‫ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﯽ‬
‫ﺳﯿﺴﺘﻢ ﻫﺎي ﭼﻨﺪرﺳﺎﻧﻪاي )‪(40-342‬‬
‫داﻧﺸﮑﺪه ﻣﻬﻨﺪﺳﯽ ﮐﺎﻣﭙﯿﻮﺗﺮ‬
‫ﺗﺮم ﺑﻬﺎر ‪1387‬‬
‫دﮐﺘﺮ ﺣﻤﯿﺪرﺿﺎ رﺑﯿﻌﯽ‬
‫ﺗﮑﻠﯿﻒ ﺷﻤﺎره‪ :2‬ﻓﺸﺮده ﺳﺎزي ﺳﯿﮕﻨﺎل‪ :‬ﮔﻔﺘﺎر و ﺻﻮت‬
‫‪ -1‬ﻣﻘﺪﻣﻪ‬
‫ﺁﻧﭽﻪ ﺗﻮﺯﻳﻊ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺕ ﻭ ﮔﻔﺘﺎﺭ ﺭﺍ ﺑﺪﻭﻥ ﻧﻴﺎﺯ ﺑﻪ ﺍﺧﺘﺼﺎﺹ ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻭﺳﻴﻌﻲ ﺑﺮﺍﻱ ﺍﻧﺘﻘﺎﻝ ﻭ ﺫﺧﻴﺮﻩ ﺣﺠﻢ ﺯﻳﺎﺩﻱ ﺍﺯ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ‬
‫ﺻﻮﺗﻲ ﻣﻤﻜﻦ ﻣﻲ ﺳﺎﺯﺩ‪ ،‬ﺗﻜﻨﻴﻚ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻳﺎ ﺑﻪ ﺑﻴﺎﻥ ﺩﻳﮕﺮ ﻛﺪ ﻛﺮﺩﻥ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﺗﻜﻨﻴﻚ ﻣﻘﺪﺍﺭ ﺩﺍﺩﻩ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺮﺍﻱ ﺍﻧﺘﻘﺎﻝ ﻭ ﺫﺧﻴﺮﻩ‬
‫ﺻﻮﺕ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺭﺍ ﻫﻢ ﺩﺭ ﻃﻮﻝ ﻣﺮﺣﻠﻪ ﺗﺒﺪﻳﻞ ﺁﻧﺎﻟﻮﮒ – ﺑﻪ – ﺩﻳﺠﻴﺘﺎﻝ ﻭ ﻫﻢ ﭘﺲ ﺍﺯ ﺫﺧﻴﺮﻩ ﻓﺎﻳﻞ ﺧﺎﻡ ﺑﻪ ﺻﻮﺭﺕ‬
‫ﺩﻳﺠﻴﺘﺎﻟﻲ‪ ،‬ﻛﺎﻫﺶ ﻣﻲ ﺩﻫﺪ‪ .‬ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻭ ﻋﻜﺲ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﺑﻮﺳﻴﻠﻪ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﻣﺘﻌﺪﺩﻱ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﺳﺖ ﻛﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺩﺭ‬
‫ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﻧﺮﻡ ﺍﻓﺰﺍﺭﻱ ﻳﺎ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﺧﺎﺹ ﻣﺪﺍﺭﻫﺎﻱ ﻣﺠﺘﻤﻊ )ﺗﺮﺍﺷﻪ ﻫﺎ( ﺑﻜﺎﺭ ﮔﺮﻓﺘﻪ ﺷﻮﺩ‪.‬‬
‫ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎﻱ ﻣﺘﻌﺪﺩ ﺟﻬﺎﻧﻲ ﺑﺮﺍﻱ ﻛﺪ ﻛﺮﺩﻥ ﻭﻳﺪﻳﻮ ﻭ ﺻﻮﺕ ﭘﺎﻳﻪ ﺭﻳﺰﻱ ﺷﺪﻩ ﺍﻧﺪ‪ .‬ﺑﺮﺧﯽ ﺍﺯ ﺍﻳﻦ ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎ ﺷﺎﻣﻞ ‪MPEG-،MPEG-1‬‬
‫‪ 2‬ﻭ ‪ MPEG-4‬ﻣﻲ ﺑﺎﺷﻨﺪ‪ .‬ﺍﻟﺒﺘﻪ ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎﻱ ﻣﺘﻌﺪﺩﻱ ﺑﺮﺍﻱ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻭ ﻋﻜﺲ ﻋﻤﻞ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﺷﻜﻞ ﻣﻮﺟﻬﺎﻱ ﺻﻮﺕ ﻭ‬
‫ﮔﻔﺘﺎﺭ ﺑﺮﺍﻱ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ‪ desktop‬ﭼﻨﺪ ﺭﺳﺎﻧﻪ ﺍﻱ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪ .‬ﺑﺨﺶ ﻫﺎﻱ ﺑﻌﺪﻱ ﺑﻪ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﻣﻌﻤﻮﻝ ﻭ ﺍﻧﻮﺍﻉ ﮔﻮﻧﺎﮔﻮﻧﻲ ﺍﺯ ﺭﻭﺷﻬﺎﻱ‬
‫ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﺑﺮﺍﻱ ﺻﻮﺕ ﻭ ﮔﻔﺘﺎﺭ ﺍﺧﺘﺼﺎﺹ ﺩﺍﺭﺩ‪.‬‬
‫‪ -2‬ﺗﺌﻮرﯾﻬﺎ و ﻃﺮﺣﻬﺎ‬
‫ﻣﺎ ﻗﺒﻼﹰ ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﺩﺭ ﺗﻜﻠﻴﻒ ‪ ١‬ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﺩﺍﺩﻩ ﺍﻳﻢ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻧﺸﺎﻥ ﺩﺍﺩﻳﻢ ﻛﻪ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺁﻧﺎﻟﻮﮒ ﻧﻤﺎﻳﺶ‬
‫ﻣﻨﺤﺼﺮ ﺑﻪ ﻓﺮﺩﻱ ﺍﺯ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻣﻲ ﺑﺎﺷﻨﺪ ﺑﻪ ﺷﺮﻃﻲ ﻛﻪ ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻣﺤﺪﻭﺩ ﺩﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ ﻭ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺣﺪﺍﻗﻞ ﺩﻭﺑﺮﺍﺑﺮ ﻓﺮﻛﺎﻧﺲ‬
‫ﺳﻴﮕﻨﺎﻝ ﺑﺎﺷﺪ‪ .‬ﺍﺯ ﺁﻧﺠﺎﻳﻲ ﻛﻪ ﻣﺎ ﺑﺎ ﻧﻤﺎﻳﺶ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺻﻮﺕ ﻭ ﮔﻔﺘﺎﺭ ﺳﺮ ﻭ ﻛﺎﺭ ﺩﺍﺭﻳﻢ‪ ،‬ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺩﺍﻧﺴﺘﻦ ﺧﺼﻮﺻﻴﺎﺕ ﻃﻴﻔﻲ ﺻﺪﺍ ﻭ ﮔﻔﺘﺎﺭ‬
‫ﺩﺍﺭﻳﻢ‪ .‬ﺑﻪ ﺭﺍﺣﺘﻲ ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺑﺮﺍﻱ ﺻﺪﺍﻫﺎﻱ ﻭﺍﮐﺪﺍﺭ‪ ،‬ﺩﺍﻣﻨﻪ ﻃﻴﻒ ﻓﺮﻛﺎﻧﺴﻲ ﺳﻴﮕﻨﺎﻝ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﺑﺎﻻﻱ ‪ ٤٠dB ،٤KHz‬ﭘﺎﻳﻴﻦ‬
‫ﺗﺮ ﺍﺯ ﻗﻠﻪ ﻃﻴﻔﻲ ﺳﻴﮕﻨﺎﻝ ﺍﺳﺖ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ‪ ،‬ﺩﺭ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺗﻲ‪ ،‬ﻃﻴﻒ ﺳﻴﮕﻨﺎﻝ ﺣﺘﻲ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﺑﺎﻻﻱ ‪ ٨KHz‬ﺑﻪ ﻃﻮﺭ ﻗﺎﺑﻞ‬
‫ﻣﻼﺣﻈﻪ ﺍﻱ ﺍﻓﺖ ﻧﻤﻲ ﻛﻨﺪ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﺍﻳﻦ‪ ،‬ﺩﺭ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﻛﺎﻣﭙﻴﻮﺗﺮﻱ ﺑﺮﺍﻱ ﻧﻤﺎﻳﺶ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﻣﻤﻜﻦ ﻳﻚ ﻧﻤﻮﻧﻪ‬
‫ﻛﻪ ﺩﺭ ﻣﺤﺪﻭﺩﺓ ﭘﻴﻮﺳﺘﻪ ﺍﻱ ﺗﻐﻴﻴﺮ ﻣﻲ ﻛﻨﻨﺪ ﺑﺎﻳﺪ ﺑﻪ ﺗﻌﺪﺍﺩ ﻣﺤﺪﻭﺩﻱ ﺍﺯ ﻣﻘﺎﺩﻳﺮ ﮔﺴﺴﺘﻪ ﺗﺒﺪﻳﻞ ﺷﻮﺩ‪ .‬ﺍﻳﻦ ﭘﺮﻭﺳﻪ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻧﺎﻣﻴﺪﻩ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫‪ -1-2‬ﮐﻮاﻧﺘﯿﺰاﺳﯿﻮن ﺳﯿﮕﻨﺎﻟﻬﺎي ﻧﻤﻮﻧﻪ ﺑﺮداري ﺷﺪه‬
‫ﻣﺤﺪﻭﺩﻩ ﻫﺎ ﻭ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﻤﻜﻦ ﺍﺳﺖ ﺑﻪ ﺻﻮﺭﺗﻬﺎﻱ ﻣﺘﻌﺪﺩﻱ ﺍﻧﺘﺨﺎﺏ ﺷﻮﻧﺪ ﻛﻪ ﺑﺴﺘﮕﻲ ﺑﻪ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﺍﺯ ﭘﻴﺶ ﺗﻌﻴﻴﻦ ﺷﺪﺓ‬
‫ﻧﻤﺎﻳﺶ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺁﻥ ﺩﺍﺭﺩ‪ .‬ﺑﺎ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻣﺤﺪﻭﺩﺓ ﺩﻳﻨﺎﻣﻴﻚ )ﺣﺪﺍﻗﻞ ﺗﺎ ﺣﺪﺍﻛﺜﺮ( ﺳﻴﮕﻨﺎﻝ ‪ ،R‬ﺑﻪ ‪ W‬ﺑﺎﺯﻩ ﺑﺎ ﻃﻮﻝ ﻳﻜﺴﺎﻥ ‪D‬‬
‫ﺗﻘﺴﻴﻢ ﻣﻲ ﺷﻮﺩ‪ .‬ﻣﺎ ‪ D‬ﺭﺍ ﭘﻠﺔ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﻲ ﻧﺎﻣﻴﻢ‪ .‬ﺭﺍﺑﻄﻪ ﻭﺭﻭﺩﻱ ﻭ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻧﺸﺪﻩ‪ ،‬ﻭ ﺧﺮﻭﺟﻲ )ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ( ﺑﺮﺍﻱ‬
‫‪‬‬
‫ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ ﺩﺭ ﺷﮑﻞ‪ ١‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻛﻪ ﺩﺭ ﺁﻥ ‪ ،xi‬ﻣﺤﺪﻭﺩﺓ ﺭﺍﺳﺖ ﺑﺎﺯﺓ ‪ i‬ﻭ ‪ xi‬ﺳﻄﺢ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﺓ ﺍﻳﻦ ﺑﺎﺯﻩ ﺍﺳﺖ‬
‫ﻛﻪ ﺷﺮﻁ ﻫﺎﻱ ﺯﻳﺮ ﺭﺍ ﺑﺮﺁﻭﺭﺩﻩ ﻣﻲ ﺳﺎﺯﺩ‪.‬‬
‫)‪(١-٣‬‬
‫‪1‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫)‪(٢-٣‬‬
‫ﻫﺮ ﻣﻘﺪﺍﺭ ﺩﺭ ﻣﺤﺪﻭﺩﺓ ‪i‬ﺍﻡ ﺑﻪ ﻣﻘﺪﺍﺭ ﻣﻴﺎﻧﻲ ﺍﻳﻦ ﻣﺤﺪﻭﺩﻩ ﻧﮕﺎﺷﺖ ﻣﻲﺷﻮﺩ‪.‬‬
‫)‪(٣-٣‬‬
‫ﺩﺭ ﻛﺎﻣﭙﻴﻮﺗﺮ‪ ،‬ﻫﺮ ﺳﻄﺢ ﺑﺎ ﻳﻚ ﻛﻠﻤﻪ ﻛﺪ ﺑﺎﻳﻨﺮﻱ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﺎ ‪ W‬ﺳﻄﺢ ﻛﻮﺍﻧﻴﺰ ﺷﺪﻩ‪ ،‬ﻫﺮ ﺳﻄﺢ ﻣﻲﺗﻮﺍﻧﺪ ﺑﺎ ])‪ B = [log2(L‬ﺑﻴﺖ‬
‫ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﻮﺩ )ﺷﮑﻞ‪.(١‬‬
‫ﺷﮑﻞ‪ -1‬ﺧﺼﻮﺻﯿﺎت ورودي – ﺧﺮوﺟﯽ ﯾﮏ ﮐﻮاﻧﯿﺰه ﮐﻨﻨﺪة ‪ 3‬ﺑﯿﺘﯽ‬
‫ﺍﮔﺮ ﻣﺤﺪﻭﺩﺓ ﺳﻴﮕﻨﺎﻝ ‪ R‬ﺑﺎﺷﺪ‪ ،‬ﻳﻚ ﻛﻮﺍﻧﻴﺰﻩ ﻛﻨﻨﺪﻩ ﻳﻜﻨﻮﺍﺧﺖ ﻓﻘﻂ ﻳﻚ ﭘﺎﺭﺍﻣﺘﺮ ﺩﺍﺭﺩ‪ :‬ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ‪ N‬ﻳﺎ ﺍﻧﺪﺍﺯﻩ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ‪ ، D‬ﻛﻪ ﻫﺮ ﺩﻭ‬
‫ﺑﺎ ﺭﺍﺑﻄﺔ ﺯﻳﺮ ﺑﻪ ﻫﻢ ﺍﺭﺗﺒﺎﻁ ﺩﺍﺭﻧﺪ‪.‬‬
‫)‪(٤-٣‬‬
‫‪B‬‬
‫ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ‪ N‬ﻣﻌﻤﻮﻻﹰ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﺷﻮﻧﺪ ﻛﻪ ﺑﻪ ﺻﻮﺭﺕ ‪ 2‬ﺑﺎﺷﻨﺪ ﺗﺎ ﺑﻬﺘﺮﻳﻦ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻛﻠﻤﺔ ﻛﺪ ‪ B‬ﺑﻴﺘﻲ ﺷﻮﺩ‪ .‬ﺍﮔﺮ ﺳﻴﮕﻨﺎﻝ‬
‫ﺗﺎﺑﻊ ﭼﮕﺎﻟﻲ ﺍﺣﺘﻤﺎﻝ ﻣﺘﻘﺎﺭﻥ ﺑﺎﺷﺪ ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﻛﻪ ‪ | x (n ) |£ x max‬ﻳﺎ ‪ R=2xmax‬ﺑﺎﺷﺪ‪،‬ﺁﻧﮕﺎﻩ ﺑﺎﻳﺪ ﻣﻘﺎﺩﻳﺮ ﺯﻳﺮ ﺗﻨﻈﻴﻢ ﺷﻮﻧﺪ‪.‬‬
‫)‪(٥-٣‬‬
‫‪‬‬
‫ﺩﺭ ﺑﺤﺚ ﺗﺎﺛﻴﺮﺍﺕ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﻔﻴﺪ ﺑﻪ ﻧﻈﺮ ﻣﻲ ﺭﺳﺪ ﻛﻪ ﻣﻘﺎﺩﻳﺮ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ )‪ x(n‬ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻧﻤﺎﻳﺶ ﺩﻫﻴﻢ‬
‫)‪(٦-٣‬‬
‫ﻛﻪ )‪ x(n‬ﻧﻤﻮﻧﻪ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻧﺸﺪﻩ‪ e(n) ،‬ﺧﻄﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻳﺎ ﻧﻮﻳﺰ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺍﺳﺖ‪ .‬ﺍﺯ ﺷﻜﻞ ‪ ١‬ﺩﻳﺪﻩ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺍﮔﺮ ‪ D‬ﻭ ‪ B‬ﻣﺎﻧﻨﺪ ﺭﺍﺑﻄﺔ )‪(٥-٣‬‬
‫ﺍﻧﺘﺨﺎﺏ ﺷﻮﻧﺪ‪ ،‬ﺁﻧﮕﺎﻩ‬
‫)‪(٧-٣‬‬
‫ﻧﺴﺒﺖ ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﻧﻮﻳﺰ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺩﺭ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﻴﺎﻥ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫‪2‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫)‪(٨-٣‬‬
‫‪R2‬‬
‫ﺑﻪ ﻳﺎﺩ ﺑﻴﺎﻭﺭﻳﻢ ﻛﻪ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻝ ﺑﺎ ﺗﻮﺯﻳﻊ ﻳﻜﻨﻮﺍﺧﺖ ﺩﺭ ﻣﺤﺪﻭﺩﺓ ‪ ،R‬ﻭﺍﺭﻳﺎﻧﺲ ﺑﺮﺍﺑﺮ‬
‫‪12‬‬
‫‪D D‬‬
‫) ‪ (- ,‬ﻳﻜﻨﻮﺍﺧﺖ ﺑﺎﺷﺪ‪ ،‬ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺮﺍﻱ ﻧﻮﻳﺰ ﻧﺘﻴﺠﻪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫‪2 2‬‬
‫ﺍﺳﺖ‪ .‬ﺍﮔﺮ ﺗﻮﺯﻳﻊ ﺩﺍﻣﻨﻪ ﻧﻮﻳﺰ ﺩﺭ ﺑﺎﺯﺓ‬
‫)‪(۹-٣‬‬
‫ﺑﺎ ﺟﺎﻳﮕﺰﻳﻨﻲ ﺭﺍﺑﻄﺔ )‪ (٩-٣‬ﺩﺭ ﺭﺍﺑﻄﺔ )‪:(٨-٣‬‬
‫)‪(١٠-٣‬‬
‫ﻳﺎ ﺑﻴﺎﻥ ﺧﻄﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺩﺭ ﻭﺍﺣﺪ ‪dB‬‬
‫)‪(۱۱-۳‬‬
‫ﺍﮔﺮ ﻣﺤﺪﻭﺩﺓ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺭﺍ ‪ xmax = 4s x‬ﻓﺮﺽ ﻛﻨﻴﻢ ﺳﭙﺲ ﺭﺍﺑﻄﺔ )‪ (١١-٣‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺩﺭ‬
‫ﻣﻲ ﺁﻳﺪ‪.‬‬
‫)‪(١٢-٣‬‬
‫ﺍﻳﻦ ﺭﺍﺑﻄﻪ ﺑﻴﺎﻥ ﻣﻲ ﻛﻨﺪ ﻛﻪ ﻫﺮ ﺑﻴﺖ ﺍﺿﺎﻓﻲ‪ 6dB ،‬ﺑﻪ ﺑﻬﺒﻮﺩ ‪ SNR‬ﻛﻤﻚ ﻣﻲ ﻛﻨﺪ‪ .‬ﺑﺮﺍﻱ ﺣﻔﻆ ﺍﻋﺘﺒﺎﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﺮﺩﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻻﺯﻡ ﺍﺳﺖ‬
‫ﺗﺎ ﺗﻌﺪﺍﺩ ﺑﻴﺖ ﺑﻴﺸﺘﺮﻱ ﻧﺴﺒﺖ ﺑﻪ ﺁﻧﺎﻟﻴﺰ ﻗﺒﻠﻲ ﻛﻪ ﺩﺭ ﺁﻥ ﺳﻴﮕﻨﺎﻝ ﺍﻳﺴﺘﺎﻥ ﻭ ﺩﺍﺭﺍﻱ ﺗﻮﺯﻳﻊ ﻣﺘﻘﺎﺭﻥ ﻓﺮﺽ ﻣﻲ ﺷﺪ ﻭ ‪ X max = 4s x‬ﺑﻮﺩ‪،‬‬
‫ﺍﺧﺘﺼﺎﺹ ﻳﺎﺑﺪ‪ .‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ‪ ،‬ﺩﺭ ﺣﺎﻟﻲ ﻛﻪ ﺭﺍﺑﻄﺔ )‪ (١٢-٣‬ﺗﻌﺪﺍﺩ ﺑﻴﺖ ﻫﺎ )‪ (B‬ﺭﺍ ﺑﺮﺍﺑﺮ‪ ۷‬ﻗﺮﺍﺭ ﻣﻲ ﺩﻫﺪ ﺗﺎ ‪) SNR‬ﺣﺪﻭﺩ ‪ (36dB‬ﻛﻴﻔﻴﺖ‬
‫ﻗﺎﺑﻞ ﻗﺒﻮﻟﻲ ﺭﺍ ﺩﺭ ﺍﻏﻠﺐ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ ﺗﺄﻣﻴﻦ ﻛﻨﺪ‪ ،‬ﺑﻪ ﻃﻮﺭ ﻣﻌﻤﻮﻝ ﺗﻌﺪﺍﺩ ﺑﻴﺖ ﻫﺎﻱ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺮﺍﻱ ﺗﺄﻣﻴﻦ ﻛﻴﻔﻴﺖ ﺑﺎﻻﻱ ﺳﻴﮕﻨﺎﻝ‬
‫ﮔﻔﺘﺎﺭ ﺑﺎ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ١١ ،‬ﺑﻴﺖ ﺍﺳﺖ‪.‬‬
‫‪m - law -2-1-2‬‬
‫ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﺮﺩﻥ ﻳﻜﻨﻮﺍﺧﺖ ﺗﻨﻬﺎ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺑﺎ ﺗﻮﺯﻳﻊ ﻳﻜﻨﻮﺍﺧﺖ ﺑﻬﻴﻨﻪ ﺍﺳﺖ‪ .‬ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻟﻬﺎﻳﻲ ﻛﻪ ﻧﺰﺩﻳﻚ ﻣﻘﺎﺩﻳﺮ ﻛﻮﭼﻚ ﺩﺍﻣﻨﻪ ﺗﺠﻤﻊ‬
‫ﺩﺍﺭﻧﺪ‪ ،‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ ﺗﻮﺯﻳﻊ ﮔﻮﺳﻲ ﺑﺎ ﻣﻴﺎﻧﮕﻴﻦ ﺻﻔﺮ‪ ،‬ﺑﻬﺘﺮ ﺍﺳﺖ ﻛﻪ ﺩﺍﻣﻨﻪ ﻫﺎﻱ ﻛﻮﭼﻚ ﺑﺎ ﺩﻗﺖ ﺑﻴﺸﺘﺮﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﻮﻧﺪ‪ .‬ﺑﺮﺍﻱ ﺗﺤﻘﻖ ﺍﻳﻦ ﺍﻣﺮ‬
‫ﺍﺑﺘﺪﺍ ﺑﺎﻳﺪ ﻧﮕﺎﺷﺘﻲ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﻛﺮﺩ ﺑﻪ ﻃﻮﺭﻱ ﻛﻪ ﻣﻘﺎﺩﻳﺮ ﻛﻮﭼﻚ ﺭﺍ ﺗﻘﻮﻳﺖ ﻛﻨﺪ ﻭ ﺳﭙﺲ ﻳﻚ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ﻳﻜﻨﻮﺍﺧﺖ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﻧﮕﺎﺷﺖ‬
‫ﺷﺪﻩ ﺍﻋﻤﺎﻝ ﻛﺮﺩ‪ .‬ﻳﻜﻲ ﺍﺯ ﻧﮕﺎﺷﺖﻫﺎ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺍﺳﺖ‪.‬‬
‫)‪(١٣-٣‬‬
‫‪3‬‬
‫])‪. sin [x(n‬‬
‫‪ù‬‬
‫‪ú‬‬
‫‪úû‬‬
‫])‪y(n) = F [x(n‬‬
‫‪é‬‬
‫)‪x(n‬‬
‫‪log ê1 + m‬‬
‫‪X max‬‬
‫‪êë‬‬
‫] ‪log[1 + m‬‬
‫‪= X max‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪ -2‬راﺑﻄﻪ ورودي – ﺧﺮوﺟﯽ ﺑﺮاي ﯾﮏ ﻣﺸﺨﺼﻪ ‪) m - law‬اﻗﺘﺒﺎس از ]‪(smith[2‬‬
‫ﺷﮑﻞ‪ ،٢‬ﻳﻚ ﺧﺎﻧﻮﺍﺩﻩ ﺍﺯ ﻣﻨﺤﻨﻲ ﻫﺎﻱ )‪ y(n‬ﺑﺮ ﺣﺴﺐ )‪ x(n‬ﺭﺍ ﺑﺮﺍﻱ ﻣﻘﺎﺩﻳﺮ ﻣﺘﻔﺎﻭﺕ ‪ m‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﻭﺍﺿﺢ ﺍﺳﺖ ﻛﻪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺎﺑﻊ‬
‫)‪ (١٣-٣‬ﺩﺍﻣﻨﻪ ﻫﺎﻱ ﻭﺭﻭﺩﻱ ﻛﻮﭼﻚ ﺗﻘﻮﻳﺖ ﻣﻲ ﺷﻮﻧﺪ‪ .‬ﺷﮑﻞ‪ ٣‬ﺗﻮﺯﻳﻊ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺭﺍ ﺑﺮﺍﻱ ﺣﺎﻟﺘﻲ ﻛﻪ ‪ m =٤٠‬ﻭ ‪ N=٨‬ﺍﺳﺖ‪،‬‬
‫ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺍﮔﺮ ‪ m =٠‬ﺑﺎﺷﺪ‪ ،‬ﻣﻌﺎﺩﻟﺔ )‪ (١٣-٣‬ﺑﻪ ﻣﻌﺎﺩﻟﺔ )‪ y(n)=x(n‬ﺧﻼﺻﻪ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺑﺎ ﻓﺎﺻﻠﻪﻫﺎﻱ ﻳﻜﻨﻮﺍﺧﺖ‬
‫ﺗﻘﺴﻴﻢ ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﺑﺎ ﺍﻳﻦ ﻭﺟﻮﺩ ﺑﺮﻱ ﻣﻘﺎﺩﻳﺮ ﺑﺰﺭﮒ ‪ m‬ﻭ ﺑﺮﺍﻱ |)‪ |x(n‬ﻫﺎﻱ ﺑﺰﺭﮒ‪:‬‬
‫)‪(١٤-٣‬‬
‫ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﻪ ﺟﺰ ﺩﺍﻣﻨﻪ ﻫﺎﻱ ﺑﺴﻴﺎﺭ ﻛﻮﭼﻚ‪ ،‬ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺑﻪ ﻃﻮﺭ ﻧﻤﺎﻳﻲ ﺑﺎ ﺍﻧﺪﻳﺲ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺍﻓﺰﺍﻳﺶ ﻣﻲ ﻳﺎﺑﻨﺪ‪ .‬ﺍﻳﻦ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ‪،‬‬
‫ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ‪ m - law‬ﻧﺎﻣﻴﺪﻩ ﻣﻲ ﺷﻮﺩ ﻭ ﺍﻭﻟﻴﻦ ﺑﺎﺭ ﺗﻮﺳﻂ ‪ smith‬ﺍﺭﺍﻳﻪ ﺷﺪ ]‪.[2‬‬
‫ﺷﮑﻞ‪ -3‬ﺗﻮزﯾﻊ ﺳﻄﻮح ﮐﻮاﻧﺘﯿﺰاﺳﯿﻮن ﺑﺮاي ﮐﻮاﻧﺘﯿﺰه ﮐﻨﻨﺪة ‪ 3‬ﺑﯿﺘﯽ ‪ -law m‬ﺑﺎ ‪ m =40‬از ]‪[1‬‬
‫ﺑﺎ ﺑﻜﺎﺭﮔﻴﺮﻱ ﻫﻤﺎﻥ ﻓﺮﺿﻴﺎﺕ ﻛﻪ ﺑﺮﺍﻱ ﺁﻧﺎﻟﻴﺰ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪ‪ smith[2] ،‬ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺮﺍﻱ ﻧﺴﺒﺖ ﺳﻴﮕﻨﺎﻝ ﺑﻬﻨﻮﻳﺰ‬
‫ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ‪ m - law‬ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪.‬‬
‫‪4‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫)‪(١٥-٣‬‬
‫‪x max‬‬
‫ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ ﺑﺴﺘﮕﻲ ﻛﻤﺘﺮ ‪ SNR‬ﺑﻪ ﻣﻘﺪﺍﺭ )‬
‫‪sx‬‬
‫( ﺭﺍ ﻛﻪ ﺑﻪ ﺗﻮﻳﻊ ﺳﻴﮕﻨﺎﻝ ﺑﺴﺘﮕﻲ ﺩﺍﺭﺩ ﺭﺍ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻣﻌﺎﺩﻟﻪ )‪ (١٢-٣‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪.‬‬
‫‪x max‬‬
‫ﻣﺸﺎﻫﺪﻩ ﻣﻲﺷﻮﺩ ﻛﻪ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ‪ SNR ، m‬ﺑﻪ ﺗﻐﻴﻴﺮﺍﺕ )‬
‫‪sx‬‬
‫( ﻛﻤﺘﺮ ﺑﺴﺘﮕﻲ ﭘﻴﺪﺍ ﻣﻲ ﻛﻨﺪ‪ ،‬ﻳﻌﻨﻲ ﺑﺎ ﻭﺟﻮﺩ ﺍﻳﻨﻜﻪ ﺗﺮﻡ‬
‫‪x max‬‬
‫]) ‪ SNR ، - 20log10[ln(1 + m‬ﺭﺍ ﻛﺎﻫﺶ ﻣﻲ ﺩﻫﺪ‪ ،‬ﻣﺤﺪﻭﺩﻩ ﺍﻱ ﺍﺯ )‬
‫‪sx‬‬
‫ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ‪ m‬ﺑﺰﺭﮒ‪ ،‬ﻛﺎﺭﺁﻳﻲ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻪ ﺁﻣﺎﺭﮔﺎﻥ ﺳﻴﮕﻨﺎﻝ ﻭﺍﺑﺴﺘﮕﻲ ﻛﻤﺘﺮﻱ ﭘﻴﺪﺍ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫( ﻛﻪ ﺩﺭ ﺁﻥ ‪ SNR‬ﺛﺎﺑﺖ ﺍﺳﺖ ﺑﺎ ‪ m‬ﺍﻓﺰﺍﻳﺶ ﻣﻲ ﻳﺎﺑﺪ‪.‬‬
‫‪ -2-2‬ﮐﺪ ﮐﺮدن ﭘﯿﺸﮕﻮﯾﺎﻧﻪ )‪(Predictive Coding‬‬
‫ﺩﺭ ﻳﻚ ﺷﻜﻞ ﻣﻮﺝ ﺻﻮﺕ ﻣﻌﻤﻮﻟﻲ‪ ،‬ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻣﺘﻮﺍﻟﻲ ﺑﺠﺰ ﺩﺭ ﮔﺬﺍﺭﻫﺎﻱ ﺑﻴﻦ ﺁﻭﺍﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﻣﺸﺎﺑﻬﻲ ﺩﺍﺭﻧﺪ‪ .‬ﻳﻚ ﺭﺍﻩ ﺑﺮﺍﻱ ﺑﻬﺮﻩ‬
‫ﮔﻴﺮﻱ ﺍﺯ ﺍﻳﻦ ﻫﻤﺒﺴﺘﮕﻲ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻛﺪ ﻛﺮﺩﻥ ﺑﻪ ﺭﻭﺵ ﭘﻴﺸﮕﻮﻳﻲ ﺧﻄﻲ ﺍﺳﺖ‪ .‬ﺍﺑﺘﺪﺍ ﻧﻤﻮﻧﻪ ﻓﻌﻠﻲ )‪ x(n‬ﺍﺯ ﺭﻭﻱ ﺗﺮﻛﻴﺐ ﺧﻄﻲ ﻧﻤﻮﻧﻪ ﻫﺎﻱ‬
‫‪‬‬
‫ﻗﺒﻠﻲ ﺳﺎﺧﺘﻪ ﺷﺪﻩ ) ‪ x(n - k‬ﺗﺨﻤﻴﻦ ﺯﺩﻩ ﻣﻲ ﺷﻮﺩ ﺗﺎ‬
‫ﺳﭙﺲ ﺧﻄﺎﻱ ﺑﻴﻦ ﻣﻘﺪﺍﺭ ﻧﻤﻮﻧﻪ ﺍﺻﻠﻲ ﻭ ﻣﻘﺪﺍﺭ ﭘﻴﺶ ﺑﻴﻨﻲ ﺷﺪﻩ‬
‫ﺑﻪ )‪ d(n‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲ ﺷﻮﺩ ﻭ ﺑﻮﺳﻴﻠﺔ ﻛﻠﻤﺔ ﻛﺪ )‪ ،c(n‬ﻛﺪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﺩﺭ ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ‪ ،‬ﺍﺑﺘﺪﺍ ﻫﻤﺎﻥ ﻣﻘﺪﺍﺭ ﭘﻴﺸﮕﻮﻳﻲ ﺷﺪﻩ ﺍﺯ ﺭﻭﻱ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻗﺒﻠﻲ ﺩﻱ ﻛﺪ‬
‫ﺷﺪﻩ ﺳﺎﺧﺘﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﺳﭙﺲ ﺑﻪ ﻣﻘﺪﺍﺭ ﺧﻄﺎﻱ ﺩﻱ ﻛﺪ ﻭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺍﺿﺎﻓﻪ ﻣﻲ ﺷﻮﺩ ﺗﺎ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺑﺮﺍﻱ ﻧﻤﻮﻧﻪ ﻓﻌﻠﻲ‬
‫ﺑﺪﺳﺖ ﺁﻳﺪ‪ .‬ﻳﻌﻨﻲ‪:‬‬
‫ﺑﻠﻮﻙ ﺩﻳﺎﮔﺮﺍﻡ ﻛﺪ ﻛﻨﻨﺪﻩ ﻭ ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ ﻳﻚ ﺳﻴﺴﺘﻢ ﻛﺪ ﻛﻨﻨﺪﺓ ﭘﻴﺸﮕﻮ ﺩﺭ ﺷﮑﻞ‪ ٤‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺳﻴﺴﺘﻢ ﻛﺪ ﻛﻨﻨﺪﻩ ﭘﻴﺸﮕﻮ ﻣﻌﻤﻮﻵً‬
‫ﺑﻪ ﻣﺪﻭﻻﺳﻴﻮﻥ ﻛﺪ ﺷﺪﻩ ﺳﻴﮕﻨﺎﻝ ﺗﻔﺎﺿﻠﻲ ﻳﺎ ”‪ “DPCM‬ﺷﻨﺎﺧﺘﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﻛﻠﻤﺔ »ﺗﻔﺎﺿﻠﻲ« ﺑﻪ ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﺍﺷﺎﺭﻩ ﻣﻲ ﻛﻨﺪ ﻛﻪ ﺳﻴﮕﻨﺎﻝ‬
‫ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﻛﺪ ﻣﻲﺷﻮﺩ ﻭ ”‪ “PCM‬ﺑﻪ ﻃﺮﺡ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺍﺷﺎﺭﻩ ﻣﻲ ﻛﻨﺪ ﻛﻪ ﺩﺭ ﺁﻥ ﻫﺮ ﺑﻴﺖ ﻛﺪ ﺷﺪﻩ ﻳﻚ ﺳﻤﺒﻞ ﺍﺳﺖ ﻛﻪ ﺑﻮﺳﻴﻠﻪ ﻳﻚ‬
‫ﭘﺎﻟﺲ )ﺑﺎ ﺩﺍﻣﻨﻪ ﺻﻔﺮ ﻳﺎ ﻳﻚ( ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﺮﺩﻥ ﻣﺴﺘﻘﻴﻢ ﻳﻚ ﻧﻤﻮﻧﺔ ﺍﻭﻟﻴﻪ ﺑﺎ ﻃﻮﻝ ﺛﺎﺑﺖ ﺩﺭ ﻛﺪ ﻛﺮﺩﻥ‪ “PCM” ،‬ﻧﺎﻣﻴﺪﻩ ﻣﻲ‬
‫ﺷﻮﺩ‪.‬‬
‫‪5‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪ -4‬ﮐﺪ ﮐﺮدن ﭘﯿﺸﮕﻮﯾﺎﻧﻪ )اﻟﻒ( ﮐﺪ ﮐﻨﻨﺪه )ب( دي ﮐﺪ ﮐﻨﻨﺪه‬
‫‪ -1-2-2‬ﻣﺪوﻻﺳﯿﻮن دﻟﺘﺎ‬
‫ﻳﻚ ﺳﻴﺴﺘﻢ ﺳﺎﺩﺓ ﭘﻴﺸﮕﻮﻳﺎﻧﻪ‪ ،‬ﺳﻴﺴﺘﻢ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ )‪ (DM‬ﺍﺳﺖ ﻛﻪ ﺩﺭ ﺷﮑﻞ‪ ٥‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﺳﻴﺴﺘﻢ‪ ،‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ‬
‫ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﻓﻘﻂ ﺩﻭ ﺳﻄﺢ ﺩﺍﺭﺩ ﻭ ﻃﻮﻝ ﭘﻠﻪ »ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ« ﺛﺎﺑﺖ ﺍﺳﺖ‪ .‬ﺳﻄﺢ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﺜﺒﺖ ﺑﺎ ‪ c(n)=0‬ﻭ ﻣﻨﻔﻲ ﺑﺎ ‪c(n)=1‬‬
‫ﻣﺸﺨﺺ ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ )‪ d(n‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫)‪(١٦-٣‬‬
‫ﻛﻪ ﺍﺯ ﻳﻚ ﭘﻴﺸﮕﻮﻳﻲ ﺧﻄﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻳﻌﻨﻲ )‪ xp(n) = x(n-1‬ﻣﻲ ﺗﻮﺍﻥ ﺍﺯ ﺷﮑﻞ‪-٥‬ﺍﻟﻒ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﻛﻪ ﻣﻌﻤﻮﻻﹰ‬
‫)‪ x(n‬ﺩﺭ ﻣﻌﺎﺩﻟﻪ ﺗﻔﺎﺿﻠﻲ ﺯﻳﺮ ﺻﺪﻕ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫)‪(١٧-٣‬‬
‫ﺑﺎ ‪ ، a = 1‬ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ‪ ،‬ﻣﻌﺎﺩﻝ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺍﻧﺘﮕﺮﺍﻝ ﺍﺳﺖ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺑﺎﻳﺪ ﺩﻗﺖ ﻛﺮﺩ ﻛﻪ ﻭﺭﻭﺩﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ‬
‫)‪(١٨-٣‬‬
‫‪‬‬
‫ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﻪ ﺟﺰ ﺧﻄﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ )‪ d(n) ، x(n - 1‬ﻳﻚ ﺗﻔﺎﺿﻠﻲ ﺑﺮﮔﺸﺘﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺍﺯ )‪ x(n‬ﺍﺳﺖ ﻛﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﻪ‬
‫ﻋﻨﻮﺍﻥ ﺗﻘﺮﻳﺐ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺑﺮﺍﻱ ﻣﺸﺘﻘﺎﺕ ﻭﺭﻭﺩﻱ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﻮﺩ‪ ،‬ﻣﻌﻜﻮﺱ ﭘﺮﻭﺳﺔ ﺍﻧﺘﮕﺮﺍﻝ ﺩﻳﺠﻴﺘﺎﻟﻲ‪.‬‬
‫ﺍﺯ ﺁﻧﺠﺎ ﻛﻪ ﺧﻄﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻓﻘﻂ ﺩﻭ ﺳﻄﺢ ﺩﺍﺭﺩ‪ ،‬ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺩﺍﺭﺍﻱ ﻧﺮﺥ ﺑﻴﺘﻲ ﺑﺮﺍﺑﺮ ‪ ۱bit/sample‬ﺍﺳﺖ‪ .‬ﺍﮔﺮ ﺑﻪ ﺩﻧﺒﺎﻟﻪ‬
‫‪ ١٦bits/sample‬ﺍﻋﻤﺎﻝ ﺷﻮﺩ‪ ،‬ﺁﻧﮕﺎﻩ ﺑﻪ ﻧﺮﺥ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ )‪ (CR‬ﺑﺮﺍﺑﺮ ‪ ١٦‬ﻣﻲ ﺭﺳﺪ‪.‬‬
‫‪6‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪ -5‬ﺑﻠﻮك دﯾﺎﮔﺮام ﺳﯿﺴﺘﻢ ﻣﺪوﻻﺳﯿﻮن دﻟﺘﺎ اﻟﻒ( ﮐﺪ ﮐﻨﻨﺪه ب( دي ﮐﺪ ﮐﻨﻨﺪه‬
‫ﺑﺮﺍﻱ ﺍﻳﻨﻜﻪ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺑﻪ ﺧﻮﺑﻲ ﻛﺎﺭ ﻛﻨﺪ‪ ،‬ﺍﻧﺪﺍﺯﻩ ﭘﻠﻪ ﺑﺎﻳﺪ ﻃﻮﺭﻱ ﺍﻧﺘﺨﺎﺏ ﺷﻮﺩ ﻛﻪ ﺗﻐﻴﻴﺮﺍﺕ ﺳﻴﮕﻨﺎﻝ ﺭﺍ ﺩﻧﺒﺎﻝ ﻛﻨﺪ‪ .‬ﺗﺤﻘﻖ ﺍﻳﻦ ﺍﻣﺮ‬
‫ﻣﺸﻜﻞ ﺍﺳﺖ ﺯﻳﺮﺍ ﻣﺸﺨﺼﺎﺕ ﺳﻴﮕﻨﺎﻝ ﺍﺯ ﻳﻚ ‪ tone‬ﺑﻪ ‪ tone‬ﺩﻳﮕﺮ ﺗﻐﻴﻴﺮ ﻣﻲ ﻛﻨﺪ‪ .‬ﺷﮑﻞ‪-٦‬ﺍﻟﻒ ﭘﺮﻭﺳﻪ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺭﺍ‬
‫ﺑﺎ ﻃﻮﻝ ﭘﻠﻪ ﻣﺘﻨﺎﺳﺐ ﻭ ﺩﻗﻴﻖ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﻣﻲ ﺗﻮﺍﻥ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﻛﻪ ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﺍﺑﺘﺪﺍ ﺑﺴﻴﺎﺭ ﻛﻮﭼﻚ ﺍﺳﺖ ﻛﻪ ﺑﺎﻋﺚ ﻣﻲﺷﻮﺩ ﺳﻴﮕﻨﺎﻝ‬
‫ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺯﻳﺮ ﺩﺍﻣﻨﻪ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﺁﻫﺴﺘﻪ ﺗﺮ ﺣﺮﻛﺖ ﻛﻨﺪ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ ﺍﮔﺮ ﻃﻮﻝ ﭘﻠﻪ ﺭﺍ ﺧﻴﻠﻲ ﺑﺰﺭﮒ ﺑﮕﻴﺮﻳﻢ‪ ،‬ﺑﺎﻋﺚ ﻣﻲ ﺷﻮﺩ ﻛﻪ‬
‫ﺳﻴﮕﻨﺎﻝ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ ﺣﻮﻝ ﻭ ﺣﻮﺵ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ﻧﻮﺳﺎﻥ ﻛﻨﺪ‪ .‬ﺑﺮﺍﻱ ﻛﺎﺭﺁﻳﻲ ﺑﻬﺘﺮ‪ ،‬ﻃﻮﻝ ﭘﻠﻪ ﺑﺎﻳﺪ ﺑﻪ ﻃﻮﺭ ﻭﻓﻘﻲ ﺑﺎﺷﺪ ﻛﻪ ﻣﻮﺿﻮﻉ‬
‫ﺑﺨﺶ ﺁﻳﻨﺪﻩ ﺍﺳﺖ‪.‬‬
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‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺷﮑﻞ‪-6‬ﻧﻤﺎﯾﺶ ﻣﺪوﻻﺳﯿﻮن دﻟﺘﺎ اﻟﻒ( اﺳﺘﻔﺎده از ﯾﮏ ﭘﻠﻪ ﺑﺎ ﻃﻮل ﺛﺎﺑﺖ ب( اﺳﺘﻔﺎده از ﻃﻮل ﭘﻠﻪ وﻓﻘﯽ‬
‫‪ -2-2-2‬ﻣﺪوﻻﺳﯿﻮن دﻟﺘﺎي وﻓﻘﯽ‬
‫ﻃﺮﺣﻬﺎﻱ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎﻱ ﻭﻓﻘﻲ )‪ (ADM‬ﻣﺘﻌﺪﺩﻱ ﭘﻴﺸﻨﻬﺎﺩ ﺷﺪﻩ ﺍﻧﺪ‪ .‬ﺑﻴﺸﺘﺮ ﺍﻳﻦ ﻃﺮﺣﻬﺎ ﺍﺯ ﻧﻮﻉ ﺑﺮﮔﺸﺘﻲ ﻫﺴﺘﻨﺪ ﻛﻪ ﺩﺭ ﺁﻧﻬﺎ ﻃﻮﻝ ﭘﻠﻪ‬
‫ﺑﺮﺍﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ﺩﻭ ﺳﻄﺤﻲ ﺑﺮ ﻣﺒﻨﺎﻱ ﻛﻠﻤﺎﺕ ﻛﺪ ﺩﺭ ﺧﺮﻭﺟﻲ ﺑﻬﻴﻨﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﺳﻴﺴﺘﻤﻲ ﻛﻪ ﻣﺎ ﺩﺭ ﺯﻳﺮ ﭘﻴﺸﻨﻬﺎﺩ ﻛﺮﺩﻩ ﺍﻳﻢ ﺑﻮﺳﻴﻠﺔ‬
‫]‪ Jayant[3‬ﻃﺮﺍﺣﻲ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﺍﻟﮕﻮﺭﻳﺘﻢ ‪ Jayant‬ﺍﺯ ﻗﺎﻧﻮﻥ ﺯﻳﺮ ﭘﻴﺮﻭﻱ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫)‪-١٩-٣‬ﺍﻟﻒ(‬
‫)‪-١٩-٣‬ﺏ(‬
‫ﺍﻟﮕﻮﺭﻳﺘﻢ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﻃﻮﻝ ﭘﻠﻪ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺍﺳﺖ‪.‬‬
‫)‪(٢٠-٣‬‬
‫ﺷﮑﻞ‪-٦‬ﺏ‪ -‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ ﻛﻪ ﭼﮕﻮﻧﻪ ﺷﻜﻞ ﻣﻮﺝ ﺷﮑﻞ‪-٦‬ﺍﻟﻒ ﻣﻲ ﺗﻮﺍﻧﺪ ﺗﻮﺳﻂ ﻳﻚ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎﻱ ﻭﻓﻘﻲ ﻛﻪ ﺩﺭ ﺭﺍﺑﻄﻪ )‪ (١٨-٣‬ﻭ‬
‫)‪ (٢٠-٣‬ﺑﻴﺎﻥ ﺷﺪ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﻮﺩ‪ .‬ﺑﺮﺍﻱ ﺭﺍﺣﺘﻲ‪ ،‬ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺳﻴﺴﺘﻢ ﺩﺭ ‪ p = 2‬ﻭ ‪ a = 1‬ﺗﻨﻈﻴﻢ ﻣﻲ ﺷﻮﻧﺪ ﻭ ﺣﺪﺍﻗﻞ ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﺷﻜﻞ‬
‫ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﻲ ﺗﻮﺍﻥ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﻛﻪ ﻧﻮﺍﺣﻲ ﺑﺎ ﺷﻴﺐ ﻣﺜﺒﺖ ﺯﻳﺎﺩ ﻫﻨﻮﺯ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺍﺯ ﺻﻔﺮ ﺗﻮﻟﻴﺪ ﻣﻲ ﻛﻨﻨﺪ ﺍﻣﺎ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻃﻮﻝ‬
‫ﭘﻠﻪ ﺁﻧﻘﺪﺭ ﺍﻓﺰﺍﻳﺶ ﻣﻲ ﻳﺎﺑﺪ ﺗﺎ ﺍﺯﺩﻳﺎﺩ ﺷﻴﺐ ﺷﻜﻞ ﻣﻮﺝ ﺭﺍ ﺩﻧﺒﺎﻝ ﻛﻨﺪ‪ .‬ﻧﻮﺍﺣﻲ ﺩﺍﻧﻪ ﺩﺍﻧﻪ ﺍﻱ ﺩﺭ ﺳﻤﺖ ﺭﺍﺳﺖ ﺷﻜﻞ ﺩﻭﺑﺎﺭﻩ ﺑﻮﺳﻴﻠﻪ ﻳﻚ ﺩﻧﺒﺎﻟﻪ‬
‫‪8‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﺍﺯ ﺻﻔﺮ ﻭ ﻳﻚ ﻫﺎﻱ ﻣﺘﻨﺎﺳﺐ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲﺷﻮﻧﺪ‪ ،‬ﺍﻣﺎ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻃﻮﻝ ﭘﻠﻪ ﺳﺮﻳﻌﺎﹰ ﺑﻪ ﻣﻘﺪﺍﺭ ﺣﺪﺍﻗﻞ ) ‪ (D min‬ﻛﺎﻫﺶ ﻣﻲ ﻳﺎﺑﺪ ﻭ ﺗﺎ ﻭﻗﺘﻲ‬
‫ﻛﻪ ﺷﻴﺐ ﻛﻢ ﺑﺎﺷﺪ ﺩﺭ ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﻣﻲ ﻣﺎﻧﺪ‪.‬‬
‫ﺷﮑﻞ‪ -7‬ﻧﺴﺒﺖ ﻫﺎي ﺳﯿﮕﻨﺎل ﺑﻪ ﻧﻮﯾﺰ از ﯾﮏ ﻣﺪوﻻﺗﻮر دﻟﺘﺎي وﻓﻘﯽ ﺑﺮ ﺣﺴﺐ ﺗﻮاﺑﻊ ‪p‬‬
‫ﺷﮑﻞ‪ ،٧‬ﻧﺘﺎﻳﺞ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺭﺍ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻝ ﮔﻔﺘﺎﺭ ﺑﺎ ‪ PQ = 1‬ﺑﺮﺍﻱ ﺳﻪ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺘﻔﺎﻭﺕ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪.‬‬
‫ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺣﺪﺍﻛﺜﺮ ‪ SNR‬ﺑﺮﺍﻱ ‪ P = ١/٥‬ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ‪ ،‬ﺑﺎ ﺍﻳﻦ ﻭﺟﻮﺩ‪ ،‬ﻗﻠﺔ ﻣﻨﺤﻨﻲ ﺑﺴﻴﺎﺭ ﭘﻬﻦ ﺍﺳﺖ ﻭ ‪ SNR‬ﭼﻨﺪ ‪ dB‬ﺑﺎﻻﺗﺮ‬
‫ﻭ ﭘﺎﻳﻴﻦ ﺗﺮ ﺍﺯ ﻣﻘﺪﺍﺭ ﺣﺪﺍﻛﺜﺮ ﺑﺮﺍﻱ ‪ ١/٢٥<p<٢‬ﻗﺮﺍﺭ ﺩﺍﺭﺩ‪ .‬ﺗﻮﺟﻪ ﻛﻨﻴﺪ ﺑﺮﺍﻱ ﺍﻳﻨﻜﻪ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺧﻮﺏ ﻛﺎﺭ ﻛﻨﺪ ﺑﺎﻳﺪ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺍﺯ‬
‫ﺳﻴﮕﻨﺎﻝ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻲ ﺑﺎﻻﺗﺮ ﺍﺯ ﺁﻧﭽﻪ ﺗﺌﻮﺭﻱ ﻧﺎﻳﻜﻮﺋﻴﺴﺖ ﺗﺤﻤﻴﻞ ﻣﻲ ﻛﻨﺪ‪ ،‬ﺍﻧﺠﺎﻡ ﺷﻮﺩ ﺗﺎ ﺗﻐﻴﻴﺮﺍﺕ ﺑﻴﻦ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻣﺘﻮﺍﻟﻲ ﻛﻮﭼﻚ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ‬
‫ﭘﺪﻳﺪﻩ ﺩﺭ ﺣﻘﻴﻘﺖ ﻣﺼﺎﻟﺤﻪ ﺑﻴﻦ ﺩﻗﺖ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻭ ﺩﻗﺖ ﺩﺍﻣﻨﻪ ﺭﺍ ﺁﺷﻜﺎﺭ ﻣﻲ ﻛﻨﺪ‪ .‬ﻳﻌﻨﻲ ﺑﺮﺍﻱ ﻛﺎﻫﺶ ﺩﻗﺖ ﺩﺍﻣﻨﻪ )ﻳﻚ ﺑﻴﺖ ﺩﺭ‬
‫ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ( ﺑﺎﻳﺪ ﺩﻗﺖ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﺍﻓﺰﺍﻳﺶ ﺩﺍﺩ‪.‬‬
‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﺷﻤﺎ ﺑﺎ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺩﺭ ﺣﺎﻟﺖ ﻃﻮﻝ ﭘﻠﻪ ﺛﺎﺑﺖ ﻭ ﻭﻓﻘﻲ ﻛﺎﺭ ﺧﻮﺍﻫﻴﺪ ﻛﺮﺩ‪.‬‬
‫‪ DPCM -3-2-2‬ﻫﺎي ﻣﺮﺗﺒﻪ ﺑﺎﻻﺗﺮ‬
‫ﻣﺪﻭﻻﺗﻮﺭﻫﺎﻱ ﺩﻟﺘﺎ‪ ،‬ﻫﻤﺎﻧﻄﻮﺭ ﻛﻪ ﺩﺭ ﺑﺨﺶ ﻗﺒﻠﻲ ﺑﻴﺎﻥ ﺷﺪ‪ ،‬ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺳﻴﺴﺘﻤﻬﺎﻱ ‪ DPCM‬ﻳﻚ ﺑﻴﺘﻲ ﻧﺎﻣﻴﺪﻩ ﺷﻮﻧﺪ‪ .‬ﺑﻪ ﻃﻮﺭ ﻛﻠﻲ‪ ،‬ﻣﻲ ﺗﻮﺍﻥ‬
‫ﺍﺯ ﺑﻴﺸﺘﺮ ﺍﺯ ﻳﻚ ﻧﻤﻮﻧﻪ ﻗﺒﻠﻲ ﺑﺮﺍﻱ ﺗﺨﻤﻴﻦ ﻧﻤﻮﻧﻪ ﻓﻌﻠﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﺮﺩ‪ .‬ﻫﻤﭽﻨﻴﻦ‪ ،‬ﻣﻲ ﺗﻮﺍﻥ ﺍﺯ ﻳﻚ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﺎ ﺑﻴﺸﺘﺮ ﺍﺯ ﺩﻭ ﺳﻄﺢ ﺍﺳﺘﻔﺎﺩﻩ‬
‫ﻛﺮﺩ‪ .‬ﺑﺮﺍﻱ ﺩﺭﻙ ﺑﻬﺘﺮ ﺍﺯ ﭼﮕﻮﻧﮕﻲ ﺗﻌﻴﻴﻦ ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮ ﻭ ﻃﺮﺍﺣﻲ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻬﻴﻨﻪ ﺑﻪ ﻣﺮﺟﻊ ]‪ [1‬ﻣﺮﺍﺟﻌﻪ ﻛﻨﻴﺪ‪ .‬ﻋﻤﻮﻣﺎﹰ‪DPCM ،‬‬
‫ﺑﺮﺍﻱ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺗﻔﺎﺿﻠﻲ ﻛﻪ ﺩﺭ ﺁﻥ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻴﺸﺘﺮ ﺍﺯ ﺩﻭ ﺳﻄﺢ ﺩﺍﺭﺩ‪ ،‬ﻣﻌﻜﻮﺱ ﻣﻲ ﺷﻮﺩ‪ .‬ﺳﻴﺴﺘﻤﻬﺎﻱ ‪ DPCM‬ﺑﺎ‬
‫ﭘﻴﺸﮕﻮﻫﺎﻱ ﺛﺎﺑﺖ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺍﺯ ‪ ٤‬ﺗﺎ ‪ dB ١١‬ﺑﻬﺒﻮﺩ ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﺴﺘﻘﻴﻢ )‪ (PCM‬ﺍﻳﺠﺎﺩ ﻛﻨﻨﺪ‪ .‬ﺑﻴﺸﺘﺮﻳﻦ ﺑﻬﺒﻮﺩ ﺩﺭ ﻣﺮﺣﻠﻪ ﺗﻐﻴﻴﺮ ﺍﺯ‬
‫ﺣﺎﻟﺖ ﺑﺪﻭﻥ ﭘﻴﺸﮕﻮﻳﻲ ﺑﻪ ﺣﺎﻟﺖ ﭘﻴﺸﮕﻮﻳﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺭﺥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺍﻳﻦ ﺑﻬﺒﻮﺩ ﺩﺭ ﮔﺬﺭ ﺑﻪ ﭘﻴﺸﮕﻮﻫﺎﻱ ﺩﺭﺟﻪ ‪ ٤‬ﻳﺎ ‪ ٥‬ﻛﻤﺘﺮ ﻣﺤﺴﻮﺱ‬
‫ﻣﻲﺑﺎﺷﺪ‪ .‬ﺩﺭ ﮔﻔﺘﺎﺭ ﺍﺯ ﭘﻴﺸﮕﻮﻫﺎﻱ ﺑﺎ ﺩﺭﺟﻪ ﺑﺎﻻﺗﺮ ﺍﺯ ‪ ١٠‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺯﻳﺮﺍ ﺳﻴﮕﻨﺎﻝ ﮔﻔﺘﺎﺭ ﺑﺎ ﺩﺭﺟﺎﺕ ﺑﺎﻻﺗﺮ ﺑﻬﺘﺮ ﻣﻲ ﺗﻮﺍﻧﺪ ﻣﺪﻝ ﺷﻮﺩ‪.‬‬
‫ﺑﻬﺮﻩ ‪ SNR‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ ﻛﻪ ﺩﺭ ﻳﻚ ﺳﻴﺴﺘﻢ ‪ ،DPCM‬ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ‪ SNR‬ﺧﻮﺍﺳﺘﻪ ﺷﺪﻩ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﻴﺖ ﻫﺎﻱ ﻛﻤﺘﺮ ﺍﺯ ﺑﻴﺖ ﻫﺎﻱ‬
‫ﻣﻮﺭﺩﻧﻴﺎﺯ‪ ،‬ﻫﻨﮕﺎﻣﻲ ﻛﻪ ﻫﻤﺎﻥ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻪ ﻃﻮﺭ ﻣﺴﺘﻘﻴﻢ ﺭﻭﻱ ﺳﻴﮕﻨﺎﻝ ﮔﻔﺘﺎﺭ ﺍﺛﺮ ﻣﻲ ﻛﻨﺪ‪ ،‬ﻋﻤﻠﻲ ﺍﺳﺖ‪ .‬ﺑﻪ ﻳﺎﺩﺁﻭﺭﻳﺪ ﻛﻪ ﻫﻨﮕﺎﻡ ﻛﻮﺍﻧﺘﻴﺰﻩ‬
‫ﻛﺮﺩﻥ ﻣﺴﺘﻘﻴﻢ ﻳﻚ ﺳﻴﮕﻨﺎﻝ‪ ،‬ﻫﺮ ﺑﻴﺖ ﺍﺿﺎﻓﻲ ﺑﻪ ﺑﻬﺮﺓ ‪ 6dB‬ﻣﻨﺠﺮ ﻣﻲ ﺷﺪ‪ ،‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺍﮔﺮ ﺳﻴﺴﺘﻢ ‪ DPCM‬ﺑﺘﻮﺍﻧﺪ ﺑﻪ ﺑﻬﺮﻩ ﭘﻴﺸﮕﻮﻳﻲ ‪6dB‬‬
‫ﺑﺮﺳﺪ ﺑﻪ ﺍﻳﻦ ﻣﻌﻨﻲ ﺍﺳﺖ ﻛﻪ ﻳﻚ ﺑﻴﺖ ﻛﻤﺘﺮ ﻧﺴﺒﺖ ﺑﻪ ﺣﺎﻟﺘﻲ ﻛﻪ ﺳﻴﺴﺘﻢ ‪ PCM‬ﻭﺟﻮﺩ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ ،‬ﻣﻮﺭﺩﻧﻴﺎﺯ ﺍﺳﺖ ﺗﺎ ﺑﻪ ﻫﻤﺎﻥ ﻛﻴﻔﻴﺖ ﺍﺯ‬
‫ﺳﻴﮕﻨﺎﻝ ﺑﺮﺳﺪ‪.‬‬
‫‪9‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫‪ADPCM -4-2-2‬‬
‫ﺩﻭ ﻃﺮﺡ ﻋﻤﺪﻩ ﺑﺮﺍﻱ ‪ DPCM‬ﻭﻓﻘﻲ ﻳﺎ ‪ ADPCM‬ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪ .‬ﻳﻜﻲ ﺍﺯ ﺁﻧﻬﺎ ‪ DPCM‬ﺑﺎ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻭﻓﻘﻲ ﻭ ﺩﻳﮕﺮﻱ ‪ DPCM‬ﺑﺎ‬
‫ﭘﻴﺸﮕﻮﻳﻲ ﻭﻓﻘﻲ ﺍﺳﺖ‪.‬‬
‫ﺑﺮﺍﻱ ‪ DPCM‬ﺑﺎ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻭﻓﻘﻲ‪ ،‬ﻃﻮﻝ ﭘﻠﻪ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﻣﺘﻨﺎﺳﺐ ﺑﺎ ﻭﺍﺭﻳﺎﻧﺲ ﻭﺭﻭﺩﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺗﻐﻴﻴﺮ ﻣﻲ ﻛﻨﺪ‪ .‬ﺑﺎ ﺍﻳﻦ ﻭﺟﻮﺩ‪ ،‬ﺍﺯ‬
‫ﺁﻧﺠﺎﻳﻲ ﻛﻪ ﺳﻴﮕﻨﺎﻝ ﺗﻔﺎﺿﻞ )‪ d(n‬ﻣﺘﻨﺎﺳﺐ ﺑﺎ ﻭﺭﻭﺩﻱ ﺍﺳﺖ‪ ،‬ﻣﻌﻘﻮﻝ ﺍﺳﺖ ﻛﻪ ﺗﻨﻈﻴﻢ ﻃﻮﻝ ﭘﻠﻪ ﺍﺯ ﺭﻭﻱ ﺳﻴﮕﻨﺎﻝ ﻭﺭﻭﺩﻱ )‪ x(n‬ﺍﻧﺠﺎﻡ ﺷﻮﺩ ﻛﻪ‬
‫ﺩﺭ ﺷﮑﻞ‪ ٨‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺭﻭﻳﻪ ﻫﺎﻱ ﻭﻓﻘﻲ ﻣﺘﻌﺪﺩﻱ ﺑﺮﺍﻱ ﺗﻨﻈﻴﻢ ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﮔﺬﺷﺘﻪ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﻧﺪ‪ .‬ﻧﺘﺎﻳﺞ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ ﻛﻪ ﺍﻳﻦ‬
‫ﻗﺒﻴﻞ ﺭﻭﻳﻪ ﻫﺎﻱ ﻭﻓﻘﻲ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺩﺭ ﺣﺪﻭﺩ ‪ ٥ dB‬ﺩﺭ ‪ SNR‬ﻧﺴﺒﺖ ﺑﻪ ﺣﺎﻟﺖ ﻏﻴﺮ ﻭﻓﻘﻲ ‪ m - law‬ﺩﺭ ‪ PCM‬ﺑﻬﺒﻮﺩ ﺍﻳﺠﺎﺩ ﻛﻨﻨﺪ‪ .‬ﺍﻳﻦ‬
‫ﺑﻬﺒﻮﺩ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﺎ ‪ ٦ dB‬ﺑﻬﺒﻮﺩ ﻛﻪ ﺍﺯ ﻭﺿﻌﻴﺖ ﺗﻔﺎﺿﻠﻲ ﺑﺎ ﭘﻴﺸﮕﻮﻳﻲ ﺛﺎﺑﺖ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ‪ ،‬ﺗﺮﻛﻴﺐ ﺷﺪﻩ ﻭ ‪ ADPCM‬ﺑﺎ ﭘﻴﺸﮕﻮﻳﻲ ﻭﻓﻘﻲ‬
‫ﺭﻭ ﺑﻪ ﺟﻠﻮ‪ ،‬ﺑﻬﺒﻮﺩ ‪SNR‬ﺍﻱ ﺑﺮﺍﺑﺮ ‪ 10-11dB‬ﻧﺴﺒﺖ ﺑﻪ ‪ PCM‬ﺑﺎ ﻫﻤﺎﻥ ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ‪ ،‬ﻧﺘﻴﺠﻪ ﺩﻫﺪ‪.‬‬
‫ﺷﮑﻞ‪ -8‬ﺳﯿﺴﺘﻢ ‪ ADPCM‬ﺑﺎ ﮐﻮاﻧﺘﯿﺰه وﻓﻘﯽ رو ﺑﻪ ﺟﻠﻮ اﻟﻒ( ﮐﺪ ﮐﻨﻨﺪه ب( دي ﮐﺪ ﮐﻨﻨﺪه‬
‫ﺑﺮﺍﻱ ‪ DPCM‬ﺑﺎ ﭘﻴﺸﮕﻮﻳﻲ ﻭﻓﻘﻲ‪ ،‬ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮﻳﻲ ﻛﻨﻨﺪﻩ ﺑﺴﺘﮕﻲ ﺑﻪ ﺯﻣﺎﻥ ﺩﺍﺭﻧﺪ‪ ،‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﭘﻴﺸﮕﻮﻳﻲ ﺷﺪﻩ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﻫﺴﺘﻨﺪ‪.‬‬
‫)‪(٢١-٣‬‬
‫ﺩﺭ ﺗﻄﺒﻴﻖ ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮﻳﻲ )‪ ، a k (n‬ﻣﻌﻤﻮﻝ ﺍﺳﺖ ﻛﻪ ﻓﺮﺽ ﻛﻨﻴﻢ ﺧﺼﻮﺻﻴﺎﺕ ﺁﻣﺎﺭﻱ ﺳﻴﮕﻨﺎﻝ ﺩﺭ ﻃﻮﻝ ﻳﻚ ﺑﺎﺯﻩ ﻛﻮﺗﺎﻩ ﺯﻣﺎﻧﻲ ﺛﺎﺑﺖ ﻣﻲ‬
‫ﻣﺎﻧﻨﺪ‪ .‬ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﺷﻮﻧﺪ ﺗﺎ ﻣﻴﺎﻧﮕﻴﻦ ﻣﺮﺑﻊ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺩﺭ ﻫﺮ ﭘﻨﺠﺮﻩ ﻛﻮﭼﻚ ﺯﻣﺎﻧﻲ ﺣﺪﺍﻗﻞ ﺷﻮﺩ‪ .‬ﺑﺮﺍﻱ‬
‫ﺁﺷﻨﺎﻳﻲ ﺑﻴﺸﺘﺮ ﺑﺎ ﻧﺤﻮﺓ ﺍﻧﺘﺨﺎﺏ ﺑﻬﻴﻨﺔ ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮﻳﻲ ﺧﻄﻲ ﺑﻪ ﻣﺮﺟﻊ ]‪ [1‬ﻣﺮﺍﺟﻌﻪ ﻛﻨﻴﺪ‪.‬‬
‫‪ -3-3‬اﺳﺘﺎﻧﺪاردﻫﺎي ﮐﺪ ﮐﺮدن ﮔﻔﺘﺎر‬
‫ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎﻱ ﺟﻬﺎﻧﻲ ﻣﺘﻌﺪﺩﻱ ﺑﺮﺍﻱ ﻛﺪ ﻛﺮﺩﻥ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﮔﻔﺘﺎﺭ ﻭﺟﻮﺩ ﺩﺍﺭﻧﺪ‪ .‬ﺗﻌﺪﺍﺩﻱ ﺍﺯ ﺍﻳﻦ ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎ ﺩﺭ ﻟﻴﺴﺖ ﭘﺎﻳﻴﻦ ﺁﻣﺪﻩ ﺍﻧﺪ‪ .‬ﺑﻪ ﺟﺰ‬
‫ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ‪ G.711‬ﻫﻤﮕﻦ ﺍﺯ ﻧﻮﻋﻲ ‪ ADPCM‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﻛﻨﻨﺪ‪.‬‬
‫‪10‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫‪ -3‬آزﻣﺎﯾﺸﺎت‬
‫‪ (١‬ﺑﺮﻧﺎﻣﻪ ‪ MATLAB‬ﻣﻮﺟﻮﺩ ﺩﺭ ‪ “demo-quant,” ،Appendix‬ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺘﻲ ﺭﻭﻱ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺍﻧﺠﺎﻡ ﻣﻲ ﺩﻫﺪ‪.‬‬
‫‪bits‬‬
‫ﺑﺮﻧﺎﻣﻪ ﺭﺍ ﺑﺎ ﺩﻗﺖ ﺑﺨﻮﺍﻧﻴﺪ ﺗﺎ ﻣﺘﻮﺟﻪ ﺷﻮﻳﺪ ﭼﮕﻮﻧﻪ ﻛﺎﺭ ﻣﻲ ﻛﻨﺪ‪ .‬ﺑﺮﻧﺎﻣﻪ ﺭﺍ ﺑﺮﺍﻱ ﻳﻚ ﻓﺎﻳﻞ ﮔﻔﺘﺎﺭ ﺿﺒﻂ ﺷﺪﻩ ﺩﺭ‬
‫‪sample‬‬
‫‪bits‬‬
‫‪ ١٦‬ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﻫﺮ ﻣﻮﺭﺩ‪ ،‬ﺍﻏﺘﺸﺎﺵ )‪ (Distortion‬ﺩﺭ ﻫﺮ ﺷﻜﻞ ﻣﻮﺝ‪ ،‬ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﺭﺍ ﺑﺎ ﺗﻐﻴﻴﺮ‬
‫ﻣﻮﺳﻴﻘﻲ ﺿﺒﻂ ﺷﺪﻩ ﺩﺭ‬
‫‪sample‬‬
‫ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺎﺯﺳﻴﻮﻥ )‪ (N‬ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﻫﺮ ﻣﻮﺭﺩ )ﮔﻔﺘﺎﺭ ﻭ ﻣﻮﺳﻴﻘﻲ(‪ N ،‬ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺮﺍﻱ ﺩﺍﺷﺘﻦ ﻳﻚ ﺻﺪﺍﻱ ﺑﺎ ﻛﻴﻔﻴﺖ ﺧﻮﺏ ﻛﺪﺍﻡ‬
‫‪ ٨‬ﻭ ﻳﻚ ﻓﺎﻳﻞ‬
‫ﺍﺳﺖ؟ ﺷﻜﻠﻬﺎﻱ ﺗﻮﻟﻴﺪ ﺷﺪﻩ ﺑﻮﺳﻴﻠﻪ ﺍﻧﺘﺨﺎﺏ ﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﺭﺍ ﭘﺮﻳﻨﺖ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٢‬ﺑﺮﻧﺎﻣﻪ ﺳﻪ ﻧﻤﻮﻧﻪ ﺑﺎﻻ ﺭﺍ ﺑﺮﺍﻱ ﻛﻮﺍﻧﺘﺰﺍﺳﻴﻮﻥ ‪) m - law‬ﺑﻪ ﺟﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ( ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪ .‬ﺷﻤﺎ ﺑﺎﻳﺪ ﻗﺎﺩﺭ ﺑﻪ ﺗﻨﻈﻴﻢ ﭘﺎﺭﺍﻣﺘﺮ‬
‫‪ m‬ﻋﻼﻭﻩ ﺑﺮ ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﺰﺍﺳﻴﻮﻥ‪ ،N ،‬ﺑﺎﺷﻴﺪ‪ .‬ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺎ ‪ m‬ﻭ ‪ N‬ﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﺭﺍ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﻳﻚ ‪ m‬ﺍﻧﺘﺨﺎﺏ‬
‫ﺷﺪﻩ‪ ،‬ﺗﻌﺪﺍﺩ ﺑﻴﺘﻬﺎﻱ ﻻﺯﻡ ﺑﺮﺍﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﻛﻴﻔﻴﺖ ﻗﺎﺑﻞ ﻗﺒﻮﻟﻲ ﺍﺯ ﮔﻔﺘﺎﺭ ﻭ ﻣﻮﺳﻴﻘﻲ ﭼﻪ ﻣﻲ ﺑﺎﺷﺪ؟ ﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﺭﺍ ﺑﺎ ﺑﻴﺖ ﻫﺎﻱ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺩﺭ‬
‫ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫ﺭﺍﻫﻨﻤﺎﻳﻲ‪ :‬ﺷﻤﺎ ﺑﺎﻳﺪ ‪ m - law‬ﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﻧﻤﻮﻧﻪ ﺍﻭﻟﻴﻪ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ ،‬ﻣﻘﺪﺍﺭ ﺗﺒﺪﻳﻞ ﻳﺎﻓﺘﻪ ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻛﻮﺍﻧﺘﻴﺰﻩ‬
‫ﻛﻨﻴﺪ‪ ،‬ﺳﭙﺲ ﻋﻜﺲ ‪ m - law‬ﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ ﺗﺎ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ ﻓﻀﺎﻱ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺪﺳﺖ ﺁﻳﺪ‪ .‬ﺑﺮﺍﻱ‬
‫ﻋﻜﺲ ‪ m - law‬ﮔﺮﻓﺘﻦ‪ ،‬ﺷﻤﺎ ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺗﻌﻴﻴﻦ )‪ x(n‬ﺍﺯ )‪ y(n‬ﺩﺍﺭﻳﺪ )ﻣﻌﺎﺩﻟﺔ ‪.(٣-١٣‬‬
‫‪ -٣‬ﺑﺮﻧﺎﻣﺔ ﻣﻄﻠﺐ ”‪ “sinadm.m‬ﻭ ”‪ “sindm.m‬ﺭﺍ ﺩﺭ ‪ Appendix‬ﺑﺨﻮﺍﻧﻴﺪ ﻛﻪ ‪ DM‬ﻭ ‪ ADM‬ﺭﺍ ﺑﺮﺍﻱ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﺳﻴﻨﻮﺳﻲ ﭘﻴﺎﺩﻩ‬
‫ﺳﺎﺯﻱ ﻣﻲ ﻛﻨﺪ‪ .‬ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺎ ‪ dmax, dmin, xmean, p, Q‬ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺭﺍ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺍﺛﺮﺍﺕ ﺗﻐﻴﻴﺮ ‪ Q‬ﺑﻪ ﻣﻘﺎﺩﻳﺮ ﺑﺴﻴﺎﺭ‬
‫ﻛﻮﭼﻚ ﻭ ﺑﺴﻴﺎﺭ ﺑﺰﺭﮒ ﺭﺍ ﺑﺮﺭﺳﻲ ﻛﻨﻴﺪ‪ .‬ﻣﺸﺎﺑﻪ ﺁﻥ ﺍﺛﺮﺍﺕ ‪ P‬ﺭﺍ ﻭﻗﺘﻲ ﺑﺴﻴﺎﺭ ﻛﻮﭼﻚ ﻳﺎ ﺑﺰﺭﮒ ﺍﺳﺖ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﺩﻫﻴﺪ‪ .‬ﻛﺪﺍﻡ ﺩﺳﺘﻪ‬
‫ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﺑﻬﺘﺮﻳﻦ ﻧﺘﺎﻳﺞ ﺭﺍ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻣﻲ ﺩﻫﺪ؟ ﺷﻜﻞ ﻫﺎﻱ ﺗﻮﻟﻴﺪ ﺷﺪﻩ ﺑﺎ ﺍﻧﺘﺨﺎﺏ ﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﺭﺍ ﭘﺮﻳﻨﺖ ﻛﻨﻴﺪ‪.‬‬
‫‪ “sindm.m” -٤‬ﺭﺍ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺗﻐﻴﻴﺮ ﺩﻫﻴﺪ ﻛﻪ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺭﺍ ﭘﺮﺩﺍﺯﺵ ﻛﻨﺪ‪ .‬ﺑﺮﻧﺎﻣﻪ ﺑﺎﻳﺪ ﻗﺎﺩﺭ ﺑﻪ‪:‬‬
‫ﺍﻟﻒ( ﺧﻮﺍﻧﺪﻥ ﻳﻚ ﻓﺎﻳﻞ ﻭﺭﻭﺩﻱ ﺑﻪ ﻓﺮﻣﺖ ‪.wav‬‬
‫ﺏ( ﺍﻋﻤﺎﻝ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺑﻪ ﻫﺮ ﻧﻤﻮﻧﻪ‬
‫ﺝ( ﺑﺎﺯﺳﺎﺯﻱ ﻧﻤﻮﻧﻪ ﺑﻌﺪ ﺍﺯ ﻛﻮﺍﻧﺘﺰﺍﺳﻴﻮﻥ‬
‫ﺩ( ﻧﻤﺎﻳﺶ ﺷﻜﻞ ﻣﻮﺝ ﺳﻴﮕﻨﺎﻝ ﻫﺎﻱ ﺍﺻﻠﻲ ﻭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ‪ :‬ﺗﺎ ﺑﻪ ﺷﻤﺎ ﻫﺮ ﺗﻐﻴﻴﺮ ﻛﻮﭼﻜﻲ ﺭﺍ ﺩﺭ ﺩﺍﻣﻨﻪ ﻧﻤﻮﻧﻪ ﻫﺎ ﻧﺸﺎﻥ ﺩﻫﺪ‪ .‬ﺷﻤﺎ ﺑﺎﻳﺪ ﻳﻚ‬
‫ﻗﺴﻤﺖ ﻛﻮﭼﻚ ﺍﺯ ﺷﻜﻞ ﻣﻮﺝ ﺭﺍ ﺩﺭ ﻫﻨﮕﺎﻡ ﻧﻤﺎﻳﺶ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ ﺗﺎ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻣﺠﺰﺍ ﺭﺍ ﻭﺍﺿﺢ ﺑﺒﻴﻨﻴﺪ‪.‬‬
‫ﻫـ( ﻓﺎﻳﻞ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺭﺍ ﺑﻪ ﻓﺮﻣﺖ ﻓﺎﻳﻞ ‪ .wav‬ﺫﺧﻴﺮﻩ ﻛﻨﻴﺪ‪.‬‬
‫ﻭ( ﻓﺎﻳﻞ ﺍﻭﻟﻴﻪ ﻭ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺭﺍ ﭘﺨﺶ ﻛﻨﻴﺪ ﺗﺎ ﻛﻴﻔﻴﺖ ﺻﻮﺕ ﺁﻧﻬﺎ ﺭﺍ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٥‬ﺑﺮﻧﺎﻣﻪ ﺭﺍ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﮔﻔﺘﺎﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ‪ 11KHz‬ﻭ ‪ 22KHz‬ﻭ ‪ 44KHz‬ﻭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺑﻪ ‪ ٨‬ﺑﻴﺖ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ‬
‫ﻫﺮ ﻓﺎﻳﻞ ﻭﺭﻭﺩﻱ‪ DM ،‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﺮﻧﺎﻣﺔ ‪ MATLAB‬ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ .‬ﺷﻤﺎ ﺑﺎﻳﺪ ﻃﻮﻝ ﭘﻠﻪ ﺭﺍ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺗﻨﻈﻴﻢ ﻛﻨﻴﺪ ﻛﻪ ﺑﻬﺘﺮﻳﻦ ﻛﻴﻔﻴﺖ‬
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‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
‫ﻣﻤﻜﻦ ﺩﺭ ﻫﺮ ﻣﻮﺭﺩ ﺑﺪﺳﺖ ﺁﻳﺪ‪ .‬ﺳﻌﻲ ﻛﻨﻴﺪ ﺍﺯ ﻫﻴﺴﺘﻮﮔﺮﺍﻡ ﺍﺧﺘﻼﻑ ﻧﻤﻮﻧﻪ ﻫﺎ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﻃﻮﻝ ﭘﻠﻪ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﻭ ﺗﻐﻴﻴﺮﺍﺕ‬
‫ﺩﺍﻣﻨﻪ ﺭﺍ ﺩﺭ ﻫﺮ ﻣﻮﺭﺩ ﻣﺸﺎﻫﺪﻩ ﻛﻨﻴﺪ‪ .‬ﺩﺭ ﭼﻪ ﻓﺮﻛﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‪ ،‬ﺳﻴﮕﻨﺎﻝ ﻓﺸﺮﺩﻩ ﺷﺪﺓ ‪ DM‬ﻛﻴﻔﻴﺖ ﻗﺎﺑﻞ ﻣﻘﺎﻳﺴﻪ ﺍﻱ ﺑﺎ ﺳﻴﮕﻨﺎﻝ ﺍﺻﻠﻲ ‪٨‬‬
‫ﺑﻴﺘﻲ ﻭ ‪ 11KHz‬ﻓﺮﺍﻫﻢ ﻣﻲ ﻛﻨﺪ؟ ﺑﺮﺍﻱ ﻫﺮ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﺩﺍﺩﻩ ﺍﺻﻠﻲ ﻭ ﺩﺍﺩﻩ ﺑﻌﺪ ﺍﺯ ‪ DM‬ﺭﺍ ﺑﺮﺍﻱ ﻫﺮ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‬
‫ﺑﺪﺳﺖ ﺁﻭﺭﻳﺪ )ﺩﻟﺨﻮﺍﻩ( ‪.‬‬
‫‪bit‬‬
‫ﺗﻮﺟﻪ ﻛﻨﻴﺪ ﻛﻪ ﺑﺎ ﺑﺮﻧﺎﻣﻪ ‪ ،MATLAB‬ﻫﺮ ﭼﻨﺪ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺑﻪ‬
‫‪sample‬‬
‫‪ double‬ﺭﺍ ﺩﺍﺭﺩ ﻭ ﻫﻨﮕﺎﻣﻲ ﻛﻪ ﺑﻪ ﻳﻚ ﻓﺎﻳﻞ ‪ .wav‬ﺗﺒﺪﻳﻞ ﻣﻲ ﺷﻮﺩ‪ ،‬ﻫﺮ ﻧﻤﻮﻧﻪ ‪ ٨‬ﻳﺎ ‪ ١٦‬ﺑﻴﺖ ﺟﺎ ﻣﻲ ﮔﻴﺮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺍﻧﺪﺍﺯﻩ ﻓﺎﻳﻞ ‪ .wav‬ﻛﻪ‬
‫‪ ١‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺳﻴﮕﻨﺎﻝ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺩﻗﺖ‬
‫ﺷﻤﺎ ﺳﺎﺧﺘﻪ ﺍﻳﺪ‪ ،‬ﻧﻤﺎﻳﺶ ﺩﺭﺳﺘﻲ ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﻓﺎﻳﻞ ﻓﺸﺮﺩﻩ ﺷﺪﻩ ﺣﻘﻴﻘﻲ ﻧﻴﺴﺖ‪ .‬ﻳﻚ ﺑﺮﻧﺎﻣﻪ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻭﺍﻗﻌﻲ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺭﺍ ﺑﺎ‬
‫‪bit‬‬
‫‪sample‬‬
‫)‪ (٤‬ﻭ )‪(٥‬ﻭ )‪ (۶‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺪﻩ ﺍﺯ ‪ ADM‬ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﺷﻤﺎ ﺑﺎﻳﺪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ P‬ﻭ ‪ xmean‬ﻭ ‪ dmin‬ﻭ ‪ dmax‬ﺭﺍ ﺑﻪ ﻃﻮﺭ‬
‫‪ ١‬ﺫﺧﻴﺮﻩ ﻣﻲ ﻛﻨﺪ‪.‬‬
‫ﻣﻨﺎﺳﺐ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ‪ .‬ﺳﻌﻲ ﻛﻨﻴﺪ ﻛﻪ ﺍﺯ ﻫﻴﺴﺘﻮﮔﺮﺍﻡ ﺍﺧﺘﻼﻑ ﻧﻤﻮﻧﻪ ﻫﺎ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﺍﺳﺘﻔﺎﺩﻩ ﻛﻨﻴﺪ‪ .‬ﻛﻴﻔﻴﺖ ‪ ADM‬ﺭﺍ ﺑﺎ ‪DM‬‬
‫ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٧‬ﺍﺧﺘﻴﺎﺭﻱ ‪ :‬ﻳﻚ ﺑﺮﻧﺎﻣﻪ ‪ MATLAB‬ﺑﺮﺍﻱ ﺗﺤﻘﻖ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ" ‪ ” ADM + m - law‬ﺩﺭ ﻳﻚ ﺳﻴﮕﻨﺎﻝ ﻭﺭﻭﺩﻱ ﺩﺍﺩﻩ ﺷﺪﻩ ﺑﻨﻮﻳﺴﻴﺪ‪.‬‬
‫ﺁﻧﺮﺍ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﻣﻮﺳﻴﻘﻲ ﻛﻪ ﻗﺒﻼﹰ ﺍﺳﺘﻔﺎﺩﻩ ﻛﺮﺩﻩ ﺍﻳﺪ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ .‬ﺁﻳﺎ ﺷﻤﺎ ﺑﻪ ﺑﻴﺖ ﻫﺎﻱ ﻛﻤﺘﺮﻱ ﺑﺮﺍﻱ ﺭﺳﻴﺪﻥ ﺑﻪ ﻫﻤﺎﻥ ﻛﻴﻔﻴﺖ ﺍﺣﺘﻴﺎﺝ ﺩﺍﺭﻳﺪ؟‬
‫ﺭﺍﻫﻨﻤﺎﻳﻲ‪ :‬ﺷﻤﺎ ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺗﻮﻟﻴﺪ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺩﺭ ﻫﺮ ﻧﻤﻮﻧﻪ ﺩﺍﺭﻳﺪ‪ m - law .‬ﺭﺍ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ .‬ﻣﻘﺪﺍﺭ ﺗﺒﺪﻳﻞ ﺷﺪﻩ ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ‬
‫ﺍﻟﮕﻮﺭﻳﺘﻢ ‪ ADM‬ﻛﻪ ﺩﺭ ﺁﻥ ﻣﻘﺪﺍﺭ ﻃﻮﻝ ﭘﻠﻪ ﺗﻌﻴﻴﻦ ﻣﻲ ﺷﻮﺩ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻴﺪ‪ .‬ﺳﭙﺲ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺭﺍ ﺑﺎ ﺍﻋﻤﺎﻝ ﻣﻌﻜﻮﺱ ‪ m - law‬ﺑﻪ‬
‫ﺣﻮﺯﻩ ﺍﺻﻠﻲ ﺑﺮﮔﺮﺩﺍﻧﻴﺪ‪ .‬ﻣﺎ ﺳﺮﺍﻧﺠﺎﻡ ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﭘﻴﺸﮕﻮﻳﻲ ﺷﺪﻩ ﺍﺿﺎﻓﻪ ﻣﻲ ﻛﻨﻴﻢ‪.‬‬
‫‪ -5‬ﮔﺰارش‬
‫ﺑﺮﻧﺎﻣﻪ ﻫﺎﻱ ‪ MATLAB‬ﻭ ﺷﻜﻞ ﻫﺎ )‪ (plots‬ﺭﺍ ﺗﺤﻮﻳﻞ ﺩﻫﻴﺪ‪ .‬ﻫﺮ ﭘﺪﻳﺪﻩ ﺍﻱ ﻛﻪ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩﻩ ﺍﻳﺪ‪ .‬ﺗﻮﺿﻴﺢ ﺩﻫﻴﺪ‪ .‬ﺭﻭﻱ ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﺑﺎ‬
‫ﺗﻨﻈﻴﻢ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﻧﻈﺮ ﺩﻫﻴﺪ ﻭ ﺳﻮﺍﻻﺕ ﺧﻮﺍﺳﺘﻪ ﺷﺪﻩ ﺩﺭ ﺁﺯﻣﺎﻳﺶ ﺭﺍ ﭘﺎﺳﺦ ﺩﻫﻴﺪ‪.‬‬
‫‪ -6‬ﻣﺮاﺟﻊ‬
‫‪[1]. L.R.Rabiner and R.W.Schafer, Digital Processing of Speech Signals, Prentice Hall 1978‬‬
‫‪[2]. B.Smith, “Instantaneous Companding of Quantized Signals”, Bell System Tech. J., Vol.36,‬‬
‫‪No.3, pp.653-709, May 1957.‬‬
‫‪[3]. N.S.Jayant, “Adaptive Quantization with a One Word Memory”, Bell System Tech. J., pp.‬‬
‫‪1119-1144, September 1973.‬‬
‫‪[4]. Guido van. Rossum, “FAQ: Audio File Formats”, http://www.cis.ohio_state.edu.‬‬
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‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Spring 2008‬‬
CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
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