‫ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﻲ‬
‫ﺳﻴﺴﺘﻢ ﻫﺎ ﭼﻨﺪﺭﺳﺎﻧﻪﺍ )‪(۴۰-۳۴۲‬‬
‫ﺩﺍﻧﺸﻜﺪﻩ ﻣﻬﻨﺪﺳﻲ ﻛﺎﻣﭙﻴﻮﺗﺮ‬
‫ﺗﺮﻡ ﭘﺎﻳﻴﺰ ‪۱۳۸۷‬‬
‫ﺩﻛﺘﺮ ﺣﻤﻴﺪﺭﺿﺎ ﺭﺑﻴﻌﻲ‬
‫ﺗﻜﻠﻴﻒ ﺷﻤﺎﺭﻩ ‪ :۱‬ﺩﻳﺠﻴﺘﺎﻝ ﻛﺮﺩﻥ ﺻﻮﺕ ﻭ ﺗﺒﺪﻳﻞ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ‬
‫‪ -١‬ﻣﻘﺪﻣﻪ‬
‫ﺩﺭ ﻳﻚ ﻣﻴﻜﺮﻭﻓﻮﻥ‪ ،‬ﺍﻣﻮﺍﺝ ﻓﺸﺎﺭ ﺻﺪﺍ ﻓﻴﺰﻳﻜﻲ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎ ﺍﻟﻜﺘﺮﻳﻜﻲ ﻣﺘﻨﺎﻇﺮ ﺑﺎ ﺧﻮﺩ‪ ،‬ﺑﻪ ﻭﺳﻴﻠﻪ ﻣﺒﺪﻟﻬﺎ ﺁﻛﻮﺳﺘﻴﻜﻲ ﻧﻈﻴﺮ ﻣﻴﻜﺮﻭﻓﻮﻥ ﻳﺎ‬
‫‪ Phonograph cartridge‬ﺗﺒﺪﻳﻞ ﻣﻲ ﺷﻮﻧﺪ‪ .‬ﺧﺮﻭﺟﻲ ﺍﻟﻜﺘﺮﻳﻜﻲ ﻣﺒﺪﻝ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺁﻧﺎﻟﻮﮒ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ ،‬ﺯﻳﺮﺍ ﺳﻴﮕﻨﺎﻝ ﺍﻟﻜﺘﺮﻳﻜﻲ‬
‫ﻣﺸﺎﺑﻪ ﺍﻟﮕﻮ ﻓﺸﺎﺭ ﻣﻮﺝ ﺻﻮﺗﻲ ﺍﺳﺖ ﻛﻪ ﺁﻥ ﺭﺍ ﺑﻮﺟﻮﺩ ﺁﻭﺭﺩﻩ ﺍﺳﺖ‪ .‬ﺳﻴﮕﻨﺎﻟﻬﺎ ﺻﻮﺕ ﺑﻪ ﺻﻮﺭﺕ ﺍﻟﮕﻮﻫﺎ ﻣﻮﺝ ﺩﻭﺑﻌﺪ ﻣﻲ ﺑﺎﺷﻨﺪ ﻛﻪ‬
‫ﻣﺤﻮﺭ ‪ y‬ﻧﺸﺎﻥ ﺩﻫﻨﺪﺓ ﺷﺪﺕ ﻳﺎ ﺩﺍﻣﻨﻪ ﻭ ﻣﺤﻮﺭ ‪ x‬ﻧﺸﺎﻥ ﺩﻫﻨﺪﺓ ﻣﺴﻴﺮ ﺯﻣﺎﻥ ﻫﺴﺘﻨﺪ‪ ،‬ﺷﻜﻞ ‪ ،١‬ﺷﻜﻞ ﻣﻮﺝ ﺁﻧﺎﻟﻮﮒ ﺍﺯ ﻳﻚ ﺳﺮ ﻣﻮﺟﻬﺎ‬
‫ﺻﻮﺕ ﺍﺯ ﻳﻚ ‪ chime‬ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺍﻳﻦ ﺳﺮ 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 ﺳﭙﺮ ﺷﺪﻩ ﺑﻴﻦ ﺗﻜﺮﺍﺭﻫﺎ ﺗﻌﻴﻴﻦ ﻣﻲﺷﻮﺩ ﻛﻪ ﻃﻮﻝ ﻣﻮﺝ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ .‬ﺑﻴﺸﺘﺮ ﻣﻮﺟﻬﺎ ﺻﻮﺕ ﺩﻗﻴﻘﺎﹰ‬
‫ﺗﻜﺮﺍﺭ ﻧﻤﻲ ﺷﻮﻧﺪ ﺍﻣﺎ ﻣﻲ ﺗﻮﺍﻥ ﻳﻚ ﺍﻟﮕﻮ ﻣﺸﺨﺺ ﺩﺭ ﺷﻜﻞ ﻣﻮﺟﻲ ﻛﻪ ﺗﻮﺳﻂ ﺑﻴﺸﺘﺮ ﺳﺎﺯﻫﺎ ﻣﻮﺳﻴﻘﻲ ﺍﻳﺠﺎﺩ ﻣﻲﺷﻮﺩ‪ ،‬ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ‪ .‬ﻃﻮﻝ‬
‫ﻣﻮﺝ ﻳﻚ ﺻﻮﺕ ﺍﻟﻜﺘﺮﻳﻜﻲ‪ ، l ،‬ﺩﺭ ﻣﻘﻴﺎﺱ ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﻳﺎ ﻣﻴﻜﺮﻭﺛﺎﻧﻴﻪ ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ‪ .‬ﻓﺮﻛﺎﻧﺲ‪ ،F،‬ﻛﻪ ﺑﺎ ﻭﺍﺣﺪ ﻫﺮﺗﺰ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮ ﻣﻲﺷﻮﺩ‬
‫‪1‬‬
‫)ﺗﻌﺪﺍﺩ ﺩﻭﺭ ﺩﺭ ﻫﺮ ﺛﺎﻧﻴﻪ( ﻣﻌﻜﻮﺱ ‪ l‬ﻣﻲ ﺑﺎﺷﺪ‪ ،‬ﻳﻌﻨﻲ‬
‫‪l‬‬
‫ﺻﺪﺍ ﺑﺸﺮ ﻳﺎ ﺻﺪﺍﻫﺎ ﺗﻮﻟﻴﺪ ﺷﺪﻩ ﺑﻪ ﻭﺳﻴﻠﻪ ﺳﺎﺯﻫﺎ ﻣﻮﺳﻴﻘﻲ ﻣﻲﺗﻮﺍﻧﻨﺪ ﺑﻪ ﻳﻚ ﻣﻮﺝ ﭘﺎﻳﻪ ﻭ ﻣﻮﺟﻬﺎ ﻣﺘﻌﺪﺩ ﺍﻟﺤﺎﻗﻲ ﺩﻳﮕﺮ ﺗﻘﺴﻴﻢ ﺷﻮﻧﺪ‪.‬‬
‫= ‪.F‬‬
‫ﻣﻮﺟﻬﺎ ﺍﻟﺤﺎﻗﻲ ﻛﻪ ﺑﻪ ﻣﻮﺝ ﭘﺎﻳﻪ ﺍﻋﻤﺎﻝ ﺷﺪﻩ ﺍﻧﺪ‪ overtone ،‬ﻧﺎﻣﻴﺪﻩ ﻣﻲ ﺷﻮﻧﺪ‪Overton .‬ﻫﺎ ﻣﻮﺟﻬﺎ ﻓﺮﻛﺎﻧﺲ ﺑﺎﻻﺗﺮ ﻣﻲﺑﺎﺷﻨﺪ ﻭ ﺑﺎ‬
‫ﻓﺮﻛﺎﻧﺲ ﻫﺎﻳﻲ ﻛﻪ ﺿﺮﺍﻳﺒﻲ ﺍﺯ ﻣﻮﺝ ﭘﺎﻳﻪ ﻣﻲ ﺑﺎﺷﻨﺪ )ﻫﺎﺭﻣﻮﻧﻴﻚ ﻫﺎ( ﺑﻪ ﺻﺪﺍ‪ ،‬ﻣﺸﺨﺼﺎﺕ ﻳﻚ ﺻﻮﺕ ﺑﺸﺮ ﻳﺎ ﺻﻮﺕ ﺳﺎﺯﻫﺎ ﻣﻮﺳﻴﻘﻲ ﺭﺍ‬
‫ﻣﻲ ﺑﺨﺸﻨﺪ‪ .‬ﻫﻨﮕﺎﻣﻲ ﻛﻪ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎ ﺩﻳﺠﻴﺘﺎﻝ ﺗﺒﺪﻳﻞ ﻣﻲﺷﻮﺩ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺴﺘﮕﻲ ﺑﻪ ﻓﺮﻛﺎﻧﺴﻬﺎ‬
‫‪overtone‬ﻫﺎ ﻣﻮﺟﻮﺩ ﺩﺭ ﺳﻴﮕﻨﺎﻝ ﺩﺍﺭﺩ‪.‬‬
‫‪1‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﺷﻤﺎ ﺍﻣﻜﺎﻥ ﺑﺎﺯ ﺑﺎ ﺳﻴﮕﻨﺎﻟﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺩﺭ ﻧﺮﺥ ﻫﺎ ﻣﺘﻔﺎﻭﺕ ﻧﻤﻮﻧﻪﺑﺮﺩﺍﺭ ﺭﺍ ﺩﺍﺭﻳﺪ‪ ،‬ﻛﻪ ﻛﻴﻔﻴﺖ ﻫﺎ ﻣﺨﺘﻠﻔﻲ‬
‫ﺍﺯ ﺻﻮﺕ ﺭﺍ ﻋﺮﺿﻪ ﻣﻲ ﻛﻨﻨﺪ‪.‬‬
‫‪ -٢‬ﺗﺌﻮﺭ‬
‫‪ -١-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﭘﻴﻮﺳﺘﻪ ﻭ ﺗﺌﻮﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‬
‫ﺳﻴﮕﻨﺎﻟﻬﺎ ﺻﻮﺕ ﺍﺯ ﻧﻮﻉ ﺳﻴﮕﻨﺎﻟﻬﺎ ﭘﻴﻮﺳﺘﻪ )ﺁﻧﺎﻟﻮﮒ( ﻫﺴﺘﻨﺪ ﻛﻪ ﺑﻪ ﺗﺪﺭﻳﺞ ﺑﺎ ﻧﻘﺼﺎﻥ ﻳﺎﻓﺘﻦ ﻣﻨﺒﻊ ﺻﺪﺍ‪ ،‬ﺍﻓﺖ ﺩﺍﻣﻨﻪ ﭘﻴﺪﺍ ﻣﻲﻛﻨﻨﺪ‪ .‬ﺍﺯ ﺳﻮ‬
‫ﺩﻳﮕﺮ‪ ،‬ﻛﺎﻣﭙﻴﻮﺗﺮﻫﺎ‪ ،‬ﺩﺍﺩﻩ ﻫﺎ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﺩﻳﺠﻴﺘﺎﻝ ﺫﺧﻴﺮﻩ ﻣﻲ ﻛﻨﻨﺪ‪ :‬ﻳﻚ ﺭﺷﺘﻪ ‪ stream‬ﺍﺯ ﺑﻴﺘﻬﺎ ﺻﻔﺮ ﻭ ﻳﻚ‪ .‬ﺩﺍﺩﻩ ﻫﺎ 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 ﺳﻴﮕﻨﺎﻟﻬﺎ ﺁﻧﺎﻟﻮﮒ ﻭ‬
‫ﺩﻳﺠﻴﺘﺎﻝ‪ ،‬ﻋﻤﻠﻴﺎﺕ ﺍﻭﻟﻴﻪ ﺗﻤﺎﻡ ﻛﺎﺭﺗﻬﺎ ‪ adapter‬ﻭ ﻛﺎﺭﺗﻬﺎ ﺻﺪﺍ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫‪ -١-١-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺗﻨﺎﻭﺑﻲ ﻭ ﺗﺒﺪﻳﻞ ﺁﻧﺎﻟﻮﮒ ﺑﻪ ﺩﻳﺠﻴﺘﺎﻝ‬
‫ﺭﻭﺵ ﻣﻌﻤﻮﻝ ﻧﻤﺎﻳﺶ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﺍﺯ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ – ﭘﻴﻮﺳﺘﻪ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻣﺘﻨﺎﻭﺏ )ﭘﺮﻳﻮﺩﻳﻚ( ﺍﺳﺖ ﻛﻪ ﺩﺭ ﺁﻥ‬
‫ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎ ]‪ x[n‬ﺍﺯ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺯﻣﺎﻥ ﭘﻴﻮﺳﺘﻪ )‪ xc(t‬ﻣﻄﺎﺑﻖ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ‪.‬‬
‫)‪(١-٢‬‬
‫ﺷﮑﻞ‪ -٢‬ﻳﻚ ﻣﺒﺪﻝ ﺁﻧﺎﻟﻮﮒ ﺑﻪ ﺩﻳﺠﻴﺘﺎﻝ )‪ (A/D‬ﺍﻳﺪﻩ ﺁﻝ‬
‫‪1‬‬
‫ﺩﺭ ﺭﺍﺑﻄﺔ )‪ T ،(١-٢‬ﺗﻨﺎﻭﺏ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻭ ﻣﻌﻜﻮﺱ ﺁﻥ‪،‬‬
‫‪T‬‬
‫ﻫﺮﺗﺰ )‪ (Hz‬ﻧﻤﺎﻳﺶ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ ،‬ﻣﻲ ﺑﺎﺷﻨﺪ‪ .‬ﻣﺎ ﻳﻚ ﺳﻴﺴﺘﻢ ﺭﺍ ﻛﻪ ﺭﺍﺑﻄﺔ )‪ (١-٢‬ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﻚ ﻣﺒﺪﻝ ﺍﻳﺪﻩ ﺁﻝ ﭘﻴﻮﺳﺘﻪ – ﺑﻪ – ﮔﺴﺴﺘﻪ‬
‫= ‪ ، f s‬ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺑﺮ ﺣﺴﺐ ﻧﻤﻮﻧﻪ ﺑﺮ ﺛﺎﻧﻴﻪ ﻛﻪ ﻣﻌﻤﻮﻻﹰ ﺑﺮ ﺣﺴﺐ‬
‫)‪ (C/D‬ﻋﻤﻠﻲ ﻣﻲ ﻛﻨﺪ ﺩﺭ ﺷﻜﻞ ‪ ٢‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺍﻳﻢ‪ .‬ﺑﺮﺍ ﺫﺧﻴﺮﺓ ﻣﻘﺎﺩﻳﺮ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺗﻮﺳﻂ ﻛﺎﻣﭙﻴﻮﺗﺮ ﺑﺎ ﺩﻗﺖ ﻣﺤﺪﻭﺩ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﭘﻴﻮﺳﺘﻪ‬
‫ﺑﺎﻳﺪ ﺑﻪ ﻳﻚ ﺳﺮ ﻣﻘﺎﺩﻳﺮ ﺍﺯ ﭘﻴﺶ ﺗﻌﻴﻴﻦ ﺷﺪﻩ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﻮﻧﺪ‪ .‬ﻋﻤﻠﻴﺎﺕ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺩﻗﻴﻘﺎﹰ ﻫﻤﺎﻥ ﻋﻤﻠﻴﺎﺗﻲ ﺍﺳﺖ ﻛﻪ ﺩﺭ‬
‫ﻣﺒﺪﻝ ﺁﻧﺎﻟﻮﮒ – ﺑﻪ – ﺩﻳﺠﻴﺘﺎﻝ‪ ،‬ﻳﺎ ﺩﻳﺠﻴﺘﺎﻝ – ﺑﻪ – ﺁﻧﺎﻟﻮﮒ‪ ،‬ﺑﻪ ﺻﻮﺭﺕ ﺑﺮﻋﻜﺲ‪ ،‬ﺻﻮﺭﺕ ﻣﻲ ﮔﻴﺮﺩ‪ .‬ﺑﻴﺸﺘﺮ ﻛﺎﺭﺗﻬﺎ ﺻﺪﺍ ﻗﺎﺑﻠﻴﺖ ﺫﺧﻴﺮﻩ‬
‫ﺻﺪﺍ ﺭﺍ ﻫﻢ ﺑﻪ ﺻﻮﺭﺕ ‪ ٨‬ﺑﻴﺘﻲ ﻭ ﻫﻢ ‪ ١٦‬ﺑﻴﺘﻲ‪ ،‬ﺑﺮﺍ ﻛﻴﻔﻴﺖ ﻫﺎ ﺑﺎﻻﺗﺮ ﺻﻮﺗﻲ ﺩﺍﺭﻧﺪ‪.‬‬
‫‪ -٢-١-٢‬ﺗﺌﻮﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‬
‫ﺗﺌﻮﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺑﻪ ﻣﺎ ﻣﻲ ﮔﻮﻳﺪ ﻛﻪ ﭼﻪ ﺍﻧﺪﺍﺯﻩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻣﺎ ﻣﻲ ﺗﻮﺍﻧﺪ ﺳﺮﻳﻊ ﺑﺎﺷﺪ ﺗﺎ ﻧﻤﺎﻳﺶ ﺑﻬﺘﺮ ﺍﺯ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺩﺍﺷﺘﻪ ﺑﺎﺷﻴﻢ‪.‬‬
‫ﻣﻲ ﺩﺍﻧﻴﻢ ﻛﻪ ﺍﮔﺮ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺗﻐﻴﻴﺮﺍﺕ ﺧﻴﻠﻲ ﺳﺮﻳﻊ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ ،‬ﻣﺎ ﻫﻢ ﺑﺎﻳﺪ ﺩﺭ ﻓﺎﺻﻠﻪ ﻫﺎ ﻧﺰﺩﻳﻜﺘﺮ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ 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, Fall 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 ﺗﺌﻮﺭ ﺗﻨﺎﻭﺏ ‪ T‬ﻣﻲ ﺍﻧﺪﺍﺯﻳﻢ ﻛﻪ ﭼﻪ ﺍﻧﺪﺍﺯﻩ ﺩﻗﻴﻖ ﺑﺎﻳﺪ ﺁﻥ ﺭﺍ ﺗﻌﻴﻴﻦ ﻛﺮﺩ‪.‬‬
‫ﺗﺌﻮﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ‪ :‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ ﻛﻪ )‪ xc(t‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎ ﭘﻬﻨﺎ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﻭ ) ‪ X c ( jW‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺁﻥ ﺍﺳﺖ ﻛﻪ‬
‫ﺷﺮﻁ ﺯﻳﺮ ﺭﺍ ﺑﺮﺁﻭﺭﺩﻩ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫)‪(٢-٢‬‬
‫ﭘﺲ )‪ xc(t‬ﻣﻨﺤﺼﺮﹰﺍ ﺗﻮﺳﻂ ﻧﻤﻮﻧﻪ ﻫﺎ‬
‫ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ‬
‫) ‪ n = 0, ±1,±2,..., x[n] = xc (nT‬ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ ﺑﻪ ﺷﺮﻃﻲ ﻛﻪ ﺗﻨﺎﻭﺏ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺁﻥ ﻳﺎ‬
‫‪ W s‬ﺷﺮﻁ ﺯﻳﺮ ﺭﺍ ﺑﺮﺁﻭﺭﺩﻩ ﻛﻨﺪ‪.‬‬
‫)‪(٣-٢‬‬
‫ﻧﺘﻴﺠﻪ ﻓﻮﻕ ﺍﺑﺘﺪﺍ ﺗﻮﺳﻂ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﺑﺪﺳﺖ ﺁﻣﺪ ﻛﻪ ﺑﻪ ﻧﺎﻡ ﺗﺌﻮﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ‬
‫ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﻣﺸﻬﻮﺭ ﺷﺪ‪ .‬ﻓﺮﻛﺎﻧﺲ ‪ 2W N‬ﻛﻪ ﺑﺎﻳﺪ ﺍﺯ‬
‫ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﻮﭼﻜﺘﺮ ﺑﺎﺷﺪ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ .‬ﺑﺮﺍ ﺍﺛﺒﺎﺕ ﺗﺌﻮﺭ ﻓﻮﻕ‪ X(ejw) ،‬ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ‬
‫ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﺩﻧﺒﺎﻟﺔ ]‪ x[n‬ﺭﺍ ﺑﺮ ﺣﺴﺐ ) ‪ ، X c ( jW‬ﺗﺒﺪﻳﻞ 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, Fall 2008‬‬
‫ﺍﺯ ﺭﺍﺑﻄﻪ )‪ (٩-٢‬ﻣﺸﺎﻫﻪ ﻣﻲ ﺷﻮﺩ ﻛﻪ )‪ X(ejw‬ﻣﺠﻤﻮﻉ ﺗﺮﻣﻬﺎ ﻣﻘﻴﺎﺱ ﺑﻨﺪ ﺷﺪﻩ ﻭ ﺷﻴﻔﺖ ﻳﺎﻓﺘﺔ ) ‪ X c ( jW‬ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﻣﻘﻴﺎﺱ ﻓﺮﻛﺎﻧﺲ‬
‫‪w‬‬
‫ﺗﻮﺳﻂ‬
‫‪T‬‬
‫= ‪ W‬ﺗﻌﻴﻴﻦ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺩﺭ ﺣﺎﻟﻲ ﻛﻪ ﺷﻴﻔﺖ ﻫﺎ ﺑﺮﺍﺑﺮ ﺑﺎ ﺿﺮﺍﻳﺐ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ‬
‫‪2p‬‬
‫‪T‬‬
‫= ‪ Ws‬ﻣﻲ ﺑﺎﺷﻨﺪ‪.‬‬
‫‪ -٣-١-٢‬ﺑﺎﺯﺳﺎﺯ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎﻳﺶ )ﺗﺒﺪﻳﻞ ﺩﻳﺠﻴﺘﺎﻝ ﺑﻪ ﺁﻧﺎﻟﻮﮒ(‬
‫‪Ws‬‬
‫ﺍﺯ ﺷﮑﻞ‪ ،٥‬ﺍﮔﺮ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺑﺎﺷﺪ‪ ،‬ﻳﻌﻨﻲ ‪ W > W N‬ﺑﺮﺍ ‪ ، xc ( jW) = 0‬ﻛﻪ‬
‫‪2‬‬
‫ﺩﻭﺑﺎﺭﻩ ﺍﺯ )‪ X(jw‬ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺑﻪ ﻃﻮﺭ ﺩﻗﻴﻘﺘﺮ ﺍﺑﺘﺪﺍ ﻣﻲ ﺗﻮﺍﻧﻴﻢ ﺳﻴﮕﻨﺎﻝ ﻗﻄﺎﺭ ﺿﺮﺑﻪ )‪ xs(t‬ﺭﺍ ﺑﻮﺟﻮﺩ ﺁﻭﺭﻳﻢ‪.‬‬
‫‪ ، W N £‬ﻣﻲ ﺗﻮﺍﻥ ) ‪ X c ( jW‬ﺭﺍ‬
‫)‪(١٠-۲‬‬
‫‪Ws p‬‬
‫ﺳﭙﺲ ﻣﻲ ﺗﻮﺍﻧﻴﻢ ﻳﻚ ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺁﻝ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﺭﺍ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ =‬
‫‪2‬‬
‫‪T‬‬
‫= ‪ W c‬ﺑﻪ )‪ xs(t‬ﺍﻋﻤﺎﻝ ﻛﻨﻴﻢ‪.‬‬
‫)‪(١١-٢‬‬
‫ﺍﮔﺮ ) ‪ X c ( jW‬ﭘﻬﻨﺎ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺑﺎﺷﺪ ﺁﻧﮕﺎﻩ ﺳﻴﮕﻨﺎﻝ ﻓﻴﻠﺘﺮ ﺷﺪﺓ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺁﻥ ﺩﻗﻴﻘﺎﹰ ﺑﺮﺍﺑﺮ ) ‪ X c ( jW‬ﺍﺳﺖ‪ .‬ﻳﻌﻨﻲ‪:‬‬
‫ﺩﺭ ﺣﻮﺯﻩ ﺯﻣﺎﻥ‪ ،‬ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯ ﺍﻳﺪﻩ ﺁﻝ ) ‪ hr (t‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫)‪(۱۲-٢‬‬
‫ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯ ﺷﺪﻩ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺍﺳﺖ‬
‫)‪(١٣-٢‬‬
‫ﺷﮑﻞ‪ ،٣‬ﻧﻤﻮﺩﺍﺭ ﺑﻠﻮﻛﻲ ﺍﻳﻦ ﻓﺮﺁﻳﻨﺪ ﺑﺎﺯﺳﺎﺯ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪.‬‬
‫ﺍﺯ ﻧﺘﻴﺠﻪ ﻓﻮﻕ‪ ،‬ﻧﻤﻮﻧﻪ ﻫﺎ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺯﻣﺎﻥ ﭘﻴﻮﺳﺘﻪ ﻛﻪ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻛﺎﻓﻲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺍﻧﺪ )ﻳﻌﻨﻲ ‪ ،( W s > 2W N‬ﺑﺮﺍ‬
‫ﻧﻤﺎﻳﺶ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﻛﺎﻓﻲ ﻫﺴﺘﻨﺪ ﭘﺲ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﺍﺯ ﺭﻭ ﻧﻤﻮﻧﻪ ﻫﺎ ﻭ ﺩﺍﻧﺴﺘﻦ ﭘﺮﻳﻮﺩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻗﺎﺑﻞ ﺑﺎﺯﺳﺎﺯ ﺍﺳﺖ‪.‬‬
‫ﺩﺭ ﻋﻤﻞ‪ ،‬ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺁﻝ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ ﺳﺎﺯ ﻧﻴﺴﺖ ﻭ ﻣﺎ ﺑﺎﻳﺪ ﺗﻘﺮﻳﺐ ﺑﺰﻧﻴﻢ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﺍﻳﻦ‪ ،‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﻭﺍﻗﻌﻲ ﻣﻤﻜﻦ ﺍﺳﺖ ﭘﻬﻨﺎ‬
‫ﺑﺎﻧﺪ ﺯﻳﺎﺩ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ ﻛﻪ ﺗﻮﺳﻂ ﺳﻴﺴﺘﻢ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻗﺎﺑﻞ ﺍﺟﺮﺍ ﻧﺒﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺩﺭ ﻋﻤﻞ ﺑﺎﻳﺪ ﺍﺑﺘﺪﺍ ﻳﻚ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ﻭ ﺑﺎ‬
‫‪Ws‬‬
‫‪W‬‬
‫ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ ‪ W c £ s‬ﺭﺍ ﺍﻋﻤﺎﻝ ﻛﺮﺩ )‬
‫‪2‬‬
‫‪2‬‬
‫‪4‬‬
‫‪.( W N £‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪) -٣‬ﺍﻟﻒ( ﻳﻚ ﺳﻴﺴﺘﻢ ﺑﺎﺯﺳﺎﺯ ﺳﻴﮕﻨﺎﻝ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺍﻳﺪﻩ ﺁﻝ )ﺏ( ﭘﺎﺳﺦ ﻓﺮﻛﺎﻧﺴﻲ ﻳﻚ ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯ ﺍﻳﺪﻩ ﺁﻝ )ﺝ( ﭘﺎﺳﺦ‬
‫ﺿﺮﺑﻪ ﺑﻪ ﻳﻚ ﻓﻴﻠﺘﺮ ﺑﺎﺯﺳﺎﺯ ﺍﻳﺪﻩ ﺁﻝ‬
‫‪ -٢-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﮐﺎﻫﺸﻲ‬
‫ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ 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 ﺳﻮ )‪xc(t‬‬
‫ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺑﻪ ﻋﻼﻭﻩ‪ ،‬ﺍﮔﺮ‬
‫‪5‬‬
‫‪ X c ( jW) = 0‬ﺑﺮﺍ‬
‫‪ | W |> WN‬ﺁﻧﮕﺎﻩ‪ xd[n] ،‬ﻳﻚ ﻧﻤﺎﻳﺶ ﺩﻗﻴﻖ ﺍﺯ )‪ xc(t‬ﺍﮔﺮ‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫‪2p 1‬‬
‫‪= W s > 2W N‬‬
‫‪T M‬‬
‫ﺣﺪﺍﻗﻞ ‪ M‬ﺑﺮﺍﺑﺮ ﻧﺮﺥ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﺑﺎﺷﺪ ‪ .‬ﺑﻪ ﻃﻮﺭ ﻛﻠﻲ‪ ،‬ﺑﺮﺍ ﺟﻠﻮﮔﻴﺮ ﺍﺯ ﺗﺪﺍﺧﻞ‪ ،‬ﭘﻬﻨﺎ ﺑﺎﻧﺪ ﺩﻧﺒﺎﻟﻪ ﺍﺑﺘﺪﺍ ﺑﺎﻳﺪ ﺑﻪ ﻭﺳﻴﻠﻪ ﻓﻴﻠﺘﺮ ﺯﻣﺎﻥ –‬
‫= ‪ W s‬ﺑﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ‪ ،‬ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﺎ ﺿﺮﻳﺐ ‪ M‬ﻛﺎﻫﺶ ﺩﺍﺩ ﺍﮔﺮ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺍﻭﻟﻴﻪ‬
‫ﮔﺴﺴﺘﻪ ﺗﺎ ‪ M‬ﺑﺮﺍﺑﺮ ﻛﺎﻫﺶ ﻳﺎﺑﺪ‪ .‬ﻧﻤﻮﺩﺍﺭ ﺑﻠﻮﻛﻲ ﻳﻚ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ – ﻛﺎﻫﺸﻲ ﺩﺭ ﺷﮑﻞ‪ ٤‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫ﺷﮑﻞ‪ -٤‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﮐﺎﻫﺸﻲ ﺑﺎ ﺿﺮﻳﺐ ‪ ،M‬ﻛﻪ ﺩﺭ ﺁﻥ )‪ H(ejw‬ﻳﻚ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﺍﺳﺖ‪ .‬ﺩﺭ ﺣﺎﻟﺖ ﺍﻳﺪﻩ ﺁﻝ )‪ H(ejw‬ﺑﺎﻳﺪ ﻳﻚ ﻓﻴﻠﺘﺮ‬
‫‪p‬‬
‫ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ‬
‫‪M‬‬
‫ﺑﺮﺍ ﺗﻌﻴﻴﻦ ﺭﺍﺑﻄﻪ ﺑﻴﻦ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ]‪ x[n‬ﻭ ]‪ ،xd[n‬ﺍﺑﺘﺪﺍ ﺑﺎﻳﺪ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺯﻣﺎﻥ ﮔﺴﺴﺘﻪ )‪ x[n]=xc(nT‬ﺭﺍ ﺑﻪ ﻳﺎﺩ ﺁﻭﺭﻳﻢ‪.‬‬
‫= ‪ W 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 ﻣﻲﺗﻮﺍﻥ 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, Fall 2008‬‬
‫ﻛﻪ ﺩﺭ ﺷﻜﻞ )‪ (٥‬ﺑﺮﺍ ‪ M=2‬ﻭ ﺩﺭ ﺷﻜﻞ )‪ (٦‬ﺑﺮﺍ ‪ M=3‬ﻧﻤﺎﻳﺶ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﻲ ﺗﻮﺍﻥ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﺯﻣﺎﻧﻲ ﻛﻪ ‪ ،M=2‬ﻧﻤﻮﻧﻪ‬
‫ﺑﺮﺩﺍﺭ ﮐﺎﻫﺸﻲ ﺑﺎﻋﺚ ﻫﻤﭙﻮﺷﺎﻧﻲ ﻃﻴﻒ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻧﻤﻲﺷﻮﺩ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ‪ ،‬ﻭﻗﺘﻲ ‪ ،M=3‬ﻫﻤﭙﻮﺷﺎﻧﻲ ﺑﻴﻦ ﻃﻴﻔﻬﺎ ﺗﻜﺮﺍﺭ ﺷﺪ )ﻫﻤﺎﻥ‬
‫ﺗﺪﺍﺧﻞ( ﺭﺥ ﻣﻲﺩﻫﺪ‪ .‬ﺑﺮﺍ ﺟﻠﻮﮔﻴﺮ ﺍﺯ ﺗﺪﺍﺧﻞ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ ﻗﺒﻞ ﺍﺯ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﮐﺎﻫﺸﻲ ﺍﻟﺰﺍﻣﻲ ﺍﺳﺖ‪.‬‬
‫ﺷﮑﻞ‪ -٥‬ﻧﻤﺎﻳﺶ ﺣﻮﺯﻩ ﻓﺮﻛﺎﻧﺲ ﺩﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ )‪(M=2‬‬
‫‪7‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٦‬ﻧﻤﺎﻳﺶ ﺣﻮﺯﻩ ﻓﺮﻛﺎﻧﺲ ﺩﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ )‪(M=2‬‬
‫)‪ (a)-(c‬ﺑﺪﻭﻥ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪ ،‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﻛﺎﻫﺸﻲ ﺗﺪﺍﺧﻞ ﺩﺍﺭﺩ‪.‬‬
‫)‪ (d)-(f‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ ﺑﺎ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ ﺑﺮﺍ ﺟﻠﻮﮔﻴﺮ ﺍﺯ ﺗﺪﺍﺧﻞ‪.‬‬
‫‪ -٣-٢‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺍﻓﺰﺍﻳﺸﻲ ﺳﻴﮕﻨﺎﻟﻬﺎ ﺩﻳﺠﻴﺘﺎﻟﻲ‬
‫ﻛﺎﻫﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﮔﺴﺴﺘﻪ – ﺯﻣﺎﻥ ﺑﺎ ﺿﺮﻳﺐ ﺻﺤﻴﺢ ﺷﺎﻣﻞ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻳﻚ ﺩﻧﺒﺎﻟﻪ‪ ،‬ﻣﺸﺎﺑﻪ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺳﻴﮕﻨﺎﻝ‬
‫ﭘﻴﻮﺳﺘﻪ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺟﺎ ﺗﻌﺠﺐ ﻧﻴﺴﺖ ﻛﻪ ﺍﻓﺰﺍﻳﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻧﻴﺰ ﺑﺎ ﻋﻤﻠﻴﺎﺕ ﻣﺸﺎﺑﻪ ﺗﺒﺪﻳﻞ ‪ D/C‬ﺳﺮ ﻭ ﻛﺎﺭ ﺩﺍﺭﺩ‪ .‬ﺑﺮﺍ ﻣﺸﺎﻫﺪﻩ ﺍﻳﻦ‬
‫‪8‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﻣﻄﻠﺐ‪ ،‬ﺳﻴﮕﻨﺎﻝ ]‪ x[n‬ﺭﺍ ﻛﻪ ﻣﻲ ﺧﻮﺍﻫﻴﻢ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺁﻥ ﺭﺍ ﺑﺎ ﺿﺮﻳﺐ ‪ L‬ﺍﻓﺰﺍﻳﺶ ﺩﻫﻴﻢ‪ ،‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﺍﮔﺮ ﻣﺎ ﺳﻴﮕﻨﺎﻝ ﭘﻴﻮﺳﺘﻪ‬
‫)‪ xc(t‬ﺭﺍ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﻢ ﻫﺪﻑ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﻧﻤﻮﻧﻪ ﻫﺎ‬
‫)‪(٢١-٢‬‬
‫)‪(٢٢-٢‬‬
‫ﺍﺯ ﻧﻤﻮﻧﻪ ﻫﺎ ﺩﻧﺒﺎﻟﺔ ﻣﺎ ﻋﻤﻠﻴﺎﺕ ﺍﻓﺰﺍﻳﺶ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺭﺍ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺍﻓﺰﺍﻳﺸﻲ ﻣﻲ ﻧﺎﻣﻴﻢ‪.‬‬
‫‪énù‬‬
‫‪æ nT ö‬‬
‫‪xi[n] = x ê ú = x c ç‬‬
‫)‪÷ , n = 0,± L,±2L,... (۲۳ -٢‬‬
‫‪ëLû‬‬
‫‪è L ø‬‬
‫ﺷﮑﻞ‪ -۷:‬ﭘﺮﻭﺳﺔ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺍﻓﺰﺍﻳﺸﻲ )ﺩﺭﻭﻥ ﻳﺎﺑﻲ(‬
‫ﺷﮑﻞ‪ -٧‬ﻳﻚ ﺳﻴﺴﺘﻢ ﺭﺍ ﺑﺮﺍ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ]‪ xi[n‬ﺍﺯ ]‪ x[n‬ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﭘﺮﺩﺍﺯﺵ ﺯﻣﺎﻥ – ﮔﺴﺴﺘﻪ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺳﻴﺴﺘﻢ ﺳﻤﺖ ﭼﭗ‬
‫ﻳﻚ ﺍﻓﺰﺍﻳﻨﺪﺓ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ 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 .‬ﺑﺮﺍ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ]‪ xi[n‬ﺍﺯ ]‪ ،xe[n‬ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺍﻋﻤﺎﻝ ﻳﻚ ﻓﻴﻠﺘﺮ ﺍﻳﺪﻩ ﺍﻝ‬
‫‪p‬‬
‫ﭘﺎﺋﻴﻦ ﮔﺬﺭ ﺑﺎ ﻓﺮﻛﺎﻧﺲ ﻗﻄﻊ‬
‫‪L‬‬
‫‪9‬‬
‫= ‪ W c‬ﻭ ﺑﺎ ﺑﻬﺮﺓ ‪ L‬ﺩﺍﺭﻳﻢ )ﻛﻪ ﺩﺭ ﺷﻜﻞ ‪ (e),(d)-٨‬ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ(‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٨‬ﻧﻤﺎﻳﺶ ﺩﺍﻣﻨﻪ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺍﻓﺰﺍﻳﺸﻲ‬
‫‪10‬‬
‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫‪ -٣‬ﺁﺯﻣﺎﻳﺶ ﻫﺎ‬
‫‪ -١-٣‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺻﻮﺕ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎ ﻣﺘﻔﺎﻭﺕ‬
‫ﺩﺭ ﺍﻳﻦ ﺗﺠﺮﺑﻪ‪ ،‬ﺷﻤﺎ ﺻﺪﺍ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﺧﻮﺍﻫﻴﺪ ﻛﺮﺩ‪،‬‬
‫‪ (١‬ﺻﺪﺍ 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 ﺭﻭ ‪ file-properties-convert‬ﻛﻠﻴﻚ ﻛﻨﻴﺪ‪.‬‬
‫ﺳﭙﺲ ‪ 8000Hz,8bit, Mono 8kB/s‬ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ‪ ٥ .‬ﺛﺎﻧﻴﻪ ﺍﺯ ﺻﺪﺍ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﻛﻨﻴﺪ ﻭ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ﻓﺎﻳﻞ ‪ rec8.wav‬ﺩﺭ‬
‫ﺁﺩﺭﺱ ﺧﻮﺩ ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﺙ( ﺑﺮﺍ 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 ﺩﻳﮕﺮ 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 ﺻﺪﺍ‬
‫‪ CD‬ﺭﺍ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎ‬
‫‪ 8k‬ﻭ ‪ 22k‬ﻭ ‪ 44k‬ﺩﺭ‬
‫‪ 8bits/sample‬ﺿﺒﻂ ﻛﻨﻴﺪ‪ .‬ﻓﺎﻳﻠﻬﺎ ﺭﺍ ﺑﻪ ﻓﺮﻣﺖ ‪ cd22.wav cd11.wav‬ﻭ ‪ cd44.wav‬ﺩﺭ ﺁﺩﺭﺱ ﺧﻮﺩ ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٣‬ﺻﺪﺍ ‪ MIDI‬ﺭﺍ ﺑﺮﺍ ﻛﺎﻣﭙﻴﻮﺗﺮ ﺧﻮﺩ ﺿﺒﻂ ﻛﻨﻴﺪ‪.‬‬
‫ﻓﺎﻳﻞ ‪ MIDI‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ‪ media player‬ﭘﺨﺶ ﻛﻨﻴﺪ‪ ٥ .‬ﺛﺎﻧﻴﻪ ﺍﺯ ﻣﻮﺳﻴﻘﻲ ‪ MIDI‬ﺭﺍ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎ ‪ 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 ﻓﺮﻛﺎﻧﺴﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ 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 ‪ MATLAB‬ﺑﺮﺍ ﺣﻞ ﻣﺴﺄﻟﻪ ﺩﺍﺭﻳﺪ‪.‬‬
‫‪ -١‬ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺩﺭ ‪ 22KHz‬ﻭ ‪ ٨‬ﺑﻴﺘﻲ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ 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 ﺑﺮﺩﺍﺭ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺮﺳﺎﻧﻴﺪ‪.‬‬
‫‪ -٢‬ﻃﻴﻒ ﺳﻴﮕﻨﺎﻟﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺍﻓﺰﺍﻳﺸﻲ ﻭ ﻛﺎﻫﺸﻲ ﺭﺍ ﻧﻤﺎﻳﺶ ﺩﻫﻴﺪ ﻭ ﺳﭙﺲ ﺁﻧﻬﺎ ﺭﺍ ﺑﺎ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺧﻄﺎ ﻣﺮﺑﻊ‬
‫ﻣﻴﺎﻧﮕﻴﻦ )‪ (MSE‬ﺑﻴﻦ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺩﺭ ﻓﺮﻛﺎﻧﺲ ‪ ٢٢KHz‬ﻭ ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯ ﺷﺪﻩ ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻛﻨﻴﺪ‪ MSE .‬ﺑﻴﻦ ﺩﻭ ﺳﻴﮕﻨﺎﻝ )‪ x(n‬ﻭ‬
‫)‪ y(n‬ﺑﺎ ﻃﻮﻝ ‪ N‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫‪N‬‬
‫‪MSE = å [ x (n ) - y(n )]2 / N‬‬
‫‪n =1‬‬
‫‪ -٣‬ﻣﺮﺍﺣﻞ ‪ ١‬ﻭ ‪ ٢‬ﺭﺍ ﺑﺮﺍ ﻣﻮﺍﺭﺩ ﺯﻳﺮ ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪.‬‬
‫ﺍﻟﻒ( ﻳﻚ ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ )ﺷﻤﺎ ﻣﻲ ﺗﻮﺍﻧﻴﺪ ﻃﻮﻝ ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ( ﺑﺮﺍ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪.‬‬
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‫‪CE 342 – Multimedia HW# 1‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺏ( ﺍﺯ ﺗﺎﺑﻊ ”‪ “FIR1‬ﺩﺭ ‪ MATLAB‬ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ ﺗﺎ ﻓﻴﻠﺘﺮ ﺑﻬﺘﺮ ﻃﺮﺍﺣﻲ ﻛﻨﻴﺪ‪ .‬ﺍﺯ ﺗﺎﺑﻊ ”)(‪ “interp‬ﺑﺮﺍ ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﻃﻮﻟﻬﺎ ﻣﺘﻔﺎﻭﺕ ﺑﺮﺍ ﻓﻴﻠﺘﺮﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﻃﻴﻒ ﻓﻴﻠﺘﺮﻫﺎ ﭘﻴﺶ ﻭ ﭘﺲ ﭘﺮﺩﺍﺯﺵ ﺭﺍ ﻋﻼﻭﻩ ﺑﺮ ﺳﻴﮕﻨﺎﻟﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ‬
‫ﻛﺎﻫﺸﻲ ﻳﺎ ﺍﻓﺰﺍﻳﺸﻲ ﻧﻤﺎﻳﺶ ﺩﻫﻴﺪ‪.‬‬
‫‪ -٤‬ﻣﺮﺍﺣﻞ ‪ ۱‬ﺗﺎ ‪ ٣‬ﺭﺍ ﺑﺮﺍ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺩﺭ ‪ 11KHz‬ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ )ﺍﺧﺘﻴﺎﺭ (‬
‫‪ -٥‬ﺗﻤﺎﻡ ﻧﺘﺎﻳﺞ ﺭﺍ ﭼﺎﭖ ﻛﻨﻴﺪ‪.‬‬
‫ﺑﺮﺍ 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 ﻓﻴﻠﺘﺮ ﺗﻮﺳﻂ ﺗﺎﺑﻊ ) (‪conv‬‬
‫ﺍﻧﺠﺎﻡ ﻣﻲ ﺷﻮﺩ‪ .‬ﺷﻤﺎ ﻣﻲ ﺗﻮﺍﻧﻴﺪ ﺍﺯ ﺩﺳﺘﻮﺭ ﺯﻳﺮ ﺑﺮﺍ ﺷﻨﺎﺧﺖ ﻳﻚ ﺗﺎﺑﻊ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ ‪ help conv.‬ﺑﻪ ﻃﻮﺭ ﺧﻼﺻﻪ‪ ،‬ﺷﻤﺎ‬
‫ﺑﺎﻳﺪ ﺑﺮﻧﺎﻣﻪ ﻫﺎ ‪ Appendix A‬ﺭﺍ ﺑﻬﺒﻮﺩ ﺩﻫﻴﺪ ﺗﺎ ﻣﻮﺍﺭﺩ ﺯﻳﺮ ﺭﺍ ﻋﻤﻠﻲ ﺳﺎﺯﻧﺪ‪.‬‬
‫ﺍﻟﻒ( ﺑﺪﻭﻥ ﭘﻴﺶ ﻓﻴﻠﺘﺮ ﻛﺮﺩﻥ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺩﻭﺑﺎﺭﻩ ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﻩ ﺍﻭﻟﻴﻪ‬
‫ﺏ( ﻓﻴﻠﺘﺮ ﻣﻴﺎﻧﮕﻴﻦ‪ ،‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﺓ ﺍﻭﻟﻴﻪ‬
‫ﺝ( ) (‪ ،fir1‬ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ،٢‬ﻭ ﺑﺮﮔﺸﺖ ﺑﻪ ﺍﻧﺪﺍﺯﺓ ﺍﻭﻟﻴﻪ‬
‫‪ -٤‬ﮔﺰﺍﺭﺵ‬
‫ﮔﺰﺍﺭﺵ ﺷﻤﺎ ﺑﺎﻳﺪ ﺷﺎﻣﻞ ‪ m‬ﻓﺎﻳﻠﻬﺎ ﻭ ﻓﻴﻠﺘﺮﻫﺎ ﻭ ﺷﻜﻠﻬﺎ ﺧﺮﻭﺟﻲ ﺑﺎﺷﺪ‪ .‬ﭘﺮﺳﺸﻬﺎ ﺯﻳﺮ ﺭﺍ ﺩﺭ ﮔﺰﺍﺭﺵ ﺧﻮﺩ ﭘﺎﺳﺦ ﺩﻫﻴﺪ‪ .‬ﺗﻤﺎﻣﻲ ﻓﺎﻳﻞ ﻫﺎ‬
‫ﮔﺰﺍﺭﺵ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﻳﻚ ﻓﺎﻳﻞ ﻓﺸﺮﺩﻩ ﺑﻪ ﺁﺩﺭﺱ ‪ TA e-mail‬ﺑﻔﺮﺳﺘﻴﺪ‪(yashil1@yahoo.com) .‬‬
‫‪ (١‬ﺍﮔﺮ ﺳﻴﮕﻨﺎﻝ ﻭﺭﻭﺩ‬
‫) ‪ sin( 2pft‬ﺍﺳﺖ ﺯﻣﺎﻧﻲ ﻛﻪ ‪ f=6KHz‬ﻭ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ‪ 8KHz‬ﺍﺳﺖ‪ ،‬ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ‬
‫ﭼﻪ ﺧﻮﺍﻫﺪ ﺑﻮﺩ؟ ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯ 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 ﻓﺎﻳﻠﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﺩﺭ ﻧﺮﺧﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻭ ‪ bits/sample‬ﻣﺘﻔﺎﻭﺕ ﻧﻈﺮ ﺩﻫﻴﺪ‪ .‬ﺩﺭﺑﺎﺭﺓ ﺗﻔﺎﻭﺕ ﺻﻮﺕ ﻭ‬
‫ﮔﻔﺘﺎﺭ ﺩﺭ ﻧﺮﺧﻬﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻣﺨﺘﻠﻒ ﺑﺤﺚ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٣‬ﺻﺪﺍ ﺩﺭﻭﻥ ﻳﺎﺑﻲ ﺷﺪﻩ ﺑﻌﺪ ﺍﺯ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﻛﺎﻫﺸﻲ ﺑﺎ ﻧﺮﺥ ‪ ٢‬ﺭﺍ ﺑﺎ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭ ﺷﺪﻩ ﻛﺎﻫﺸﻲ ﻭ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫ﺗﻮﺿﻴﺢ ﺩﻫﻴﺪ ﻛﻪ ﭼﺮﺍ ﺳﻴﮕﻨﺎﻟﻬﺎ ﺑﺎﺯﺳﺎﺯ 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
‫‪H. Rabiee, Fall 2008‬‬
CE 342 – Multimedia HW# 1
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 1
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 1
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 1
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 1
H. Rabiee, Fall 2008
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