩﺍﻣﻨﺔ ‪± 0.5‬‬
‫ﻭﻟﺖ )ﺩﺍﻣﻨﺔ ﻗﻠﻪ ﺑﻪ ﻗﻠﻪ ﻳﺎ ‪ (VPP‬ﺗﺒﺪﻳﻞ ﺷﺪﻩ ﺍﻧﺪ‪.‬‬
‫ﺷﮑﻞ‪ -١‬ﺷﻜﻞ ﻣﻮﺝ ﻣﻌﻤﻮﻝ ﺻﻮﺕ‬
‫ﻓﺮﻛﺎﻧﺲ ﻳﻚ ﻣﻮﺝ ﺑﻪ ﻭﺳﻴﻠﻪ ﺯﻣﺎﻥ ﺳﭙﺮﻱ ﺷﺪﻩ ﺑﻴﻦ ﺗﻜﺮﺍﺭﻫﺎ ﺗﻌﻴﻴﻦ ﻣﻲﺷﻮﺩ ﻛﻪ ﻃﻮﻝ ﻣﻮﺝ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ .‬ﺑﻴﺸﺘﺮ ﻣﻮﺟﻬﺎﻱ ﺻﻮﺕ ﺩﻗﻴﻘﺎﹰ‬
‫ﺗﻜﺮﺍﺭ ﻧﻤﻲ ﺷﻮﻧﺪ ﺍﻣﺎ ﻣﻲ ﺗﻮﺍﻥ ﻳﻚ ﺍﻟﮕﻮﻱ ﻣﺸﺨﺺ ﺩﺭ ﺷﻜﻞ ﻣﻮﺟﻲ ﻛﻪ ﺗﻮﺳﻂ ﺑﻴﺸﺘﺮ ﺳﺎﺯﻫﺎﻱ ﻣﻮﺳﻴﻘﻲ ﺍﻳﺠﺎﺩ ﻣﻲﺷﻮﺩ‪ ،‬ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ‪ .‬ﻃﻮﻝ‬
‫ﻣﻮﺝ ﻳﻚ ﺻﻮﺕ ﺍﻟﻜﺘﺮﻳﻜﻲ‪ ، λ ،‬ﺩﺭ ﻣﻘﻴﺎﺱ ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﻳﺎ ﻣﻴﻜﺮﻭﺛﺎﻧﻴﻪ ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ‪ .‬ﻓﺮﻛﺎﻧﺲ‪ ،F،‬ﻛﻪ ﺑﺎ ﻭﺍﺣﺪ ﻫﺮﺗﺰ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻣﻲﺷﻮﺩ‬
‫‪1‬‬
‫)ﺗﻌﺪﺍﺩ ﺩﻭﺭ ﺩﺭ ﻫﺮ ﺛﺎﻧﻴﻪ( ﻣﻌﻜﻮﺱ ‪ λ‬ﻣﻲ ﺑﺎﺷﺪ‪ ،‬ﻳﻌﻨﻲ‬
‫‪λ‬‬
‫ﺻﺪﺍﻱ ﺑﺸﺮ ﻳﺎ ﺻﺪﺍﻫﺎﻱ ﺗﻮﻟﻴﺪ ﺷﺪﻩ ﺑﻪ ﻭﺳﻴﻠﻪ ﺳﺎﺯﻫﺎﻱ ﻣﻮﺳﻴﻘﻲ ﻣﻲﺗﻮﺍﻧﻨﺪ ﺑﻪ ﻳﻚ ﻣﻮﺝ ﭘﺎﻳﻪ ﻭ ﻣﻮﺟﻬﺎﻱ ﻣﺘﻌﺪﺩ ﺍﻟﺤﺎﻗﻲ ﺩﻳﮕﺮ ﺗﻘﺴﻴﻢ ﺷﻮﻧﺪ‪.‬‬
‫= ‪.F‬‬
‫ﻣﻮﺟﻬﺎﻱ ﺍﻟﺤﺎﻗﻲ ﻛﻪ ﺑﻪ ﻣﻮﺝ ﭘﺎﻳﻪ ﺍﻋﻤﺎﻝ ﺷﺪﻩ ﺍﻧﺪ‪ overtone ،‬ﻧﺎﻣﻴﺪﻩ ﻣﻲ ﺷﻮﻧﺪ‪Overton .‬ﻫﺎ ﻣﻮﺟﻬﺎﻱ ﻓﺮﻛﺎﻧﺲ ﺑﺎﻻﺗﺮﻣﯽ ﺑﺎﺷﻨﺪ ﻭ ﺑﺎ‬
‫ﻓﺮﻛﺎﻧﺲ ﻫﺎﻳﻲ ﻛﻪ ﺿﺮﺍﻳﺒﻲ ﺍﺯ ﻣﻮﺝ ﭘﺎﻳﻪ ﻣﻲ ﺑﺎﺷﻨﺪ )ﻫﺎﺭﻣﻮﻧﻴﻚ ﻫﺎ( ﺑﻪ ﺻﺪﺍ‪ ،‬ﻣﺸﺨﺼﺎﺕ ﻳﻚ ﺻﻮﺕ ﺑﺸﺮﻱ ﻳﺎ ﺻﻮﺕ ﺳﺎﺯﻫﺎﻱ ﻣﻮﺳﻴﻘﻲ ﺭﺍ‬
‫ﻣﻲ ﺑﺨﺸﻨﺪ‪ .‬ﻫﻨﮕﺎﻣﻲ ﻛﻪ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺩﻳﺠﻴﺘﺎﻝ ﺗﺒﺪﻳﻞ ﻣﻲﺷﻮﺩ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺴﺘﮕﻲ ﺑﻪ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ‬
‫‪overtone‬ﻫﺎﻱ ﻣﻮﺟﻮﺩ ﺩﺭ ﺳﻴﮕﻨﺎﻝ ﺩﺍﺭﺩ‪.‬‬
‫‪1‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﺷﻤﺎ ﺍﻣﻜﺎﻥ ﺑﺎﺯﻱ ﺑﺎ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ﻧﺮﺥ ﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﺩﺍﺭﻳﺪ‪ ،‬ﻛﻪ ﻛﻴﻔﻴﺖ ﻫﺎﻱ ﻣﺨﺘﻠﻔﻲ‬
‫ﺍﺯ ﺻﻮﺕ ﺭﺍ ﻋﺮﺿﻪ ﻣﻲ ﻛﻨﻨﺪ‪.‬‬
‫‪ -٢‬ﺗﺌﻮﺭﻱ‬
‫‪ -١-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﭘﻴﻮﺳﺘﻪ ﻭ ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‬
‫ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺕ ﺍﺯ ﻧﻮﻉ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﭘﻴﻮﺳﺘﻪ )ﺁﻧﺎﻟﻮﮒ( ﻫﺴﺘﻨﺪ ﻛﻪ ﺑﻪ ﺗﺪﺭﻳﺞ ﺑﺎ ﻧﻘﺼﺎﻥ ﻳﺎﻓﺘﻦ ﻣﻨﺒﻊ ﺻﺪﺍ‪ ،‬ﺍﻓﺖ ﺩﺍﻣﻨﻪ ﭘﻴﺪﺍ ﻣﻲﻛﻨﻨﺪ‪ .‬ﺍﺯ ﺳﻮﻱ‬
‫ﺩﻳﮕﺮ‪ ،‬ﻛﺎﻣﭙﻴﻮﺗﺮﻫﺎ‪ ،‬ﺩﺍﺩﻩ ﻫﺎﻱ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﺩﻳﺠﻴﺘﺎﻝ ﺫﺧﻴﺮﻩ ﻣﻲ ﻛﻨﻨﺪ‪ :‬ﻳﻚ ﺭﺷﺘﻪ ‪ stream‬ﺍﺯ ﺑﻴﺘﻬﺎﻱ ﺻﻔﺮ ﻭ ﻳﻚ‪ .‬ﺩﺍﺩﻩ ﻫﺎﻱ ﺩﻳﺠﻴﺘﺎﻝ‬
‫ﻃﺒﻴﻌﺘﺎﹰ ﮔﺴﺴﺘﻪ ﻫﺴﺘﻨﺪ ﺯﻳﺮﺍ ﻣﻘﺪﺍﺭ ”‪ “0‬ﻳﺎ ”‪ “1‬ﺩﺍﺩﺓ ﺩﻳﺠﻴﺘﺎﻝ ﻓﻘﻂ ﺩﺭ ﻳﻚ ﻟﺤﻈﺔ ﻣﺸﺨﺺ ﻣﻌﺘﺒﺮ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ‪ ،‬ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺁﻧﺎﻟﻮﮒ‬
‫ﻛﻪ ﭘﻴﻮﺳﺘﻪ ﺍﺳﺖ ﺑﺎﻳﺪ ﺑﻪ ﻓﺮﻡ ﺩﻳﺠﻴﺘﺎﻟﻲ ﻧﺎﭘﻴﻮﺳﺘﻪ ﺗﺒﺪﻳﻞ ﺷﻮﺩ ﺗﺎ ﻛﺎﻣﭙﻴﻮﺗﺮ ﺗﻮﺍﻧﺎﻳﻲ ﺫﺧﻴﺮﻩ ﻳﺎ ﭘﺮﺩﺍﺯﺵ ﺻﻮﺕ ﺭﺍ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﺍﻟﺒﺘﻪ ﺩﺍﺩﺓ ﺩﻳﺠﻴﺘﺎﻝ‬
‫ﺩﻭﺑﺎﺭﻩ ﺑﺎﻳﺪ ﺑﻪ ﻓﺮﻡ ﺁﻧﺎﻟﻮﮒ ﺗﺒﺪﻳﻞ ﺷﻮﺩ ﺗﺎ ﺍﺯ ﻃﺮﻳﻖ ﻳﻚ ﺳﻴﺴﺘﻢ ﺻﻮﺗﻲ ﻗﺎﺑﻞ ﺷﻨﻴﺪﻥ ﺑﺎﺷﺪ‪ .‬ﺗﺒﺪﻳﻞ ﺩﻭ ﻃﺮﻓﻪ ﺑﻴﻦ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺁﻧﺎﻟﻮﮒ ﻭ‬
‫ﺩﻳﺠﻴﺘﺎﻝ‪ ،‬ﻋﻤﻠﻴﺎﺕ ﺍﻭﻟﻴﻪ ﺗﻤﺎﻡ ﻛﺎﺭﺗﻬﺎﻱ ‪ adapter‬ﻭ ﻛﺎﺭﺗﻬﺎﻱ ﺻﺪﺍ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫‪ -١-١-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺗﻨﺎﻭﺑﻲ ﻭ ﺗﺒﺪﻳﻞ ﺁﻧﺎﻟﻮﮒ ﺑﻪ ﺩﻳﺠﻴﺘﺎﻝ‬
‫ﺭﻭﺵ ﻣﻌﻤﻮﻝ ﻧﻤﺎﻳﺶ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﺍﺯ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ – ﭘﻴﻮﺳﺘﻪ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺘﻨﺎﻭﺏ )ﭘﺮﻳﻮﺩﻳﻚ( ﺍﺳﺖ ﻛﻪ ﺩﺭ ﺁﻥ‬
‫ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ]‪ x[n‬ﺍﺯ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ ﭘﻴﻮﺳﺘﻪ )‪ xc(t‬ﻣﻄﺎﺑﻖ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ‪.‬‬
‫)‪(١-٢‬‬
‫ﺷﮑﻞ‪ -٢‬ﻳﻚ ﻣﺒﺪﻝ ﺁﻧﺎﻟﻮﮒ ﺑﻪ ﺩﻳﺠﻴﺘﺎﻝ )‪ (A/D‬ﺍﻳﺪﻩ ﺁﻝ‬
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‫ﺩﺭ ﺭﺍﺑﻄﺔ )‪ T ،(١-٢‬ﺗﻨﺎﻭﺏ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻭ ﻣﻌﻜﻮﺱ ﺁﻥ‪،‬‬
‫‪T‬‬
‫ﻫﺮﺗﺰ )‪ (Hz‬ﻧﻤﺎﻳﺶ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ ،‬ﻣﯽ ﺑﺎﺷﻨﺪ‪ .‬ﻣﺎ ﻳﻚ ﺳﻴﺴﺘﻢ ﺭﺍ ﻛﻪ ﺭﺍﺑﻄﺔ )‪ (١-٢‬ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﻚ ﻣﺒﺪﻝ ﺍﻳﺪﻩ ﺁﻝ ﭘﻴﻮﺳﺘﻪ – ﺑﻪ – ﮔﺴﺴﺘﻪ‬
‫= ‪ ، f s‬ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺑﺮ ﺣﺴﺐ ﻧﻤﻮﻧﻪ ﺑﺮ ﺛﺎﻧﻴﻪ ﻛﻪ ﻣﻌﻤﻮﻻﹰ ﺑﺮ ﺣﺴﺐ‬
‫)‪ (C/D‬ﻋﻤﻠﻲ ﻣﻲ ﻛﻨﺪ ﺩﺭ ﺷﻜﻞ ‪ ٢‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺍﻳﻢ‪ .‬ﺑﺮﺍﻱ ﺫﺧﻴﺮﺓ ﻣﻘﺎﺩﻳﺮ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺗﻮﺳﻂ ﻛﺎﻣﭙﻴﻮﺗﺮ ﺑﺎ ﺩﻗﺖ ﻣﺤﺪﻭﺩ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﭘﻴﻮﺳﺘﻪ‬
‫ﺑﺎﻳﺪ ﺑﻪ ﻳﻚ ﺳﺮﻱ ﻣﻘﺎﺩﻳﺮ ﺍﺯ ﭘﻴﺶ ﺗﻌﻴﻴﻦ ﺷﺪﻩ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﻮﻧﺪ‪ .‬ﻋﻤﻠﻴﺎﺕ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺩﻗﻴﻘﺎﹰ ﻫﻤﺎﻥ ﻋﻤﻠﻴﺎﺗﻲ ﺍﺳﺖ ﻛﻪ ﺩﺭ‬
‫ﻣﺒﺪﻝ ﺁﻧﺎﻟﻮﮒ – ﺑﻪ – ﺩﻳﺠﻴﺘﺎﻝ‪ ،‬ﻳﺎ ﺩﻳﺠﻴﺘﺎﻝ – ﺑﻪ – ﺁﻧﺎﻟﻮﮒ‪ ،‬ﺑﻪ ﺻﻮﺭﺕ ﺑﺮﻋﻜﺲ‪ ،‬ﺻﻮﺭﺕ ﻣﻲ ﮔﻴﺮﺩ‪ .‬ﺑﻴﺸﺘﺮ ﻛﺎﺭﺗﻬﺎﻱ ﺻﺪﺍ ﻗﺎﺑﻠﻴﺖ ﺫﺧﻴﺮﻩ‬
‫ﺻﺪﺍ ﺭﺍ ﻫﻢ ﺑﻪ ﺻﻮﺭﺕ ‪ ٨‬ﺑﻴﺘﻲ ﻭ ﻫﻢ ‪ ١٦‬ﺑﻴﺘﻲ‪ ،‬ﺑﺮﺍﻱ ﻛﻴﻔﻴﺖ ﻫﺎﻱ ﺑﺎﻻﺗﺮ ﺻﻮﺗﻲ ﺩﺍﺭﻧﺪ‪.‬‬
‫‪ -٢-١-٢‬ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‬
‫ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺑﻪ ﻣﺎ ﻣﻲ ﮔﻮﻳﺪ ﻛﻪ ﭼﻪ ﺍﻧﺪﺍﺯﻩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺎ ﻣﻲ ﺗﻮﺍﻧﺪ ﺳﺮﻳﻊ ﺑﺎﺷﺪ ﺗﺎ ﻧﻤﺎﻳﺶ ﺑﻬﺘﺮﻱ ﺍﺯ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺩﺍﺷﺘﻪ ﺑﺎﺷﻴﻢ ‪.‬‬
‫ﻣﻲ ﺩﺍﻧﻴﻢ ﻛﻪ ﺍﮔﺮ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺗﻐﻴﻴﺮﺍﺕ ﺧﻴﻠﻲ ﺳﺮﻳﻊ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ ،‬ﻣﺎ ﻫﻢ ﺑﺎﻳﺪ ﺩﺭ ﻓﺎﺻﻠﻪ ﻫﺎﻱ ﻧﺰﺩﻳﻜﺘﺮﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﻨﻴﻢ ﺗﺎ ﻫﻴﭻ ﺗﻐﻴﻴﺮ‬
‫ﻣﻴﺎﻧﻲ ﺭﺍ ﺍﺯ ﺩﺳﺖ ﻧﺪﻫﻴﻢ‪ .‬ﻳﻚ ﻣﺜﺎﻝ ﺧﻮﺏ‪ ،‬ﻧﻤﺎﻳﺶ ﺳﻬﺎﻡ ﺑﻮﺭﺱ ﺑﺮ ﺣﺴﺐ ﻧﻤﺎﻳﺶ ﻭﺿﻊ ﻫﻮﺍ ﺍﺳﺖ‪ .‬ﺍﺯ ﺁﻧﺠﺎ ﻛﻪ ﺗﻐﻴﻴﺮﺍﺕ ﺑﻮﺭﺱ ﺑﺴﻴﺎﺭ‬
‫‪2‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺳﺮﻳﻊ ﺍﺳﺖ‪ ،‬ﺑﻪ ﻃﻮﺭ ﻣﻌﻤﻮﻝ ﺑﺎﻳﺪ ﻫﺮﭼﻨﺪ ﺩﻗﻴﻘﻪ ﻳﻜﺒﺎﺭ ﺍﻋﻼﻡ ﺷﻮﺩ‪ ،‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ‪ ،‬ﺩﺭﺑﺎﺭﺓ ﻭﺿﻊ ﻫﻮﺍ‪ ،‬ﻧﻤﺎﻳﺶ ﺍﻳﻦ ﺗﻐﻴﻴﺮﺍﺕ ﺩﺭ ﻫﺮ ﺳﺎﻋﺖ‬
‫ﻛﺎﻓﻲ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬
‫ﺣﺎﻻ‪ ،‬ﻧﮕﺎﻫﻲ ﺑﻪ ﺗﺌﻮﺭﻱ ﺗﻨﺎﻭﺏ ‪ T‬ﻣﻲ ﺍﻧﺪﺍﺯﻳﻢ ﻛﻪ ﭼﻪ ﺍﻧﺪﺍﺯﻩ ﺩﻗﻴﻖ ﺑﺎﻳﺪ ﺁﻥ ﺭﺍ ﺗﻌﻴﻴﻦ ﻛﺮﺩ‪.‬‬
‫ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‪ :‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ ﻛﻪ )‪ xc(t‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎ ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﻭ )‪ X c ( jΩ‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺁﻥ ﺍﺳﺖ ﻛﻪ‬
‫ﺷﺮﻁ ﺯﻳﺮ ﺭﺍ ﺑﺮﺁﻭﺭﺩﻩ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫)‪(٢-٢‬‬
‫ﭘﺲ )‪ xc(t‬ﻣﻨﺤﺼﺮﺍﹰ ﺗﻮﺳﻂ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ) ‪ n = 0,±1,±2,..., x[n] = xc (nT‬ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ ﺑﻪ ﺷﺮﻃﻲ ﻛﻪ ﺗﻨﺎﻭﺏ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺁﻥ ﻳﺎ‬
‫ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ‪ Ω s‬ﺷﺮﻁ ﺯﻳﺮ ﺭﺍ ﺑﺮﺁﻭﺭﺩﻩ ﻛﻨﺪ‪.‬‬
‫)‪(٣-٢‬‬
‫ﻧﺘﻴﺠﻪ ﻓﻮﻕ ﺍﺑﺘﺪﺍ ﺗﻮﺳﻂ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﺑﺪﺳﺖ ﺁﻣﺪ ﻛﻪ ﺑﻪ ﻧﺎﻡ ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﻣﺸﻬﻮﺭ ﺷﺪ‪ .‬ﻓﺮﻛﺎﻧﺲ ‪ 2Ω N‬ﻛﻪ ﺑﺎﻳﺪ ﺍﺯ‬
‫ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﻮﭼﻜﺘﺮ ﺑﺎﺷﺪ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ .‬ﺑﺮﺍﻱ ﺍﺛﺒﺎﺕ ﺗﺌﻮﺭﻱ ﻓﻮﻕ‪ X(ejw) ،‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ‬
‫ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﺩﻧﺒﺎﻟﺔ ]‪ x[n‬ﺭﺍ ﺑﺮ ﺣﺴﺐ )‪ ، X c ( jΩ‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﭘﻴﻮﺳﺘﻪ )‪ ،xc(t‬ﺑﺪﺳﺖ ﻣﻲ ﺁﻭﺭﻳﻢ‪.‬‬
‫ﺑﻪ ﻫﻤﻴﻦ ﻣﻨﻈﻮﺭ ﺳﻴﮕﻨﺎﻝ ﻗﻄﺎﺭ ﺿﺮﺑﻪ ﺯﻳﺮ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ‪.‬‬
‫)‪(٤-٢‬‬
‫ﻣﻲ ﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﻛﻪ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ )‪ xs(t‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﻲ ﺑﺎﺷﺪ‪:‬‬
‫)‪(٥-٢‬‬
‫ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﻌﺮﻳﻒ‬
‫)‪(٦-٢‬‬
‫)‪(٧-٢‬‬
‫ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ‬
‫)‪(٨-٢‬‬
‫ﺍﺯ ﺭﻭﺍﺑﻂ )‪ (٥-٢‬ﻭ )‪ (٨-٢‬ﻧﺘﻴﺠﻪ ﻣﻲ ﮔﻴﺮﻳﻢ ﻛﻪ‬
‫)‪(٩-٢‬‬
‫‪3‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺍﺯ ﺭﺍﺑﻄﻪ )‪ (٩-٢‬ﻣﺸﺎﻫﻪ ﻣﻲ ﺷﻮﺩ ﻛﻪ )‪ X(ejw‬ﻣﺠﻤﻮﻉ ﺗﺮﻣﻬﺎﻱ ﻣﻘﻴﺎﺱ ﺑﻨﺪﻱ ﺷﺪﻩ ﻭ ﺷﻴﻔﺖ ﻳﺎﻓﺘﺔ )‪ X c ( jΩ‬ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﻣﻘﻴﺎﺱ ﻓﺮﻛﺎﻧﺲ‬
‫‪2π‬‬
‫‪w‬‬
‫= ‪ Ω‬ﺗﻌﻴﻴﻦ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺩﺭ ﺣﺎﻟﻲ ﻛﻪ ﺷﻴﻔﺖ ﻫﺎ ﺑﺮﺍﺑﺮ ﺑﺎ ﺿﺮﺍﻳﺐ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‬
‫ﺗﻮﺳﻂ‬
‫‪T‬‬
‫‪T‬‬
‫= ‪ Ωs‬ﻣﻲ ﺑﺎﺷﻨﺪ‪.‬‬
‫‪ -٣-١-٢‬ﺑﺎﺯﺳﺎﺯﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎﻳﺶ )ﺗﺒﺪﻳﻞ ﺩﻳﺠﻴﺘﺎﻝ ﺑﻪ ﺁﻧﺎﻟﻮﮒ(‬
‫‪Ωs‬‬
‫ﺍﺯ ﺷﮑﻞ‪ ،٥‬ﺍﮔﺮ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺑﺎﺷﺪ‪ ،‬ﻳﻌﻨﻲ ‪ Ω > Ω N‬ﺑﺮﺍﻱ ‪ ، xc ( jΩ) = 0‬ﻛﻪ‬
‫‪2‬‬
‫ﺩﻭﺑﺎﺭﻩ ﺍﺯ )‪ X(jw‬ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺑﻪ ﻃﻮﺭ ﺩﻗﻴﻘﺘﺮ ﺍﺑﺘﺪﺍ ﻣﻲ ﺗﻮﺍﻧﻴﻢ ﺳﻴﮕﻨﺎﻝ ﻗﻄﺎﺭ ﺿﺮﺑﻪ )‪ xs(t‬ﺭﺍ ﺑﻮﺟﻮﺩ ﺁﻭﺭﻳﻢ‪.‬‬
‫≤ ‪ ، Ω N‬ﻣﻲ ﺗﻮﺍﻥ )‪ X c ( jΩ‬ﺭﺍ‬
‫)‪(١٠-۲‬‬
‫‪Ωs π‬‬
‫ﺳﭙﺲ ﻣﻲ ﺗﻮﺍﻧﻴﻢ ﻳﻚ ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺁﻝ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﺭﺍ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ =‬
‫‪2‬‬
‫‪T‬‬
‫= ‪ Ω c‬ﺑﻪ )‪ xs(t‬ﺍﻋﻤﺎﻝ ﻛﻨﻴﻢ‪.‬‬
‫)‪(١١-٢‬‬
‫ﺍﮔﺮ )‪ X c ( jΩ‬ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺑﺎﺷﺪ ﺁﻧﮕﺎﻩ ﺳﻴﮕﻨﺎﻝ ﻓﻴﻠﺘﺮ ﺷﺪﺓ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺁﻥ ﺩﻗﻴﻘﺎﹰ ﺑﺮﺍﺑﺮ )‪ X c ( jΩ‬ﺍﺳﺖ‪ .‬ﻳﻌﻨﻲ‪:‬‬
‫ﺩﺭ ﺣﻮﺯﻩ ﺯﻣﺎﻥ‪ ،‬ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯﻱ ﺍﻳﺪﻩ ﺁﻝ ) ‪ hr (t‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫)‪(۱۲-٢‬‬
‫ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺍﺳﺖ‬
‫)‪(١٣-٢‬‬
‫ﺷﮑﻞ‪ ،٣‬ﻧﻤﻮﺩﺍﺭ ﺑﻠﻮﻛﻲ ﺍﻳﻦ ﻓﺮﺁﻳﻨﺪ ﺑﺎﺯﺳﺎﺯﻱ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪.‬‬
‫ﺍﺯ ﻧﺘﻴﺠﻪ ﻓﻮﻕ‪ ،‬ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺯﻣﺎﻥ ﭘﻴﻮﺳﺘﻪ ﻛﻪ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻛﺎﻓﻲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺍﻧﺪ )ﻳﻌﻨﻲ ‪ ،( Ω s > 2Ω N‬ﺑﺮﺍﻱ‬
‫ﻧﻤﺎﻳﺶ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﻛﺎﻓﻲ ﻫﺴﺘﻨﺪ ﭘﺲ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﺍﺯ ﺭﻭﻱ ﻧﻤﻮﻧﻪ ﻫﺎ ﻭ ﺩﺍﻧﺴﺘﻦ ﭘﺮﻳﻮﺩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻗﺎﺑﻞ ﺑﺎﺯﺳﺎﺯﻱ ﺍﺳﺖ‪.‬‬
‫ﺩﺭ ﻋﻤﻞ‪ ،‬ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺁﻝ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﻧﻴﺴﺖ ﻭ ﻣﺎ ﺑﺎﻳﺪ ﺗﻘﺮﻳﺐ ﺑﺰﻧﻴﻢ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﺍﻳﻦ‪ ،‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﻭﺍﻗﻌﻲ ﻣﻤﻜﻦ ﺍﺳﺖ ﭘﻬﻨﺎﻱ‬
‫ﺑﺎﻧﺪ ﺯﻳﺎﺩﻱ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ ﻛﻪ ﺗﻮﺳﻂ ﺳﻴﺴﺘﻢ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻗﺎﺑﻞ ﺍﺟﺮﺍ ﻧﺒﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺩﺭ ﻋﻤﻞ ﺑﺎﻳﺪ ﺍﺑﺘﺪﺍ ﻳﻚ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﻭ ﺑﺎ‬
‫‪Ωs‬‬
‫‪Ω‬‬
‫ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ ‪ Ω c ≤ s‬ﺭﺍ ﺍﻋﻤﺎﻝ ﻛﺮﺩ )‬
‫‪2‬‬
‫‪2‬‬
‫‪4‬‬
‫≤ ‪.( Ω N‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪) -٣‬ﺍﻟﻒ( ﻳﻚ ﺳﻴﺴﺘﻢ ﺑﺎﺯﺳﺎﺯﻱ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺍﻳﺪﻩ ﺁﻝ )ﺏ( ﭘﺎﺳﺦ ﻓﺮﻛﺎﻧﺴﻲ ﻳﻚ ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯﻱ ﺍﻳﺪﻩ ﺁﻝ )ﺝ( ﭘﺎﺳﺦ‬
‫ﺿﺮﺑﻪ ﺑﻪ ﻳﻚ ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯﻱ ﺍﻳﺪﻩ ﺁﻝ‬
‫‪ -٢-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮐﺎﻫﺸﯽ‬
‫ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﺯ ﺁﻥ ﻛﺎﻫﺶ ﻳﺎﺑﺪ‪.‬‬
‫)‪(١٤-٢‬‬
‫)‪xd[n] = x[nM] = xc(nMT‬‬
‫ﺩﺭ ﺭﺍﺑﻄﺔ )‪ (١٤-٢‬ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ ﻛﻪ ]‪ xd[n‬ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺻﻮﺭﺕ ﻣﺴﺘﻘﻴﻢ ﺑﺎ ﺗﻨﺎﻭﺏ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻳﻚ ‪ T′ = MT‬ﺍﺯ ﺳﻮﻱ )‪xc(t‬‬
‫ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺑﻪ ﻋﻼﻭﻩ‪ ،‬ﺍﮔﺮ‬
‫‪5‬‬
‫‪ X c ( jΩ) = 0‬ﺑﺮﺍﻱ‬
‫‪ | Ω |> ΩN‬ﺁﻧﮕﺎﻩ‪ xd[n] ،‬ﻳﻚ ﻧﻤﺎﻳﺶ ﺩﻗﻴﻖ ﺍﺯ )‪ xc(t‬ﺍﮔﺮ‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫‪2π 1‬‬
‫‪= Ω s > 2Ω N‬‬
‫‪T M‬‬
‫ﺣﺪﺍﻗﻞ ‪ M‬ﺑﺮﺍﺑﺮ ﻧﺮﺥ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﺑﺎﺷﺪ ‪ .‬ﺑﻪ ﻃﻮﺭ ﻛﻠﻲ‪ ،‬ﺑﺮﺍﻱ ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﺗﺪﺍﺧﻞ‪ ،‬ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﺩﻧﺒﺎﻟﻪ ﺍﺑﺘﺪﺍ ﺑﺎﻳﺪ ﺑﻪ ﻭﺳﻴﻠﻪ ﻓﻴﻠﺘﺮ ﺯﻣﺎﻥ –‬
‫= ‪ Ω s‬ﺑﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﺎ ﺿﺮﻳﺐ ‪ M‬ﻛﺎﻫﺶ ﺩﺍﺩ ﺍﮔﺮ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﻭﻟﻴﻪ‬
‫ﮔﺴﺴﺘﻪ ﺗﺎ ‪ M‬ﺑﺮﺍﺑﺮ ﻛﺎﻫﺶ ﻳﺎﺑﺪ‪ .‬ﻧﻤﻮﺩﺍﺭ ﺑﻠﻮﻛﻲ ﻳﻚ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ – ﻛﺎﻫﺸﻲ ﺩﺭ ﺷﮑﻞ‪ ٤‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫ﺷﮑﻞ‪ -٤‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮐﺎﻫﺸﯽ ﺑﺎ ﺿﺮﻳﺐ ‪ ،M‬ﻛﻪ ﺩﺭ ﺁﻥ )‪ H(ejw‬ﻳﻚ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﺍﺳﺖ‪ .‬ﺩﺭ ﺣﺎﻟﺖ ﺍﻳﺪﻩ ﺁﻝ )‪ H(ejw‬ﺑﺎﻳﺪ ﻳﻚ ﻓﻴﻠﺘﺮ‬
‫‪π‬‬
‫ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ‬
‫‪M‬‬
‫ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﺭﺍﺑﻄﻪ ﺑﻴﻦ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ]‪ x[n‬ﻭ ]‪ ،xd[n‬ﺍﺑﺘﺪﺍ ﺑﺎﻳﺪ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺯﻣﺎﻥ ﮔﺴﺴﺘﻪ )‪ x[n]=xc(nT‬ﺭﺍ ﺑﻪ ﻳﺎﺩ ﺁﻭﺭﻳﻢ‪.‬‬
‫= ‪ Ω c‬ﺑﺎﺷﺪ‪.‬‬
‫)‪(١٥-٢‬‬
‫ﻣﺸﺎﺑﻪ ﺭﺍﺑﻄﻪ ﺑﺎﻻ‪ ،‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ )‪ xd[n]=x[nw]=xc(nT‬ﻳﺎ ‪ T′ = MT‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫)‪(١٦-٢‬‬
‫ﺍﻧﺪﻳﺲ ﺟﻤﻊ ‪ r‬ﺩﺭ ﺭﺍﺑﻄﺔ )‪ (١٦-٢‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫)‪(١٧-٢‬‬
‫‪r = i + BM‬‬
‫ﻛﻪ ‪ B‬ﻭ ‪ i‬ﺍﻋﺪﺍﺩ ﺻﺤﻴﺢ ﻣﻲ ﺑﺎﺷﻨﺪ‪ − ∞ < B < −∞ ،‬ﻭ ‪ 0<i<M-1‬ﺍﺳﺖ‪.‬‬
‫ﻭﺍﺿﺢ ﺍﺳﺖ ﻛﻪ ‪ r‬ﻫﻨﻮﺯ ﻳﻚ ﻋﺪﺩ ﺻﺤﻴﺢ ﺩﺭ ﺩﺍﻣﻨﺔ ∞ ‪ −‬ﺗﺎ ∞ ‪ +‬ﺍﺳﺖ‪ ،‬ﺣﺎﻻ ﻣﻌﺎﺩﻟﻪ )‪ (۱۷-٢‬ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺑﻴﺎﻥ ﻛﺮﺩ‪.‬‬
‫)‪(١٨-٢‬‬
‫ﻋﺒﺎﺭﺕ ﺩﺭﻭﻥ ﻛﺮﻭﺷﻪ ﺩﺭ ﺭﺍﺑﻄﺔ )‪ (١٨-٢‬ﺍﺯ ﺭﺍﺑﻄﺔ )‪ (١٥-٢‬ﻗﺎﺑﻞ ﺟﺎﻳﮕﺰﻳﻨﻲ ﺍﺳﺖ‪.‬‬
‫)‪(١٩-٢‬‬
‫ﺑﻨﺎﺑﺮﺍﻳﻦ ﻣﺎ ﻣﻲ ﺗﻮﺍﻧﻴﻢ ﺭﺍﺑﻄﺔ )‪ (١٨-٢‬ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺑﺎﺯﻧﻮﻳﺴﻲ ﻛﻨﻴﻢ‪.‬‬
‫)‪(٢٠-٢‬‬
‫‪6‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﻛﻪ ﺩﺭ ﺷﻜﻞ )‪ (٥‬ﺑﺮﺍﻱ ‪ M=2‬ﻭ ﺩﺭ ﺷﻜﻞ )‪ (٦‬ﺑﺮﺍﻱ ‪ M=3‬ﻧﻤﺎﻳﺶ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﻲ ﺗﻮﺍﻥ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﺯﻣﺎﻧﻲ ﻛﻪ ‪ ،M=2‬ﻧﻤﻮﻧﻪ‬
‫ﺑﺮﺩﺍﺭﻱ ﮐﺎﻫﺸﯽ ﺑﺎﻋﺚ ﻫﻤﭙﻮﺷﺎﻧﻲ ﻃﻴﻒ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻧﻤﻲﺷﻮﺩ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ‪ ،‬ﻭﻗﺘﻲ ‪ ،M=3‬ﻫﻤﭙﻮﺷﺎﻧﻲ ﺑﻴﻦ ﻃﻴﻔﻬﺎﻱ ﺗﻜﺮﺍﺭ ﺷﺪ )ﻫﻤﺎﻥ‬
‫ﺗﺪﺍﺧﻞ( ﺭﺥ ﻣﻲﺩﻫﺪ‪ .‬ﺑﺮﺍﻱ ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﺗﺪﺍﺧﻞ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ ﻗﺒﻞ ﺍﺯ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮐﺎﻫﺸﯽ ﺍﻟﺰﺍﻣﻲ ﺍﺳﺖ‪.‬‬
‫ﺷﮑﻞ‪ -٥‬ﻧﻤﺎﻳﺶ ﺣﻮﺯﻩ ﻓﺮﻛﺎﻧﺲ ﺩﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ )‪(M=2‬‬
‫‪7‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪ -٦‬ﻧﻤﺎﻳﺶ ﺣﻮﺯﻩ ﻓﺮﻛﺎﻧﺲ ﺩﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ )‪(M=2‬‬
‫)‪ (a)-(c‬ﺑﺪﻭﻥ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪ ،‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﻛﺎﻫﺸﻲ ﺗﺪﺍﺧﻞ ﺩﺍﺭﺩ‪.‬‬
‫)‪ (d)-(f‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ ﺑﺎ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ ﺑﺮﺍﻱ ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﺗﺪﺍﺧﻞ‪.‬‬
‫‪ -٣-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﻓﺰﺍﻳﺸﻲ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺩﻳﺠﻴﺘﺎﻟﻲ‬
‫ﻛﺎﻫﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﮔﺴﺴﺘﻪ – ﺯﻣﺎﻥ ﺑﺎ ﺿﺮﻳﺐ ﺻﺤﻴﺢ ﺷﺎﻣﻞ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻳﻚ ﺩﻧﺒﺎﻟﻪ‪ ،‬ﻣﺸﺎﺑﻪ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺳﻴﮕﻨﺎﻝ‬
‫ﭘﻴﻮﺳﺘﻪ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺟﺎﻱ ﺗﻌﺠﺐ ﻧﻴﺴﺖ ﻛﻪ ﺍﻓﺰﺍﻳﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻧﻴﺰ ﺑﺎ ﻋﻤﻠﻴﺎﺕ ﻣﺸﺎﺑﻪ ﺗﺒﺪﻳﻞ ‪ D/C‬ﺳﺮ ﻭ ﻛﺎﺭ ﺩﺍﺭﺩ‪ .‬ﺑﺮﺍﻱ ﻣﺸﺎﻫﺪﻩ ﺍﻳﻦ‬
‫‪8‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﻣﻄﻠﺐ‪ ،‬ﺳﻴﮕﻨﺎﻝ ]‪ x[n‬ﺭﺍ ﻛﻪ ﻣﻲ ﺧﻮﺍﻫﻴﻢ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺁﻥ ﺭﺍ ﺑﺎ ﺿﺮﻳﺐ ‪ L‬ﺍﻓﺰﺍﻳﺶ ﺩﻫﻴﻢ‪ ،‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﺍﮔﺮ ﻣﺎ ﺳﻴﮕﻨﺎﻝ ﭘﻴﻮﺳﺘﻪ‬
‫)‪ xc(t‬ﺭﺍ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﻢ ﻫﺪﻑ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﻧﻤﻮﻧﻪ ﻫﺎﻱ‬
‫)‪(٢١-٢‬‬
‫)‪(٢٢-٢‬‬
‫ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﺩﻧﺒﺎﻟﺔ ﻣﺎ ﻋﻤﻠﻴﺎﺕ ﺍﻓﺰﺍﻳﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﻓﺰﺍﻳﺸﻲ ﻣﻲ ﻧﺎﻣﻴﻢ‪.‬‬
‫‪n‬‬
‫‪ nT ‬‬
‫)‪xi[n] = x   = x c   , n = 0,± L,±2 L,... (۲۳ -٢‬‬
‫‪L‬‬
‫‪ L ‬‬
‫ﺷﮑﻞ‪ -۷:‬ﭘﺮﻭﺳﺔ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﻓﺰﺍﻳﺸﻲ )ﺩﺭﻭﻥ ﻳﺎﺑﻲ(‬
‫ﺷﮑﻞ‪ -٧‬ﻳﻚ ﺳﻴﺴﺘﻢ ﺭﺍ ﺑﺮﺍﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ]‪ xi[n‬ﺍﺯ ]‪ x[n‬ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﭘﺮﺩﺍﺯﺵ ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺳﻴﺴﺘﻢ ﺳﻤﺖ ﭼﭗ‬
‫ﻳﻚ ﺍﻓﺰﺍﻳﻨﺪﺓ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻳﺎ ﺑﻪ ﻃﻮﺭ ﺳﺎﺩﻩ ﻳﻚ ﺍﻓﺰﺍﻳﻨﺪﻩ ﻧﺎﻣﻴﺪﻩ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﺧﺮﻭﺟﻲ ﺁﻥ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫)‪(٢٤-٢‬‬
‫ﻳﺎ ﺑﻪ ﺑﻴﺎﻥ ﺩﻳﮕﺮ‬
‫)‪(٢٥-٢‬‬
‫ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ]‪ xe[n‬ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺑﻴﺎﻥ ﺷﻮﺩ‪.‬‬
‫)‪(٢٦-٢‬‬
‫ﺭﺍﺑﻄﻪ ﺑﺎﻻ ﺩﺭ ﺷﮑﻞ ‪ (b)-٨‬ﻭ ‪ (c )-٨‬ﻧﻤﺎﻳﺶ ﺩﺍﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺑﺮﺍﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ]‪ xi[n‬ﺍﺯ ]‪ ،xe[n‬ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺍﻋﻤﺎﻝ ﻳﻚ ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺍﻝ‬
‫‪π‬‬
‫ﭘﺎﺋﻴﻦ ﮔﺬﺭ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ‬
‫‪L‬‬
‫‪9‬‬
‫= ‪ Ω c‬ﻭ ﺑﺎ ﺑﻬﺮﺓ ‪ L‬ﺩﺍﺭﻳﻢ )ﻛﻪ ﺩﺭ ﺷﻜﻞ ‪ (e),(d)-٨‬ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ(‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪ -٨‬ﻧﻤﺎﻳﺶ ﺩﺍﻣﻨﻪ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﻓﺰﺍﻳﺸﻲ‬
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‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫‪ -٣‬ﺁﺯﻣﺎﻳﺶ ﻫﺎ‬
‫‪ -١-٣‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺻﻮﺕ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﻣﺘﻔﺎﻭﺕ‬
‫ﺩﺭ ﺍﻳﻦ ﺗﺠﺮﺑﻪ‪ ،‬ﺷﻤﺎ ﺻﺪﺍﻱ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﺧﻮﺍﻫﻴﺪ ﻛﺮﺩ‪،‬‬
‫‪ (١‬ﺻﺪﺍﻱ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﻛﻨﻴﺪ‪.‬‬
‫ﺍﻟﻒ( ﻣﻄﻤﺌﻦ ﺷﻮﻳﺪ ﻛﻪ ﺍﺭﺗﺒﺎﻁ ﻣﻴﻜﺮﻭﻓﻮﻥ ﺩﺭﺳﺖ ﺍﺳﺖ ﻳﻌﻨﻲ ﻣﻴﻜﺮﻭﻓﻮﻥ ﺑﻪ ”‪ “MIC-in‬ﺩﺭ ﻛﺎﺭﺕ ﺻﺪﺍ ﻣﺘﺼﻞ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺩﺭ ﺳﻤﺖ‬
‫ﭘﺸﺖ ﻛﺎﻣﭙﻴﻮﺗﺮ‪.‬‬
‫ﺏ( ﺳﻪ ﭘﻨﺠﺮﻩ ”‪ “sound recorder‬ﺭﺍ ﺑﺎﺯ ﻛﻨﻴﺪ‪ .‬ﺍﺑﺘﺪﺍ ﺭﻭﻱ ‪ file-properties-convert‬ﻛﻠﻴﻚ ﻛﻨﻴﺪ‪.‬‬
‫ﺳﭙﺲ ‪ 8000Hz,8bit, Mono 8kB/s‬ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ‪ ٥ .‬ﺛﺎﻧﻴﻪ ﺍﺯ ﺻﺪﺍﻱ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﻛﻨﻴﺪ ﻭ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ﻓﺎﻳﻞ ‪ rec8.wav‬ﺩﺭ‬
‫ﺁﺩﺭﺱ ﺧﻮﺩ ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﺙ( ﺑﺮﺍﻱ ﺩﻭﻣﻴﻦ ﻭ ﺳﻮﻣﻴﻦ ﺿﺒﻂ ﺻﺪﺍ ﺍﺯ ﻓﻮﺭﻣﺖ ‪ Mono 11 kB/s‬ﻭ ‪ 11025Hz,8Bit‬ﺭﺍ ﺍﺯ ‪22,050Hz,8bit, Mono 22‬‬
‫‪ kB/s‬ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ :‬ﻓﺎﻳﻠﻬﺎ ﺭﺍ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ‪ recll.wav‬ﻭ ‪ rec22.wav‬ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﺕ( ﺻﺪﺍﻫﺎ ﺭﺍ ﻳﻜﻲ ﭘﺲ ﺍﺯ ﺩﻳﮕﺮﻱ ﮔﻮﺵ ﺩﺍﺩﻩ ﻭ ﻛﻴﻔﻴﺖ ﺁﻧﻬﺎ ﺭﺍ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪:‬‬
‫‪ (٢‬ﺻﺪﺍ ﺭﺍ ﺍﺯ ‪ CD-Rom‬ﺿﺒﻂ ﻛﻨﻴﺪ‪.‬‬
‫ﻳﻚ ‪ CD‬ﺻﻮﺗﻲ ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ‪ CD player‬ﭘﺨﺶ ﻛﻨﻴﺪ‪ .‬ﭘﻨﺞ ﺛﺎﻧﻴﻪ ﺍﺯ ﺻﺪﺍﻱ ‪ CD‬ﺭﺍ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ‪ 8k‬ﻭ ‪ 22k‬ﻭ ‪ 44k‬ﺩﺭ‬
‫‪ 8bits/sample‬ﺿﺒﻂ ﻛﻨﻴﺪ‪ .‬ﻓﺎﻳﻠﻬﺎ ﺭﺍ ﺑﻪ ﻓﺮﻣﺖ ‪ cd22.wav cd11.wav‬ﻭ ‪ cd44.wav‬ﺩﺭ ﺁﺩﺭﺱ ﺧﻮﺩ ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٣‬ﺻﺪﺍﻱ ‪ MIDI‬ﺭﺍ ﺑﺮﺍﻱ ﻛﺎﻣﭙﻴﻮﺗﺮ ﺧﻮﺩ ﺿﺒﻂ ﻛﻨﻴﺪ‪.‬‬
‫ﻓﺎﻳﻞ ‪ MIDI‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ‪ media player‬ﭘﺨﺶ ﻛﻨﻴﺪ‪ ٥ .‬ﺛﺎﻧﻴﻪ ﺍﺯ ﻣﻮﺳﻴﻘﻲ ‪ MIDI‬ﺭﺍ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ‪ 11k‬ﻭ ‪ 22k‬ﻭ ‪ 44k‬ﺿﺒﻂ‬
‫ﻛﻨﻴﺪ‪ .‬ﺳﭙﺲ ﻓﺎﻳﻠﻬﺎ ﺭﺍ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ‪.midi11.wav‬‬
‫‪ Midi22.wav‬ﻭ ‪ midi44.wav‬ﺩﺭ ﺁﺩﺭﺱ ﺧﻮﺩ ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫‪ -٤‬ﺣﺎﻻ ﺩﺭﺑﺎﺭﺓ ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﺍﺯ ﻣﻨﺎﺑﻊ ﻭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺨﺘﻠﻒ ﻧﻈﺮ ﺩﻫﻴﺪ‪.‬‬
‫‪ -٥‬ﻣﺮﺍﺣﻞ ‪ ١‬ﺗﺎ ‪ ٤‬ﺭﺍ ﺑﺎ ﺗﻐﻴﻴﺮ ‪ 16bit/sample‬ﺑﻪ ‪ 8bit/sample‬ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪.‬‬
‫‪ -٢-٣‬ﭘﺮﺩﺍﺯﺵ ﺻﻮﺕ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ‪MATLAB‬‬
‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ‪ ،‬ﺷﻤﺎ ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﻧﻮﺷﺘﻦ ﺑﺮﻧﺎﻣﻪ ‪ MATLAB‬ﺑﺮﺍﻱ ﺣﻞ ﻣﺴﺄﻟﻪ ﺩﺍﺭﻳﺪ‪.‬‬
‫‪ -١‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ‪ 22KHz‬ﻭ ‪ ٨‬ﺑﻴﺘﻲ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺁﻥ ﺭﺍ ﺑﻪ ﻧﺼﻒ ﺑﺮﺳﺎﻧﻴﺪ) ﺑﺪﻭﻥ‬
‫ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ( ﻭ ﺳﭙﺲ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ﻓﻴﻠﺘﺮ ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺧﻄﻲ ﺁﻥ ﺭﺍ ﺩﻭﺑﺎﺭﻩ ﺑﻪ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺮﺳﺎﻧﻴﺪ‪.‬‬
‫‪ -٢‬ﻃﻴﻒ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺍﻓﺰﺍﻳﺸﻲ ﻭ ﻛﺎﻫﺸﻲ ﺭﺍ ﻧﻤﺎﻳﺶ ﺩﻫﻴﺪ ﻭ ﺳﭙﺲ ﺁﻧﻬﺎ ﺭﺍ ﺑﺎ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺧﻄﺎﻱ ﻣﺮﺑﻊ‬
‫ﻣﻴﺎﻧﮕﻴﻦ )‪ (MSE‬ﺑﻴﻦ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺩﺭ ﻓﺮﻛﺎﻧﺲ ‪ ٢٢KHz‬ﻭ ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻛﻨﻴﺪ‪ MSE .‬ﺑﻴﻦ ﺩﻭ ﺳﻴﮕﻨﺎﻝ )‪ x(n‬ﻭ‬
‫)‪ y(n‬ﺑﺎ ﻃﻮﻝ ‪ N‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫‪N‬‬
‫‪MSE = ∑ [x (n ) − y(n )]2 / N‬‬
‫‪n =1‬‬
‫‪ -٣‬ﻣﺮﺍﺣﻞ ‪ ١‬ﻭ ‪ ٢‬ﺭﺍ ﺑﺮﺍﻱ ﻣﻮﺍﺭﺩ ﺯﻳﺮ ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪.‬‬
‫ﺍﻟﻒ( ﻳﻚ ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ )ﺷﻤﺎ ﻣﻲ ﺗﻮﺍﻧﻴﺪ ﻃﻮﻝ ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ( ﺑﺮﺍﻱ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪.‬‬
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‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺏ( ﺍﺯ ﺗﺎﺑﻊ ”‪ “FIR1‬ﺩﺭ ‪ MATLAB‬ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ ﺗﺎ ﻓﻴﻠﺘﺮ ﺑﻬﺘﺮﻱ ﻃﺮﺍﺣﻲ ﻛﻨﻴﺪ‪ .‬ﺍﺯ ﺗﺎﺑﻊ ”)(‪ “interp‬ﺑﺮﺍﻱ ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﻃﻮﻟﻬﺎﻱ ﻣﺘﻔﺎﻭﺕ ﺑﺮﺍﻱ ﻓﻴﻠﺘﺮﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﻃﻴﻒ ﻓﻴﻠﺘﺮﻫﺎﻱ ﭘﻴﺶ ﻭ ﭘﺲ ﭘﺮﺩﺍﺯﺵ ﺭﺍ ﻋﻼﻭﻩ ﺑﺮ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ‬
‫ﻛﺎﻫﺸﻲ ﻳﺎ ﺍﻓﺰﺍﻳﺸﻲ ﻧﻤﺎﻳﺶ ﺩﻫﻴﺪ‪.‬‬
‫‪ -٤‬ﻣﺮﺍﺣﻞ ‪ ۱‬ﺗﺎ ‪ ٣‬ﺭﺍ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ‪ 11KHz‬ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ )ﺍﺧﺘﻴﺎﺭﻱ(‬
‫‪ -٥‬ﺗﻤﺎﻡ ﻧﺘﺎﻳﺞ ﺭﺍ ﭼﺎﭖ ﻛﻨﻴﺪ‪.‬‬
‫ﺑﺮﺍﻱ ﻣﻮﺍﺭﺩ ‪ ١‬ﻭ ‪ ،٢‬ﺳﻪ ﻧﻤﻮﻧﻪ ﻣﺘﻦ ‪ MATLAB‬ﺩﺭ ‪ Appendix A‬ﺁﻭﺭﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .(sp.m,sp1.m, spfilter.m) .‬ﺷﻤﺎ ﺑﺎﻳﺪ ﻗﺎﺩﺭ‬
‫ﺑﺎﺷﻴﺪ ﺗﺎ ﺑﻘﻴﻪ ﻣﻮﺍﺭﺩ ﺭﺍ ﺑﺎ ﺑﻬﺒﻮﺩ ﺍﻳﻦ ﻣﺘﻨﻬﺎ ﺍﻧﺠﺎﻡ ﺩﻫﻴﺪ‪ .‬ﺭﺍﻫﻨﻤﺎﻳﻲ ‪ :‬ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ ﻳﻚ ﺩﻧﺒﺎﻟﺔ ) (‪ x‬ﺑﻪ ﻭﺳﻴﻠﻪ ﻳﻚ ﻓﻴﻠﺘﺮﻱ ﺗﻮﺳﻂ ﺗﺎﺑﻊ ) (‪conv‬‬
‫ﺍﻧﺠﺎﻡ ﻣﻲ ﺷﻮﺩ‪ .‬ﺷﻤﺎ ﻣﻲ ﺗﻮﺍﻧﻴﺪ ﺍﺯ ﺩﺳﺘﻮﺭ ﺯﻳﺮ ﺑﺮﺍﻱ ﺷﻨﺎﺧﺖ ﻳﻚ ﺗﺎﺑﻊ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ ‪ help conv.‬ﺑﻪ ﻃﻮﺭ ﺧﻼﺻﻪ‪ ،‬ﺷﻤﺎ‬
‫ﺑﺎﻳﺪ ﺑﺮﻧﺎﻣﻪ ﻫﺎﻱ ‪ Appendix A‬ﺭﺍ ﺑﻬﺒﻮﺩ ﺩﻫﻴﺪ ﺗﺎ ﻣﻮﺍﺭﺩ ﺯﻳﺮ ﺭﺍ ﻋﻤﻠﻲ ﺳﺎﺯﻧﺪ‪.‬‬
‫ﺍﻟﻒ( ﺑﺪﻭﻥ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺩﻭﺑﺎﺭﻩ ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﻩ ﺍﻭﻟﻴﻪ‬
‫ﺏ( ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﺓ ﺍﻭﻟﻴﻪ‬
‫ﺝ( ) (‪ ،fir1‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﺓ ﺍﻭﻟﻴﻪ‬
‫‪ -٤‬ﮔﺰﺍﺭﺵ‬
‫ﮔﺰﺍﺭﺵ ﺷﻤﺎ ﺑﺎﻳﺪ ﺷﺎﻣﻞ ‪ m‬ﻓﺎﻳﻠﻬﺎ ﻭ ﻓﻴﻠﺘﺮﻫﺎ ﻭ ﺷﻜﻠﻬﺎﻱ ﺧﺮﻭﺟﻲ ﺑﺎﺷﺪ‪ .‬ﭘﺮﺳﺸﻬﺎﻱ ﺯﻳﺮ ﺭﺍ ﺩﺭ ﮔﺰﺍﺭﺵ ﺧﻮﺩ ﭘﺎﺳﺦ ﺩﻫﻴﺪ‪ .‬ﺗﻤﺎﻣﻲ ﻓﺎﻳﻞ ﻫﺎﻱ‬
‫ﮔﺰﺍﺭﺵ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﻳﻚ ﻓﺎﻳﻞ ﻓﺸﺮﺩﻩ ﺑﻪ ﺁﺩﺭﺱ ‪ TA e-mail‬ﺑﻔﺮﺳﺘﻴﺪ‪([email protected]) .‬‬
‫‪ (١‬ﺍﮔﺮ ﺳﻴﮕﻨﺎﻝ ﻭﺭﻭﺩﻱ ) ‪ sin( 2πft‬ﺍﺳﺖ ﺯﻣﺎﻧﻲ ﻛﻪ ‪ f=6KHz‬ﻭ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ‪ 8KHz‬ﺍﺳﺖ‪ ،‬ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ‬
‫ﭼﻪ ﺧﻮﺍﻫﺪ ﺑﻮﺩ؟ ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﻛﻪ ﺍﺯ ﻓﻴﻠﺘﺮ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ ‪ 4KHz‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﻛﻨﺪ ﭼﻪ ﺧﻮﺍﻫﺪ ﺑﻮﺩ؟ )ﻣﺴﺌﻠﻪ ﺭﺍ‬
‫ﺑﺮﺭﺳﻲ ﻛﺮﺩﻩ ﻭ ﺗﻤﺎﻡ ﻣﺮﺍﺣﻞ ﺁﻥ ﺭﺍ ﺩﺭ ﮔﺰﺍﺭﺵ ﺧﻮﺩ ﺑﻨﻮﻳﺴﻴﺪ(‬
‫‪ (٢‬ﺩﺭﺑﺎﺭﻩ ﻛﻴﻔﻴﺖ ﻓﺎﻳﻠﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ﻧﺮﺧﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻭ ‪ bits/sample‬ﻣﺘﻔﺎﻭﺕ ﻧﻈﺮ ﺩﻫﻴﺪ‪ .‬ﺩﺭﺑﺎﺭﺓ ﺗﻔﺎﻭﺕ ﺻﻮﺕ ﻭ‬
‫ﮔﻔﺘﺎﺭ ﺩﺭ ﻧﺮﺧﻬﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺨﺘﻠﻒ ﺑﺤﺚ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٣‬ﺻﺪﺍﻱ ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺷﺪﻩ ﺑﻌﺪ ﺍﺯ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ٢‬ﺭﺍ ﺑﺎ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﻛﺎﻫﺸﻲ ﻭ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫ﺗﻮﺿﻴﺢ ﺩﻫﻴﺪ ﻛﻪ ﭼﺮﺍ ﺳﻴﮕﻨﺎﻟﻬﺎﯼ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺩﺭ ﺑﻌﻀﻲ ﻣﻮﺍﺭﺩ ﺑﻬﺘﺮ ﻫﺴﺘﻨﺪ‪.‬‬
‫‪ -٥‬ﻣﺮﺍﺟﻊ‬
‫‪[1]. The Math Works Inc., Matlab User’s Guide, 1993, MATLAB USERS’S GUIDE, 1993.‬‬
‫‪[2]. The Math Works Inc., MATLAB REFRENCE GUIDE, 1992.‬‬
‫‪[3]. Wilsky and Openheim, Signals & Systems, Chapter 8.‬‬
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‫‪CE 342 – Multimedia HW# 1‬‬
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CE 342 – Multimedia HW# 1
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CE 342 – Multimedia HW# 1
H. Rabiee, Spring 2008
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CE 342 – Multimedia HW# 1
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CE 342 – Multimedia HW# 1
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CE 342 – Multimedia HW# 1
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