‫ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﻲ‬
‫ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﭼﻨﺪﺭﺳﺎﻧﻪﺍﻱ )‪(۴۰-۳۴۲‬‬
‫ﺩﺍﻧﺸﻜﺪﻩ ﻣﻬﻨﺪﺳﻲ ﻛﺎﻣﭙﻴﻮﺗﺮ‬
‫ﺗﺮﻡ ﭘﺎﻳﻴﺰ ‪۱۳۸۷‬‬
‫ﺩﻛﺘﺮ ﺣﻤﻴﺪﺭﺿﺎ ﺭﺑﻴﻌﻲ‬
‫ﺗﻜﻠﻴﻒ ﺷﻤﺎﺭﻩ‪ :٢‬ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺗﻲ‪/‬ﺗﺼﻮﻳﺮﻱ‪ :‬ﮔﻔﺘﺎﺭ ﻭ ﺻﻮﺕ‬
‫‪ -١‬ﻣﻘﺪﻣﻪ‬
‫ﺁﻧﭽﻪ ﺗﻮﺯﻳﻊ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺕ ﻭ ﮔﻔﺘﺎﺭ ﺭﺍ ﺑﺪﻭﻥ ﻧﻴﺎﺯ ﺑﻪ ﺍﺧﺘﺼﺎﺹ ﭘﻬﻨﺎﻱ ﺑﺎﻧﺪ ﻭﺳﻴﻌﻲ ﺑﺮﺍﻱ ﺍﻧﺘﻘﺎﻝ ﻭ ﺫﺧﻴﺮﻩ ﺣﺠﻢ‬
‫ﺯﻳﺎﺩﻱ ﺍﺯ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺗﻲ ﻣﻤﻜﻦ ﻣﻲﺳﺎﺯﺩ‪ ،‬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 ﻣﻲﺩﻫﺪ‪ .‬ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻭ ﻋﻜﺲ ﻓﺸﺮﺩﻩ‬
‫ﺳﺎﺯﻱ ﺑﻮﺳﻴﻠﻪ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﻣﺘﻌﺪﺩﻱ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﺳﺖ ﻛﻪ ﻣﻲﺗﻮﺍﻧﺪ 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 .‬ﺑﺮﺧﻲ ﺍﺯ ﺍﻳﻦ ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎ ﺷﺎﻣﻞ‬
‫‪ MPEG-2 ،MPEG-1‬ﻭ ‪ MPEG-4‬ﻣﻲﺑﺎﺷﻨﺪ‪ .‬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.‬‬
‫‪ -٢‬ﺗﺌﻮﺭﻳﻬﺎ ﻭ ﻃﺮﺣﻬﺎ‬
‫ﻼ ﺗﺌﻮﺭﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ﺩﺭ ﺗﻜﻠﻴﻒ ‪ ١‬ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﺩﺍﺩﻩ ﺍﻳﻢ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻧﺸﺎﻥ ﺩﺍﺩﻳﻢ ﻛﻪ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻳﻚ‬
‫ﻣﺎ ﻗﺒ ﹰ‬
‫ﺳﻴﮕﻨﺎﻝ ﺁﻧﺎﻟﻮﮒ ﻧﻤﺎﻳﺶ ﻣﻨﺤﺼﺮ ﺑﻪ ﻓﺮﺩﻱ ﺍﺯ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﻣﻲﺑﺎﺷﻨﺪ 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 ﻣﻲﺷﻮﺩ ﻛﻪ ﺑﺮﺍﻱ ﺻﺪﺍﻫﺎﻱ‬
‫ﻭﺍﮐﺪﺍﺭ‪ ،‬ﺩﺍﻣﻨﻪ ﻃﻴﻒ ﻓﺮﻛﺎﻧﺴﻲ ﺳﻴﮕﻨﺎﻝ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﺑﺎﻻﻱ ‪ ٤٠dB ،٤KHz‬ﭘﺎﻳﻴﻦ ﺗﺮ ﺍﺯ ﻗﻠﻪ ﻃﻴﻔﻲ ﺳﻴﮕﻨﺎﻝ ﺍﺳﺖ‪.‬‬
‫ﻭﻟﻲ‪ ،‬ﺩﺭ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﺻﻮﺗﻲ‪ ،‬ﺍﻓﺖ ﻃﻴﻒ ﺳﻴﮕﻨﺎﻝ ﺣﺘﻲ ﺩﺭ ﻓﺮﻛﺎﻧﺴﻬﺎﻱ ﺑﺎﻻﻱ ‪ ٨KHz‬ﻗﺎﺑﻞ ﻣﻼﺣﻈﻪ ﻧﻴﺴﺖ‪ .‬ﻋﻼﻭﻩ ﺑﺮ‬
‫ﺍﻳﻦ‪ ،‬ﺩﺭ ﻛﺎﺭﺑﺮﺩﻫﺎﻱ ﻛﺎﻣﭙﻴﻮﺗﺮﻱ ﺑﺮﺍﻱ ﻧﻤﺎﻳﺶ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﻣﻤﻜﻦ ﻳﻚ ﻧﻤﻮﻧﻪ ﻛﻪ ﺩﺭ ﻣﺤﺪﻭﺩﺓ‬
‫‪1‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﭘﻴﻮﺳﺘﻪ ﺍﻱ ﺗﻐﻴﻴﺮ ﻣﻲﻛﻨﻨﺪ ﺑﺎﻳﺪ ﺑﻪ ﺗﻌﺪﺍﺩ ﻣﺤﺪﻭﺩﻱ ﺍﺯ ﻣﻘﺎﺩﻳﺮ ﮔﺴﺴﺘﻪ ﺗﺒﺪﻳﻞ ﺷﻮﺩ‪ .‬ﺍﻳﻦ ﭘﺮﻭﺳﻪ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻧﺎﻣﻴﺪﻩ‬
‫ﻣﻲﺷﻮﺩ‪.‬‬
‫‪ -١-٢‬ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ 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 )ﻓﺎﺻﻠﻪ ﻱ ﺣﺪﺍﻗﻞ ﺗﺎ‬
‫ﺣﺪﺍﻛﺜﺮ( ﺳﻴﮕﻨﺎﻝ ‪ ،R‬ﺑﻪ ‪ W‬ﺑﺎﺯﻩ ﺑﺎ ﻃﻮﻝ ﻳﻜﺴﺎﻥ ∆ ﺗﻘﺴﻴﻢ ﻣﻲﺷﻮﺩ‪ .‬ﻣﺎ ∆ ﺭﺍ ﭘﻠﺔ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﻲﻧﺎﻣﻴﻢ‪ .‬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 ﻣﻲﺳﺎﺯﺩ‪.‬‬
‫)‪(١-٣‬‬
‫)‪(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 ﻣﻲﺷﻮﺩ‪ .‬ﺑﺎ ‪ W‬ﺳﻄﺢ ﻛﻮﺍﻧﻴﺰ ﺷﺪﻩ‪ ،‬ﻫﺮ ﺳﻄﺢ ﻣﻲﺗﻮﺍﻧﺪ ﺑﺎ ‪B‬‬
‫])‪ = [log2(L‬ﺑﻴﺖ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﻮﺩ )ﺷﮑﻞ‪.(١‬‬
‫‪2‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -١‬ﺧﺼﻮﺻﻴﺎﺕ ﻭﺭﻭﺩﻱ – ﺧﺮﻭﺟﻲ ﻳﻚ ﻛﻮﺍﻧﻴﺰﻩ ﻛﻨﻨﺪﺓ ‪ ٣‬ﺑﻴﺘﻲ‬
‫ﺍﮔﺮ ﻣﺤﺪﻭﺩﺓ ﺳﻴﮕﻨﺎﻝ ‪ R‬ﺑﺎﺷﺪ‪ ،‬ﻳﻚ ﻛﻮﺍﻧﻴﺰﻩ ﻛﻨﻨﺪﻩ ﻳﻜﻨﻮﺍﺧﺖ ﻓﻘﻂ ﻳﻚ ﭘﺎﺭﺍﻣﺘﺮ ﺩﺍﺭﺩ‪ :‬ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ‪ N‬ﻳﺎ ﺍﻧﺪﺍﺯﻩ‬
‫ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ∆ ‪ ،‬ﻛﻪ ﻫﺮ ﺩﻭ ﺑﺎ ﺭﺍﺑﻄﺔ ﺯﻳﺮ ﺑﻪ ﻫﻢ ﺍﺭﺗﺒﺎﻁ ﺩﺍﺭﻧﺪ‪.‬‬
‫)‪(٤-٣‬‬
‫ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ‪ N‬ﻣﻌﻤﻮ ﹰﻻ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﻣﻲﺷﻮﻧﺪ ﻛﻪ ﺑﻪ ﺻﻮﺭﺕ ‪ 2B‬ﺑﺎﺷﻨﺪ ﺗﺎ ﺑﻬﺘﺮﻳﻦ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻛﻠﻤﺔ ﻛﺪ ‪B‬‬
‫ﺑﻴﺘﻲ 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 ﻣﻲﺭﺳﺪ 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 ﻣﻲﺷﻮﺩ ﻛﻪ ﺍﮔﺮ ∆ ﻭ‬
‫‪ B‬ﻣﺎﻧﻨﺪ ﺭﺍﺑﻄﺔ )‪ (٥-٣‬ﺍﻧﺘﺨﺎﺏ ﺷﻮﻧﺪ‪ ،‬ﺁﻧﮕﺎﻩ‬
‫)‪(٧-٣‬‬
‫ﻧﺴﺒﺖ ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﻧﻮﻳﺰ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺩﺭ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﻴﺎﻥ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫‪3‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫)‪(٨-٣‬‬
‫‪R2‬‬
‫ﺑﻪ ﻳﺎﺩ ﺑﻴﺎﻭﺭﻳﻢ ﻛﻪ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻝ ﺑﺎ ﺗﻮﺯﻳﻊ ﻳﻜﻨﻮﺍﺧﺖ ﺩﺭ ﻣﺤﺪﻭﺩﺓ ‪ ،R‬ﻭﺍﺭﻳﺎﻧﺲ ﺑﺮﺍﺑﺮ‬
‫‪12‬‬
‫∆ ∆‬
‫ﻧﻮﻳﺰ ﺩﺭ ﺑﺎﺯﺓ ) ‪ (− ,‬ﻳﻜﻨﻮﺍﺧﺖ ﺑﺎﺷﺪ‪ ،‬ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺮﺍﻱ ﻧﻮﻳﺰ ﻧﺘﻴﺠﻪ ﻣﻲﺷﻮﺩ‪.‬‬
‫‪2 2‬‬
‫ﺍﺳﺖ‪ .‬ﺍﮔﺮ ﺗﻮﺯﻳﻊ ﺩﺍﻣﻨﻪ‬
‫)‪(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 = 4σ x‬ﻓﺮﺽ ﻛﻨﻴﻢ ﺳﭙﺲ ﺭﺍﺑﻄﺔ )‪ (١١-٣‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺩﺭ‬
‫ﻣﻲﺁﻳﺪ‪.‬‬
‫)‪(١٢-٣‬‬
‫ﺍﻳﻦ ﺭﺍﺑﻄﻪ ﺑﻴﺎﻥ ﻣﻲﻛﻨﺪ ﻛﻪ ﻫﺮ ﺑﻴﺖ ﺍﺿﺎﻓﻲ‪ 6dB ،‬ﺑﻪ ﺑﻬﺒﻮﺩ ‪ SNR‬ﻛﻤﻚ ﻣﻲﻛﻨﺪ‪ .‬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 ﻣﻲﺷﺪ ﻭ ‪ X max = 4σ x‬ﺑﻮﺩ‪ ،‬ﺍﺧﺘﺼﺎﺹ ﻳﺎﺑﺪ‪ .‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺜﺎﻝ‪ ،‬ﺩﺭ ﺣﺎﻟﻲ ﻛﻪ ﺭﺍﺑﻄﺔ )‪ (١٢-٣‬ﺗﻌﺪﺍﺩ ﺑﻴﺖ ﻫﺎ )‪(B‬‬
‫ﺭﺍ ﺑﺮﺍﺑﺮ‪ ۷‬ﻗﺮﺍﺭ ﻣﻲﺩﻫﺪ 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.‬‬
‫‪µ − law -٢-١-٢‬‬
‫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
‫‪4‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﻛﻨﺪ ﻭ ﺳﭙﺲ ﻳﻚ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ﻳﻜﻨﻮﺍﺧﺖ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﻧﮕﺎﺷﺖ ﺷﺪﻩ ﺍﻋﻤﺎﻝ ﻛﺮﺩ‪ .‬ﻳﻜﻲ ﺍﺯ ﻧﮕﺎﺷﺖﻫﺎ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ‬
‫ﺍﺳﺖ‪.‬‬
‫)‪(١٣-٣‬‬
‫ﺷﮑﻞ‪ -٢‬ﺭﺍﺑﻄﻪ ﻭﺭﻭﺩﻱ – ﺧﺮﻭﺟﻲ ﺑﺮﺍﻱ ﻳﻚ ﻣﺸﺨﺼﻪ ‪) µ − law‬ﺍﻗﺘﺒﺎﺱ ﺍﺯ ]‪(smith[2‬‬
‫ﺷﮑﻞ‪ ،٢‬ﻳﻚ ﺧﺎﻧﻮﺍﺩﻩ ﺍﺯ ﻣﻨﺤﻨﻲ ﻫﺎﻱ )‪ y(n‬ﺑﺮ ﺣﺴﺐ )‪ x(n‬ﺭﺍ ﺑﺮﺍﻱ ﻣﻘﺎﺩﻳﺮ ﻣﺘﻔﺎﻭﺕ ‪ µ‬ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ‪ .‬ﻭﺍﺿﺢ ﺍﺳﺖ‬
‫ﻛﻪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺎﺑﻊ )‪ (١٣-٣‬ﺩﺍﻣﻨﻪ ﻫﺎﻱ ﻭﺭﻭﺩﻱ ﻛﻮﭼﻚ ﺗﻘﻮﻳﺖ ﻣﻲﺷﻮﻧﺪ‪ .‬ﺷﮑﻞ‪ ٣‬ﺗﻮﺯﻳﻊ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺭﺍ‬
‫ﺑﺮﺍﻱ ﺣﺎﻟﺘﻲ ﻛﻪ ‪ µ =٤٠‬ﻭ ‪ N=٨‬ﺍﺳﺖ‪ ،‬ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ‪ .‬ﺍﮔﺮ ‪ µ =٠‬ﺑﺎﺷﺪ‪ ،‬ﻣﻌﺎﺩﻟﺔ )‪ (١٣-٣‬ﺑﻪ ﻣﻌﺎﺩﻟﺔ )‪y(n)=x(n‬‬
‫ﺧﻼﺻﻪ ﻣﻲﺷﻮﺩ‪ ،‬ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺑﺎ ﻓﺎﺻﻠﻪﻫﺎﻱ ﻳﻜﻨﻮﺍﺧﺖ ﺗﻘﺴﻴﻢ ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﺑﺎ ﺍﻳﻦ ﻭﺟﻮﺩ ﺑﺮﻱ ﻣﻘﺎﺩﻳﺮ ﺑﺰﺭﮒ ‪µ‬‬
‫ﻭ ﺑﺮﺍﻱ |)‪ |x(n‬ﻫﺎﻱ ﺑﺰﺭﮒ‪:‬‬
‫)‪(١٤-٣‬‬
‫ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﻪ ﺟﺰ ﺩﺍﻣﻨﻪ ﻫﺎﻱ ﺑﺴﻴﺎﺭ ﻛﻮﭼﻚ‪ ،‬ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺑﻪ ﻃﻮﺭ ﻧﻤﺎﻳﻲ ﺑﺎ ﺍﻧﺪﻳﺲ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺍﻓﺰﺍﻳﺶ‬
‫ﻣﻲﻳﺎﺑﻨﺪ‪ .‬ﺍﻳﻦ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ‪ ،‬ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ‪ µ − law‬ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ ﻭ ﺍﻭﻟﻴﻦ ﺑﺎﺭ ﺗﻮﺳﻂ ‪ smith‬ﺍﺭﺍﻳﻪ ﺷﺪ ]‪.[2‬‬
‫‪5‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٣‬ﺗﻮﺯﻳﻊ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺑﺮﺍﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ‪ ٣‬ﺑﻴﺘﻲ ‪ -law µ‬ﺑﺎ ‪ µ =٤٠‬ﺍﺯ ]‪[1‬‬
‫ﺑﺎ ﺑﻜﺎﺭﮔﻴﺮﻱ ﻫﻤﺎﻥ ﻓﺮﺿﻴﺎﺕ ﻛﻪ ﺑﺮﺍﻱ ﺁﻧﺎﻟﻴﺰ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪ‪ smith[2] ،‬ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺮﺍﻱ ﻧﺴﺒﺖ‬
‫ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﻧﻮﻳﺰ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﺓ ‪ µ − law‬ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪.‬‬
‫)‪(١٥-٣‬‬
‫‪x max‬‬
‫ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ ﺑﺴﺘﮕﻲ ﻛﻤﺘﺮ ‪ SNR‬ﺑﻪ ﻣﻘﺪﺍﺭ )‬
‫‪σx‬‬
‫‪ (١٢‬ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ‪.‬‬
‫( ﺭﺍ ﻛﻪ ﺑﻪ ﺗﻮﻳﻊ ﺳﻴﮕﻨﺎﻝ ﺑﺴﺘﮕﻲ ﺩﺍﺭﺩ ﺭﺍ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻣﻌﺎﺩﻟﻪ )‪-٣‬‬
‫‪x max‬‬
‫ﻣﺸﺎﻫﺪﻩ ﻣﻲﺷﻮﺩ ﻛﻪ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ‪ SNR ، µ‬ﺑﻪ ﺗﻐﻴﻴﺮﺍﺕ )‬
‫‪σx‬‬
‫( ﻛﻤﺘﺮ ﺑﺴﺘﮕﻲ ﭘﻴﺪﺍ ﻣﻲﻛﻨﺪ‪ ،‬ﻳﻌﻨﻲ ﺑﺎ ﻭﺟﻮﺩ ﺍﻳﻨﻜﻪ ﺗﺮﻡ‬
‫‪x max‬‬
‫]) ‪ SNR ، - 20log10[ln (1 + µ‬ﺭﺍ ﻛﺎﻫﺶ ﻣﻲﺩﻫﺪ‪ ،‬ﻣﺤﺪﻭﺩﻩ ﺍﻱ ﺍﺯ )‬
‫‪σx‬‬
‫‪ µ‬ﺍﻓﺰﺍﻳﺶ ﻣﻲﻳﺎﺑﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ‪ µ‬ﺑﺰﺭﮒ‪ ،‬ﻛﺎﺭﺁﻳﻲ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻪ ﺁﻣﺎﺭﮔﺎﻥ ﺳﻴﮕﻨﺎﻝ ﻭﺍﺑﺴﺘﮕﻲ ﻛﻤﺘﺮﻱ‬
‫( ﻛﻪ ﺩﺭ ﺁﻥ ‪ SNR‬ﺛﺎﺑﺖ ﺍﺳﺖ ﺑﺎ‬
‫ﭘﻴﺪﺍ ﻣﻲﻛﻨﺪ‪.‬‬
‫‪ -٢-٢‬ﻛﺪ ﻛﺮﺩﻥ ﭘﻴﺸﮕﻮﻳﺎﻧﻪ )‪(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 ﻣﻲﺷﻮﺩ ﺗﺎ‬
‫‪6‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺳﭙﺲ ﺧﻄﺎﻱ ﺑﻴﻦ ﻣﻘﺪﺍﺭ ﻧﻤﻮﻧﻪ ﺍﺻﻠﻲ ﻭ ﻣﻘﺪﺍﺭ ﭘﻴﺶ ﺑﻴﻨﻲ ﺷﺪﻩ‬
‫ﺑﻪ )‪ d(n‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲﺷﻮﺩ ﻭ ﺑﻮﺳﻴﻠﺔ ﻛﻠﻤﺔ ﻛﺪ )‪ ،c(n‬ﻛﺪ ﻣﻲﺷﻮﺩ‪.‬‬
‫ﺩﺭ ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ‪ ،‬ﺍﺑﺘﺪﺍ ﻫﻤﺎﻥ ﻣﻘﺪﺍﺭ ﭘﻴﺸﮕﻮﻳﻲ ﺷﺪﻩ ﺍﺯ ﺭﻭﻱ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻗﺒﻠﻲ ﺩﻱ ﻛﺪ‬
‫ﺷﺪﻩ ﺳﺎﺧﺘﻪ ﻣﻲﺷﻮﺩ‪ .‬ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﺳﭙﺲ ﺑﻪ ﻣﻘﺪﺍﺭ ﺧﻄﺎﻱ ﺩﻱ ﻛﺪ ﻭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺍﺿﺎﻓﻪ ﻣﻲﺷﻮﺩ 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 ﻣﻌﻤﻮ ًﻵ ﺑﻪ ﻣﺪﻭﻻﺳﻴﻮﻥ ﻛﺪ ﺷﺪﻩ ﺳﻴﮕﻨﺎﻝ ﺗﻔﺎﺿﻠﻲ ﻳﺎ ”‪ “DPCM‬ﺷﻨﺎﺧﺘﻪ ﻣﻲﺷﻮﺩ‪ .‬ﻛﻠﻤﺔ »ﺗﻔﺎﺿﻠﻲ« ﺑﻪ‬
‫ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﺍﺷﺎﺭﻩ ﻣﻲﻛﻨﺪ ﻛﻪ ﺳﻴﮕﻨﺎﻝ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﻛﺪ ﻣﻲﺷﻮﺩ ﻭ ”‪ “PCM‬ﺑﻪ ﻃﺮﺡ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺍﺷﺎﺭﻩ ﻣﻲﻛﻨﺪ‬
‫ﻛﻪ ﺩﺭ ﺁﻥ ﻫﺮ ﺑﻴﺖ ﻛﺪ ﺷﺪﻩ ﻳﻚ ﺳﻤﺒﻞ ﺍﺳﺖ ﻛﻪ ﺑﻮﺳﻴﻠﻪ ﻳﻚ ﭘﺎﻟﺲ )ﺑﺎ ﺩﺍﻣﻨﻪ ﺻﻔﺮ ﻳﺎ ﻳﻚ( ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﻣﻲﺷﻮﺩ‪ .‬ﻛﻮﺍﻧﺘﻴﺰﻩ‬
‫ﻛﺮﺩﻥ ﻣﺴﺘﻘﻴﻢ ﻳﻚ ﻧﻤﻮﻧﺔ ﺍﻭﻟﻴﻪ ﺑﺎ ﻃﻮﻝ ﺛﺎﺑﺖ ﺩﺭ ﻛﺪ ﻛﺮﺩﻥ‪ “PCM” ،‬ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪.‬‬
‫‪7‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٤‬ﻛﺪ ﻛﺮﺩﻥ ﭘﻴﺸﮕﻮﻳﺎﻧﻪ )ﺍﻟﻒ( ﻛﺪ ﻛﻨﻨﺪﻩ )ﺏ( ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ‬
‫‪ -١-٢-٢‬ﻣﺪﻭﻻﺳﻴﻮﻥ 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)=1‬ﻣﺸﺨﺺ ﻣﻲﺷﻮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ )‪ d(n‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻣﻲﺷﻮﺩ‪.‬‬
‫)‪(١٦-٣‬‬
‫ﻛﻪ ﺍﺯ ﻳﻚ ﭘﻴﺸﮕﻮﻳﻲ ﺧﻄﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻳﻌﻨﻲ )‪ xp(n) = x(n-1‬ﻣﻲﺗﻮﺍﻥ ﺍﺯ ﺷﮑﻞ‪-٥‬ﺍﻟﻒ ﻣﺸﺎﻫﺪﻩ‬
‫ﻛﺮﺩ ﻛﻪ ﻣﻌﻤﻮ ﹰﻻ )‪ x(n‬ﺩﺭ ﻣﻌﺎﺩﻟﻪ ﺗﻔﺎﺿﻠﻲ ﺯﻳﺮ ﺻﺪﻕ ﻣﻲﻛﻨﺪ‪.‬‬
‫)‪(١٧-٣‬‬
‫ﺑﺎ ‪ ، α = 1‬ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ‪ ،‬ﻣﻌﺎﺩﻝ ﺩﻳﺠﻴﺘﺎﻟﻲ ﺍﻧﺘﮕﺮﺍﻝ ﺍﺳﺖ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺑﺎﻳﺪ ﺩﻗﺖ ﻛﺮﺩ ﻛﻪ ﻭﺭﻭﺩﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ‬
‫)‪(١٨-٣‬‬
‫)‬
‫ﻣﻲﺑﺎﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﻪ ﺟﺰ ﺧﻄﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ )‪ d(n) ، x ( n − 1‬ﻳﻚ ﺗﻔﺎﺿﻠﻲ ﺑﺮﮔﺸﺘﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺍﺯ )‪ x(n‬ﺍﺳﺖ‬
‫ﻛﻪ ﻣﻲﺗﻮﺍﻧﺪ 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 ‪ ١٦‬ﻣﻲﺭﺳﺪ‪.‬‬
‫‪8‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٥‬ﺑﻠﻮﻙ ﺩﻳﺎﮔﺮﺍﻡ ﺳﻴﺴﺘﻢ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺍﻟﻒ( ﻛﺪ ﻛﻨﻨﺪﻩ ﺏ( ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ‬
‫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 ﻣﻲﻛﻨﺪ‪ .‬ﺷﮑﻞ‪-٦‬ﺍﻟﻒ ﭘﺮﻭﺳﻪ‬
‫ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺭﺍ ﺑﺎ ﻃﻮﻝ ﭘﻠﻪ ﻣﺘﻨﺎﺳﺐ ﻭ ﺩﻗﻴﻖ ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ‪ .‬ﻣﻲﺗﻮﺍﻥ 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 ﻣﻲﺷﻮﺩ 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.‬‬
‫‪9‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪-٦‬ﻧﻤﺎﻳﺶ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎ ﺍﻟﻒ( ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻳﻚ ﭘﻠﻪ ﺑﺎ ﻃﻮﻝ ﺛﺎﺑﺖ ﺏ( ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻃﻮﻝ ﭘﻠﻪ ﻭﻓﻘﻲ‬
‫‪ -٢-٢-٢‬ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎﻱ ﻭﻓﻘﻲ‬
‫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 ﻣﻲﺷﻮﺩ‪ .‬ﺳﻴﺴﺘﻤﻲﻛﻪ ﻣﺎ ﺩﺭ‬
‫ﺯﻳﺮ ﭘﻴﺸﻨﻬﺎﺩ ﻛﺮﺩﻩ ﺍﻳﻢ ﺑﻮﺳﻴﻠﺔ ]‪ Jayant[3‬ﻃﺮﺍﺣﻲ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﺍﻟﮕﻮﺭﻳﺘﻢ ‪ Jayant‬ﺍﺯ ﻗﺎﻧﻮﻥ ﺯﻳﺮ ﭘﻴﺮﻭﻱ‬
‫ﻣﻲﻛﻨﺪ‪.‬‬
‫)‪-١٩-٣‬ﺍﻟﻒ(‬
‫)‪-١٩-٣‬ﺏ(‬
‫ﺍﻟﮕﻮﺭﻳﺘﻢ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﻃﻮﻝ ﭘﻠﻪ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺍﺳﺖ‪.‬‬
‫)‪(٢٠-٣‬‬
‫‪10‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪-٦‬ﺏ‪ -‬ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ ﻛﻪ ﭼﮕﻮﻧﻪ ﺷﻜﻞ ﻣﻮﺝ ﺷﮑﻞ‪-٦‬ﺍﻟﻒ ﻣﻲﺗﻮﺍﻧﺪ ﺗﻮﺳﻂ ﻳﻚ ﻣﺪﻭﻻﺳﻴﻮﻥ ﺩﻟﺘﺎﻱ ﻭﻓﻘﻲ ﻛﻪ ﺩﺭ‬
‫ﺭﺍﺑﻄﻪ )‪ (١٨-٣‬ﻭ )‪ (٢٠-٣‬ﺑﻴﺎﻥ ﺷﺪ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﻮﺩ‪ .‬ﺑﺮﺍﻱ ﺭﺍﺣﺘﻲ‪ ،‬ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺳﻴﺴﺘﻢ ﺩﺭ ‪ p = 2‬ﻭ ‪ α = 1‬ﺗﻨﻈﻴﻢ‬
‫ﻣﻲﺷﻮﻧﺪ ﻭ ﺣﺪﺍﻗﻞ ﻃﻮﻝ ﭘﻠﻪ ﺩﺭ ﺷﻜﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﻲﺗﻮﺍﻥ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩ ﻛﻪ ﻧﻮﺍﺣﻲ ﺑﺎ ﺷﻴﺐ ﻣﺜﺒﺖ ﺯﻳﺎﺩ‬
‫ﻫﻨﻮﺯ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺍﺯ ﺻﻔﺮ ﺗﻮﻟﻴﺪ ﻣﻲﻛﻨﻨﺪ ﺍﻣﺎ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻃﻮﻝ ﭘﻠﻪ ﺁﻧﻘﺪﺭ ﺍﻓﺰﺍﻳﺶ ﻣﻲﻳﺎﺑﺪ ﺗﺎ ﺍﺯﺩﻳﺎﺩ ﺷﻴﺐ ﺷﻜﻞ ﻣﻮﺝ ﺭﺍ‬
‫ﺩﻧﺒﺎﻝ ﻛﻨﺪ‪ .‬ﻧﻮﺍﺣﻲ ﺩﺍﻧﻪ ﺩﺍﻧﻪ ﺍﻱ ﺩﺭ ﺳﻤﺖ ﺭﺍﺳﺖ ﺷﻜﻞ ﺩﻭﺑﺎﺭﻩ ﺑﻮﺳﻴﻠﻪ ﻳﻚ ﺩﻧﺒﺎﻟﻪ ﺍﺯ ﺻﻔﺮ ﻭ ﻳﻚ ﻫﺎﻱ ﻣﺘﻨﺎﺳﺐ‬
‫ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲﺷﻮﻧﺪ‪ ،‬ﺍﻣﺎ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻃﻮﻝ ﭘﻠﻪ ﺳﺮﻳﻌﹰﺎ ﺑﻪ ﻣﻘﺪﺍﺭ ﺣﺪﺍﻗﻞ ) ‪ (∆ min‬ﻛﺎﻫﺶ ﻣﻲﻳﺎﺑﺪ ﻭ ﺗﺎ ﻭﻗﺘﻲ ﻛﻪ ﺷﻴﺐ‬
‫ﻛﻢ ﺑﺎﺷﺪ ﺩﺭ ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﻣﻲﻣﺎﻧﺪ‪.‬‬
‫ﺷﮑﻞ‪ -٧‬ﻧﺴﺒﺖ ﻫﺎﻱ ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﻧﻮﻳﺰ ﺍﺯ ﻳﻚ ﻣﺪﻭﻻﺗﻮﺭ ﺩﻟﺘﺎﻱ ﻭﻓﻘﻲ ﺑﺮ ﺣﺴﺐ ﺗﻮﺍﺑﻊ ‪p‬‬
‫ﺷﮑﻞ‪ ،٧‬ﻧﺘﺎﻳﺞ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺭﺍ ﺑﺮﺍﻱ ﺳﻴﮕﻨﺎﻝ ﮔﻔﺘﺎﺭ ﺑﺎ ‪ PQ = 1‬ﺑﺮﺍﻱ ﺳﻪ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﺘﻔﺎﻭﺕ ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ‪.‬‬
‫ﻣﺸﺎﻫﺪﻩ ﻣﻲﺷﻮﺩ ﻛﻪ ﺣﺪﺍﻛﺜﺮ ‪ SNR‬ﺑﺮﺍﻱ ‪ P = ١/٥‬ﺑﺪﺳﺖ ﻣﻲﺁﻳﺪ‪ ،‬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 ﻣﻲﻛﻨﺪ‪،‬‬
‫ﺍﻧﺠﺎﻡ ﺷﻮﺩ ﺗﺎ ﺗﻐﻴﻴﺮﺍﺕ ﺑﻴﻦ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﻣﺘﻮﺍﻟﻲ ﻛﻮﭼﻚ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﭘﺪﻳﺪﻩ ﺩﺭ ﺣﻘﻴﻘﺖ ﻣﺼﺎﻟﺤﻪ ﺑﻴﻦ ﺩﻗﺖ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‬
‫ﻭ ﺩﻗﺖ ﺩﺍﻣﻨﻪ ﺭﺍ ﺁﺷﻜﺎﺭ ﻣﻲﻛﻨﺪ‪ .‬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 -٣-٢-٢‬ﻫﺎﻱ ﻣﺮﺗﺒﻪ ﺑﺎﻻﺗﺮ‬
‫ﻣﺪﻭﻻﺗﻮﺭﻫﺎﻱ ﺩﻟﺘﺎ‪ ،‬ﻫﻤﺎﻧﻄﻮﺭ ﻛﻪ ﺩﺭ ﺑﺨﺶ ﻗﺒﻠﻲ ﺑﻴﺎﻥ ﺷﺪ‪ ،‬ﻣﻲﺗﻮﺍﻧﻨﺪ ﺳﻴﺴﺘﻤﻬﺎﻱ ‪ DPCM‬ﻳﻚ ﺑﻴﺘﻲ ﻧﺎﻣﻴﺪﻩ ﺷﻮﻧﺪ‪ .‬ﺑﻪ‬
‫ﻃﻮﺭ ﻛﻠﻲ‪ ،‬ﻣﻲﺗﻮﺍﻥ ﺍﺯ ﺑﻴﺸﺘﺮ ﺍﺯ ﻳﻚ ﻧﻤﻮﻧﻪ ﻗﺒﻠﻲ ﺑﺮﺍﻱ ﺗﺨﻤﻴﻦ ﻧﻤﻮﻧﻪ ﻓﻌﻠﻲ ﺍﺳﺘﻔﺎﺩﻩ ﻛﺮﺩ‪ .‬ﻫﻤﭽﻨﻴﻦ‪ ،‬ﻣﻲﺗﻮﺍﻥ ﺍﺯ ﻳﻚ‬
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‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫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 .‬ﻋﻤﻮﻣﺎﹰ‪ DPCM ،‬ﺑﺮﺍﻱ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺗﻔﺎﺿﻠﻲ ﻛﻪ ﺩﺭ ﺁﻥ‬
‫ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻴﺸﺘﺮ ﺍﺯ ﺩﻭ ﺳﻄﺢ ﺩﺍﺭﺩ‪ ،‬ﻣﻌﻜﻮﺱ ﻣﻲﺷﻮﺩ‪ .‬ﺳﻴﺴﺘﻤﻬﺎﻱ ‪ DPCM‬ﺑﺎ ﭘﻴﺸﮕﻮﻫﺎﻱ ﺛﺎﺑﺖ ﻣﻲﺗﻮﺍﻧﻨﺪ ﺍﺯ ‪٤‬‬
‫ﺗﺎ ‪ dB ١١‬ﺑﻬﺒﻮﺩ ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻣﺴﺘﻘﻴﻢ )‪ (PCM‬ﺍﻳﺠﺎﺩ ﻛﻨﻨﺪ‪ .‬ﺑﻴﺸﺘﺮﻳﻦ ﺑﻬﺒﻮﺩ ﺩﺭ ﻣﺮﺣﻠﻪ ﺗﻐﻴﻴﺮ ﺍﺯ ﺣﺎﻟﺖ ﺑﺪﻭﻥ‬
‫ﭘﻴﺸﮕﻮﻳﻲ ﺑﻪ ﺣﺎﻟﺖ ﭘﻴﺸﮕﻮﻳﻲ ﺩﺭﺟﻪ ﺍﻭﻝ ﺭﺥ ﻣﻲﺩﻫﺪ‪ .‬ﺍﻳﻦ ﺑﻬﺒﻮﺩ ﺩﺭ ﮔﺬﺭ ﺑﻪ ﭘﻴﺸﮕﻮﻫﺎﻱ ﺩﺭﺟﻪ ‪ ٤‬ﻳﺎ ‪ ٥‬ﻛﻤﺘﺮ ﻣﺤﺴﻮﺱ‬
‫ﻣﻲﺑﺎﺷﺪ‪ .‬ﺩﺭ ﮔﻔﺘﺎﺭ ﺍﺯ ﭘﻴﺸﮕﻮﻫﺎﻱ ﺑﺎ ﺩﺭﺟﻪ ﺑﺎﻻﺗﺮ ﺍﺯ ‪ ١٠‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲﺷﻮﺩ‪ ،‬ﺯﻳﺮﺍ ﺳﻴﮕﻨﺎﻝ ﮔﻔﺘﺎﺭ ﺑﺎ ﺩﺭﺟﺎﺕ ﺑﺎﻻﺗﺮ ﺑﻬﺘﺮ‬
‫ﻣﻲﺗﻮﺍﻧﺪ ﻣﺪﻝ ﺷﻮﺩ‪ .‬ﺑﻬﺮﻩ ‪ SNR‬ﻧﺸﺎﻥ ﻣﻲﺩﻫﺪ ﻛﻪ ﺩﺭ ﻳﻚ ﺳﻴﺴﺘﻢ ‪ ،DPCM‬ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ‪ SNR‬ﺧﻮﺍﺳﺘﻪ ﺷﺪﻩ ﺑﺎ‬
‫ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺑﻴﺖ ﻫﺎﻱ ﻛﻤﺘﺮ ﺍﺯ ﺑﻴﺖ ﻫﺎﻱ ﻣﻮﺭﺩﻧﻴﺎﺯ‪ ،‬ﻫﻨﮕﺎﻣﻲﻛﻪ ﻫﻤﺎﻥ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻨﺪﻩ ﺑﻪ ﻃﻮﺭ ﻣﺴﺘﻘﻴﻢ ﺭﻭﻱ ﺳﻴﮕﻨﺎﻝ‬
‫ﮔﻔﺘﺎﺭ ﺍﺛﺮ ﻣﻲﻛﻨﺪ‪ ،‬ﻋﻤﻠﻲ ﺍﺳﺖ‪ .‬ﺑﻪ ﻳﺎﺩﺁﻭﺭﻳﺪ ﻛﻪ ﻫﻨﮕﺎﻡ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﺮﺩﻥ ﻣﺴﺘﻘﻴﻢ ﻳﻚ ﺳﻴﮕﻨﺎﻝ‪ ،‬ﻫﺮ ﺑﻴﺖ ﺍﺿﺎﻓﻲ ﺑﻪ ﺑﻬﺮﺓ‬
‫‪ 6dB‬ﻣﻨﺠﺮ ﻣﻲﺷﺪ‪ ،‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺍﮔﺮ ﺳﻴﺴﺘﻢ ‪ DPCM‬ﺑﺘﻮﺍﻧﺪ ﺑﻪ ﺑﻬﺮﻩ ﭘﻴﺸﮕﻮﻳﻲ ‪ 6dB‬ﺑﺮﺳﺪ 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.‬‬
‫‪ADPCM -٤-٢-٢‬‬
‫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 ﻣﻲﻛﻨﺪ‪.‬‬
‫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 ﻣﻲﺩﻫﺪ ﻛﻪ ﺍﻳﻦ ﻗﺒﻴﻞ ﺭﻭﻳﻪ ﻫﺎﻱ ﻭﻓﻘﻲ ﻣﻲﺗﻮﺍﻧﻨﺪ ﺩﺭ ﺣﺪﻭﺩ ‪ ٥ dB‬ﺩﺭ ‪SNR‬‬
‫ﻧﺴﺒﺖ ﺑﻪ ﺣﺎﻟﺖ ﻏﻴﺮ ﻭﻓﻘﻲ ‪ µ − law‬ﺩﺭ ‪ PCM‬ﺑﻬﺒﻮﺩ ﺍﻳﺠﺎﺩ ﻛﻨﻨﺪ‪ .‬ﺍﻳﻦ ﺑﻬﺒﻮﺩ ﻣﻲﺗﻮﺍﻧﺪ ﺑﺎ ‪ ٦ dB‬ﺑﻬﺒﻮﺩ ﻛﻪ ﺍﺯ‬
‫ﻭﺿﻌﻴﺖ ﺗﻔﺎﺿﻠﻲ ﺑﺎ ﭘﻴﺸﮕﻮﻳﻲ ﺛﺎﺑﺖ ﺑﺪﺳﺖ ﻣﻲﺁﻳﺪ‪ ،‬ﺗﺮﻛﻴﺐ ﺷﺪﻩ ﻭ ‪ ADPCM‬ﺑﺎ ﭘﻴﺸﮕﻮﻳﻲ ﻭﻓﻘﻲ ﺭﻭ ﺑﻪ ﺟﻠﻮ‪ ،‬ﺑﻬﺒﻮﺩ‬
‫‪SNR‬ﺍﻱ ﺑﺮﺍﺑﺮ ‪ 10-11dB‬ﻧﺴﺒﺖ ﺑﻪ ‪ PCM‬ﺑﺎ ﻫﻤﺎﻥ ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ‪ ،‬ﻧﺘﻴﺠﻪ ﺩﻫﺪ‪.‬‬
‫‪12‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﺷﮑﻞ‪ -٨‬ﺳﻴﺴﺘﻢ ‪ ADPCM‬ﺑﺎ ﻛﻮﺍﻧﺘﻴﺰﻩ ﻭﻓﻘﻲ ﺭﻭ ﺑﻪ ﺟﻠﻮ ﺍﻟﻒ( ﻛﺪ ﻛﻨﻨﺪﻩ ﺏ( ﺩﻱ ﻛﺪ ﻛﻨﻨﺪﻩ‬
‫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 )‪ ، α k (n‬ﻣﻌﻤﻮﻝ ﺍﺳﺖ ﻛﻪ ﻓﺮﺽ ﻛﻨﻴﻢ ﺧﺼﻮﺻﻴﺎﺕ ﺁﻣﺎﺭﻱ ﺳﻴﮕﻨﺎﻝ ﺩﺭ ﻃﻮﻝ ﻳﻚ ﺑﺎﺯﻩ‬
‫ﻛﻮﺗﺎﻩ ﺯﻣﺎﻧﻲ ﺛﺎﺑﺖ ﻣﻲﻣﺎﻧﻨﺪ‪ .‬ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﻣﻲﺷﻮﻧﺪ ﺗﺎ ﻣﻴﺎﻧﮕﻴﻦ ﻣﺮﺑﻊ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺩﺭ ﻫﺮ‬
‫ﭘﻨﺠﺮﻩ ﻛﻮﭼﻚ ﺯﻣﺎﻧﻲ ﺣﺪﺍﻗﻞ ﺷﻮﺩ‪ .‬ﺑﺮﺍﻱ ﺁﺷﻨﺎﻳﻲ ﺑﻴﺸﺘﺮ ﺑﺎ ﻧﺤﻮﺓ ﺍﻧﺘﺨﺎﺏ ﺑﻬﻴﻨﺔ ﺿﺮﺍﻳﺐ ﭘﻴﺸﮕﻮﻳﻲ ﺧﻄﻲ ﺑﻪ ﻣﺮﺟﻊ ]‪[1‬‬
‫ﻣﺮﺍﺟﻌﻪ ﻛﻨﻴﺪ‪.‬‬
‫‪ -٣-٣‬ﺍﺳﺘﺎﻧﺪﺍﺭﺩﻫﺎﻱ ﻛﺪ ﻛﺮﺩﻥ 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 ﻣﻲﻛﻨﻨﺪ‪.‬‬
‫‪13‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫‪ -٣‬ﺁﺯﻣﺎﻳﺸﺎﺕ‬
‫‪ (۱‬ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﻗﺮﺍﺭ ﺍﺳﺖ ﺷﮑﻞ ﮐﻠﻲ ‪ Formant‬ﺳﻴﮕﻨﺎﻝ ﭼﻨﺪ ﺣﺮﻑ ﺭﺍ ﭘﻴﺪﺍ ﮐﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﺍﻳﻦ ﻣﻨﻈﻮﺭ ﮐﻠﻤﺎﺕ‬
‫ﻣﺨﺘﻠﻔﻲ ﮐﻪ ﺷﺎﻣﻞ ﺣﺮﻭﻑ ﻣﻮﺭﺩ ﻧﻈﺮ ﻫﺴﺘﻨﺪ ﺭﺍ ﺑﻴﺎﻥ ﮐﻨﻴﺪ‪ ،‬ﺻﺪﺍﻱ ﺧﻮﺩ ﺭﺍ ﺿﺒﻂ ﮐﺮﺩﻩ ﻭ ﺍﺳﭙﮑﺘﺮﻭﮔﺮﺍﻡ ﺳﻴﮕﻨﺎﻝ ﺻﺪﺍﻱ‬
‫ﺿﺒﻂ ﺷﺪﻩ ﺭﺍ ﺩﺭ ‪ MATLAB‬ﻳﺎ ‪ CoolEdit‬ﺑﺮﺭﺳﻲ ﮐﻨﻴﺪ‪.‬‬
‫‪ (٢‬ﺑﺮﻧﺎﻣﻪ ‪ MATLAB‬ﻣﻮﺟﻮﺩ ﺩﺭ ‪ “demo-quant,” ،Appendix‬ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺘﻲ ﺭﻭﻱ ﺳﻴﮕﻨﺎﻝ‬
‫ﺻﻮﺕ ﺍﻧﺠﺎﻡ ﻣﻲﺩﻫﺪ‪ .‬ﺑﺮﻧﺎﻣﻪ ﺭﺍ ﺑﺎ ﺩﻗﺖ ﺑﺨﻮﺍﻧﻴﺪ ﺗﺎ ﻣﺘﻮﺟﻪ ﺷﻮﻳﺪ ﭼﮕﻮﻧﻪ ﻛﺎﺭ ﻣﻲﻛﻨﺪ‪ .‬ﺻﺪﺍﻱ ﺧﻮﺩ ﺭﺍ ﺑﺎ ﺩﻗﺖ‬
‫)‪ 16bps(bits per sample‬ﺿﺒﻂ ﮐﻨﻴﺪ‪ .‬ﺍﻏﺘﺸﺎﺵ )‪ (Distortion‬ﺩﺭ ﺷﻜﻞ ﻣﻮﺝ ﻭ ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﺭﺍ ﺑﺎ ﺗﻐﻴﻴﺮ‬
‫ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﻴﺎﺯﺳﻴﻮﻥ )‪ (N‬ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ N .‬ﻣﻮﺭﺩﻧﻴﺎﺯ ﺑﺮﺍﻱ ﺩﺍﺷﺘﻦ ﻳﻚ ﺻﺪﺍﻱ ﺑﺎ ﻛﻴﻔﻴﺖ ﺧﻮﺏ ﻛﺪﺍﻡ ﺍﺳﺖ؟‬
‫ﺷﻜﻞﻫﺎﻱ ﺗﻮﻟﻴﺪ ﺷﺪﻩ ﺑﻮﺳﻴﻠﻪ ﺍﻧﺘﺨﺎﺏ ﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﺭﺍ ﭘﺮﻳﻨﺖ ﻛﻨﻴﺪ‪.‬‬
‫‪ (٣‬ﺑﺮﻧﺎﻣﻪ ﻧﻤﻮﻧﻪ ﻣﻮﺳﻴﻘﻲ ﺭﺍ ﺑﺮﺍﻱ ﻛﻮﺍﻧﺘﺰﺍﺳﻴﻮﻥ ‪) µ − law‬ﺑﻪ ﺟﺎﻱ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ( ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪ .‬ﺷﻤﺎ ﺑﺎﻳﺪ‬
‫ﻗﺎﺩﺭ ﺑﻪ ﺗﻨﻈﻴﻢ ﭘﺎﺭﺍﻣﺘﺮ ‪ µ‬ﻋﻼﻭﻩ ﺑﺮ ﺗﻌﺪﺍﺩ ﺳﻄﻮﺡ ﻛﻮﺍﻧﺘﺰﺍﺳﻴﻮﻥ‪ ،N ،‬ﺑﺎﺷﻴﺪ‪ .‬ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺎ ‪ µ‬ﻭ ‪ N‬ﻫﺎﻱ‬
‫ﻣﺘﻔﺎﻭﺕ ﺭﺍ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﻳﻚ ‪ µ‬ﺍﻧﺘﺨﺎﺏ ﺷﺪﻩ‪ ،‬ﺗﻌﺪﺍﺩ ﺑﻴﺘﻬﺎﻱ ﻻﺯﻡ ﺑﺮﺍﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﻛﻴﻔﻴﺖ ﻗﺎﺑﻞ ﻗﺒﻮﻟﻲ ﺍﺯ‬
‫ﻣﻮﺳﻴﻘﻲ ﭼﻪ ﻣﻲﺑﺎﺷﺪ؟ ﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﺭﺍ ﺑﺎ ﺑﻴﺖ ﻫﺎﻱ ﻣﻮﺭﺩﻧﻴﺎﺯ ﺩﺭ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫ﺭﺍﻫﻨﻤﺎﻳﻲ‪ :‬ﺷﻤﺎ ﺑﺎﻳﺪ ‪ µ − law‬ﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﻧﻤﻮﻧﻪ ﺍﻭﻟﻴﻪ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ‪ ،‬ﻣﻘﺪﺍﺭ ﺗﺒﺪﻳﻞ ﻳﺎﻓﺘﻪ ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ‬
‫ﻳﻜﻨﻮﺍﺧﺖ‪ ،‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻛﻨﻴﺪ‪ ،‬ﺳﭙﺲ ﻋﻜﺲ ‪ µ − law‬ﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺍﻋﻤﺎﻝ ﻛﻨﻴﺪ ﺗﺎ ﻣﻘﺪﺍﺭ ﻛﻮﺍﻧﺘﻴﺰﻩ ﺷﺪﻩ ﺩﺭ‬
‫ﻓﻀﺎﻱ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺑﺪﺳﺖ ﺁﻳﺪ‪ .‬ﺑﺮﺍﻱ ﻋﻜﺲ ‪ µ − law‬ﮔﺮﻓﺘﻦ‪ ،‬ﺷﻤﺎ ﺍﺣﺘﻴﺎﺝ ﺑﻪ ﺗﻌﻴﻴﻦ )‪ x(n‬ﺍﺯ )‪ y(n‬ﺩﺍﺭﻳﺪ )ﻣﻌﺎﺩﻟﺔ‬
‫‪.(٣-١٣‬‬
‫‪ (٤‬ﺑﺮﻧﺎﻣﺔ ﻣﻄﻠﺐ ”‪ “sinadm.m‬ﻭ ”‪ “sindm.m‬ﺭﺍ ﺩﺭ ‪ Appendix‬ﺑﺨﻮﺍﻧﻴﺪ ﻛﻪ ‪ DM‬ﻭ ‪ ADM‬ﺭﺍ ﺑﺮﺍﻱ ﻳﻚ‬
‫ﺳﻴﮕﻨﺎﻝ ﺳﻴﻨﻮﺳﻲ ﭘﻴﺎﺩﻩﺳﺎﺯﻱ ﻣﻲﻛﻨﺪ‪.‬‬
‫ﺑﺮﻧﺎﻣﻪ ﺭﺍ ﺑﻪ ﺳﻴﮕﻨﺎﻟﻬﺎﻱ ﮔﻔﺘﺎﺭ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﺩﺭ ‪ 11KHz‬ﻭ ‪ 22KHz‬ﻭ 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 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 ‪ ٨‬ﺑﻴﺘﻲ ﻭ ‪ 11KHz‬ﻓﺮﺍﻫﻢ ﻣﻲﻛﻨﺪ؟‬
‫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
‫ﺑﺎﺯﺳﺎﺯﻱ ﺷﺪﻩ ﺩﻗﺖ ‪ double‬ﺭﺍ ﺩﺍﺭﺩ ﻭ ﻫﻨﮕﺎﻣﻲﻛﻪ ﺑﻪ ﻳﻚ ﻓﺎﻳﻞ ‪ .wav‬ﺗﺒﺪﻳﻞ ﻣﻲﺷﻮﺩ‪ ،‬ﻫﺮ ﻧﻤﻮﻧﻪ ‪ ٨‬ﻳﺎ ‪ ١٦‬ﺑﻴﺖ ﺟﺎ‬
‫‪ ١‬ﻛﻮﺍﻧﺘﻴﺰﻩ ﻣﻲﺷﻮﺩ‪ ،‬ﺳﻴﮕﻨﺎﻝ‬
‫‪14‬‬
‫‪CE 342 – Multimedia HW# 2‬‬
‫‪H. Rabiee, Fall 2008‬‬
‫ﻣﻲﮔﻴﺮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺍﻧﺪﺍﺯﻩ ﻓﺎﻳﻞ ‪ .wav‬ﻛﻪ ﺷﻤﺎ ﺳﺎﺧﺘﻪﺍﻳﺪ‪ ،‬ﻧﻤﺎﻳﺶ ﺩﺭﺳﺘﻲ ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﻓﺎﻳﻞ ﻓﺸﺮﺩﻩ ﺷﺪﻩ ﺣﻘﻴﻘﻲ ﻧﻴﺴﺖ‪.‬‬
‫‪bit‬‬
‫ﻳﻚ ﺑﺮﻧﺎﻣﻪ ﻓﺸﺮﺩﻩ ﺳﺎﺯﻱ ﻭﺍﻗﻌﻲ ﺧﻄﺎﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺭﺍ ﺑﺎ‬
‫‪sample‬‬
‫‪ (٤) (٥‬ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ‪ ADM‬ﺗﻜﺮﺍﺭ ﻛﻨﻴﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﺷﻤﺎ ﺑﺎﻳﺪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ P‬ﻭ ‪ xmean‬ﻭ ‪ dmin‬ﻭ ‪dmax‬‬
‫‪ ١‬ﺫﺧﻴﺮﻩ ﻣﻲﻛﻨﺪ‪.‬‬
‫ﺭﺍ ﺑﻪ ﻃﻮﺭ ﻣﻨﺎﺳﺐ ﺍﻧﺘﺨﺎﺏ ﻛﻨﻴﺪ‪ .‬ﺳﻌﻲ ﻛﻨﻴﺪ ﻛﻪ ﺍﺯ ﻫﻴﺴﺘﻮﮔﺮﺍﻡ ﺍﺧﺘﻼﻑ ﻧﻤﻮﻧﻪﻫﺎ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﺍﺳﺘﻔﺎﺩﻩ‬
‫ﻛﻨﻴﺪ‪ .‬ﻛﻴﻔﻴﺖ ‪ ADM‬ﺭﺍ ﺑﺎ ‪ DM‬ﺩﺭ ﻧﺮﺥ ﻛﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﻳﻜﻨﻮﺍﺧﺖ ﻣﻘﺎﻳﺴﻪ ﻛﻨﻴﺪ‪.‬‬
‫‪ (۶‬ﺍﺯ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺕ ﺑﺎﻻ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺑﮕﻴﺮﻳﺪ )ﻧﻤﻮﻧﻪ ﺍﻱ ﺍﺯ ﮐﺪ ﻓﻴﻠﺘﺮﻳﻨﮓ ﺩﺭ ﺍﻧﺘﻬﺎﻱ ﺗﻤﺮﻳﻨﻬﺎ ﺁﻣﺪﻩ ﺍﺳﺖ( ﻭ ﺑﺎ ﺍﻋﻤﺎﻝ‬
‫ﻓﻴﻠﺘﺮ ﻳﻮﻧﻴﻔﺮﻡ‪ ،‬ﻓﺮﮐﺎﻧﺲﻫﺎﻱ ﺑﺎﻻ ﺭﺍ ﺣﺬﻑ ﮐﻨﻴﺪ ﺗﺎ ﺣﺪﻱ ﮐﻪ ﮐﻴﻔﻴﺖ ﺻﺪﺍﻱ ﺍﻭﻟﻴﻪ ﻭ ﺻﺪﺍﻱ ﻓﻴﻠﺘﺮ ﺷﺪﻩ ﺗﻘﺮﻳﺒﺎ ﻳﮑﺴﺎﻥ‬
‫ﺑﺎﺷﺪ‪ ،‬ﺍﮐﻨﻮﻥ ﻣﺮﺍﺣﻞ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺩﺭ ﺳﻮﺍﻝ ‪ ۳‬ﺭﺍ ﺭﻭﻱ ﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﻓﻴﻠﺘﺮ ﺷﺪﻩ ﺍﻋﻤﺎﻝ ﮐﻨﻴﺪ‪ .‬ﺁﻳﺎ ﺑﺮﺍﻱ ﺑﻪ ﺩﺳﺖ ﺁﻭﺭﺩﻥ‬
‫ﮐﻴﻔﻴﺖ ﻗﺒﻠﻲ‪ ،‬ﻣﻘﺎﺩﻳﺮ ‪ N‬ﻭ ‪ µ‬ﺗﻐﻴﻴﺮ ﮐﺮﺩﻩ؟‬
‫‪ -٥‬ﮔﺰﺍﺭﺵ‬
‫ﺑﺮﻧﺎﻣﻪ ﻫﺎﻱ ‪ MATLAB‬ﻭ ﺷﻜﻞ ﻫﺎ )‪ (plots‬ﺭﺍ ﺗﺤﻮﻳﻞ ﺩﻫﻴﺪ‪ .‬ﻫﺮ ﭘﺪﻳﺪﻩ ﺍﻱ ﻛﻪ ﻣﺸﺎﻫﺪﻩ ﻛﺮﺩﻩ ﺍﻳﺪ‪ .‬ﺗﻮﺿﻴﺢ ﺩﻫﻴﺪ‪.‬‬
‫ﭼﻬﺎﺭ ﺭﻭﺵ ﮐﻮﺍﻧﺘﻴﺰﺍﺳﻴﻮﻥ ﺭﺍ ﺩﺭ ﻳﮏ ﺟﺪﻭﻝ ﺑﺎ ﻫﻢ ﻣﻘﺎﻳﺴﻪ ﮐﻨﻴﺪ‪.‬‬
‫ﺭﻭﻱ ﻛﻴﻔﻴﺖ ﺻﺪﺍ ﺑﺎ ﺗﻨﻈﻴﻢ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﻣﺘﻔﺎﻭﺕ ﻧﻈﺮ ﺩﻫﻴﺪ ﻭ ﺳﻮﺍﻻﺕ ﺧﻮﺍﺳﺘﻪ ﺷﺪﻩ ﺩﺭ ﺁﺯﻣﺎﻳﺶ ﺭﺍ ﭘﺎﺳﺦ ﺩﻫﻴﺪ‪.‬‬
‫‪ -٦‬ﻣﺮﺍﺟﻊ‬
‫‪[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
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CE 342 – Multimedia HW# 2
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CE 342 – Multimedia HW# 2
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 2
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 2
H. Rabiee, Fall 2008
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CE 342 – Multimedia HW# 2
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