‫ﺩﺍﻧﺸﮑﺪﻩ ﻣﻬﻨﺪﺳﻲ ﮐﺎﻣﭙﻴﻮﺗﺮ‬
‫ﻣﻬﻠﺖ ﺍﺭﺳﺎﻝ‪ :‬ﻳﮏﺷﻨﺒﻪ ‪ 19‬ﺧﺮﺩﺍﺩ ‪1387‬‬
‫ﺗﻤﺮﻳﻦ ﮐﺎﻣﭙﻴﻮﺗﺮﻱ ﺳﺮﻱ ﺳﻮﻡ ﺳﻴﮕﻨﺎﻝﻫﺎﻭ ﺳﻴﺴﺘﻢﻫﺎ‬
‫ﺗﻮﺟﻪ‪:‬‬
‫‪-‬‬
‫ﺧﻼﺻﻪ ﮐﻮﺗﺎﻫﻲ ﺍﺯ ﻧﺘﺎﻳﺞ ﮐﺎﺭﻫﺎﻱ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﻫﻤﺮﺍﻩ ﻧﻤﻮﺩﺍﺭﻫﺎﻱ ﺧﻮﺍﺳﺘﻪ ﺷﺪﻩ ﺩﺭ ﻳﮏ ﮔﺰﺍﺭﺵ ﺟﻤﻊ ﮐﻨﻴﺪ‪.‬‬
‫‪-‬‬
‫ﺗﻤﺎﻡ ‪ m‬ﻓﺎﻳﻞ ﻫﺎﻱ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﻫﻤﺮﺍﻩ ﻓﺎﻳﻞ ﮔﺰﺍﺭﺵ‪ ،‬ﺩﺭ ﻳﮏ ﭘﺮﻭﻧﺪﻩ ﺭﻳﺨﺘﻪ ﻭ ﺑﺎ ﻓﺮﻣﺖ ‪ zip‬ﻭ ﻳﺎ ‪ rar‬ﻓﺸﺮﺩﻩ ﮐﺮﺩﻩ ﻭ ﻓﺎﻳﻞ ﻧﻬﺎﻳﻲ ﺭﺍ ﺑﺎ ﻧﺎﻡ ‪HW3_ID‬‬
‫ﺑﻪ ﺁﺩﺭﺱ ‪ [email protected]‬ﺍﺭﺳﺎﻝ ﮐﻨﻴﺪ‪) .‬ﺳﻮﺍﻻﺕ ﻳﺎ ﺍﺑﻬﺎﻣﺎﺕ ﺧﻮﺩ ﺭﺍ ﺑﻪ ‪ [email protected]‬ﺑﻔﺮﺳﺘﻴﺪ‪(.‬‬
‫‪-‬‬
‫ﺑﺮﻧﺎﻣﻪﻫﺎﻱ ‪ Matlab‬ﺷﻤﺎ ﺑﺎﻳﺪ ﺑﺪﻭﻥ ﺧﻄﺎ ﻭ ﻧﻴﺎﺯ ﺑﻪ ﺗﻨﻈﻴﻤﺎﺕ‪ ،‬ﺍﺟﺮﺍ ﺷﻮﻧﺪ‪.‬‬
‫ﻣﺴﺎﻟﻪ ﺍﻭﻝ ‪. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫ﺗﺸﺨﻴﺺ ﺳﻴﮕﻨﺎﻝ ‪DTMF‬‬
‫ﻳﮑﻲ ﺍﺯ ﺳﻴﮕﻨﺎﻝﻫﺎﻱ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ﺩﺭ ﺳﻴﺴﺘﻢﻫﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ‪ ،‬ﺳﻴﮕﻨﺎﻝ ‪ DTMF1‬ﺍﺳﺖ ﮐﻪ ﺩﺭ ﮐﺎﺭﺑﺮﺩ ﻫﺎﻱ ﻣﺘﻨﻮﻋﻲ ﺍﺯ ﺟﻤﻠﻪ ﺩﺭ ﺍﺭﺳﺎﻝ ﺷﻤﺎﺭﻩﻫﺎﻱ‬
‫ﺗﻠﻔﻦ ﺑﻪ ﮐﺎﺭ ﻣﻲﺭﻭﺩ‪ .‬ﺑﻪ ﻃﻮﺭﻱ ﮐﻪ ﺑﺎ ﻓﺸﺮﺩﻥ ﻫﺮ ﮐﻠﻴﺪ ﺍﺯ ﺻﻔﺤﻪ ﺳﻴﮕﻨﺎﻟﻲ ﻣﺘﺸﮑﻞ ﺍﺯ ‪ 2‬ﺳﻴﻨﻮﺳﻲ ﺗﻮﻟﻴﺪ ﻣﻲﺷﻮﺩ ﮐﻪ ﻓﺮﮐﺎﻧﺲ ﻳﮑﻲ ﻣﺮﺑﻮﻁ ﺑﻪ ﺳﻄﺮ ﻭ‬
‫ﺩﻳﮕﺮﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﺳﺘﻮﻥ ﮐﻠﻴﺪ ﻓﺸﺮﺩﻩ ﺷﺪﻩ ﺩﺭ ﺁﺭﺍﻳﻪ ﮐﻠﻴﺪﻫﺎ ﻣﻲﺑﺎﺷﺪ‪ .‬ﺷﮑﻞ ﺯﻳﺮ ﻓﺮﮐﺎﻧﺲﻫﺎﻱ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ﻣﺮﺑﻮﻁ ﺑﻪ ﺻﻔﺤﻪ ﮐﻠﻴﺪ ﺗﻠﻔﻦ ﺭﺍ ﻧﺸﺎﻥ‬
‫ﻣﻲﺩﻫﺪ‪:‬‬
‫‪1633‬‬
‫‪1477‬‬
‫‪1336‬‬
‫‪1209‬‬
‫‪Hz‬‬
‫‪A‬‬
‫‪3‬‬
‫‪2‬‬
‫‪1‬‬
‫‪697‬‬
‫‪B‬‬
‫‪6‬‬
‫‪5‬‬
‫‪4‬‬
‫‪770‬‬
‫‪C‬‬
‫‪9‬‬
‫‪8‬‬
‫‪7‬‬
‫‪852‬‬
‫‪D‬‬
‫‪#‬‬
‫‪0‬‬
‫*‬
‫‪941‬‬
‫‪Dual Tone Multi Frequency‬‬
‫‪1‬‬
‫ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺳﻴﮕﻨﺎﻝ ﻣﺮﺑﻮﻁ ﺑﻪ ﮐﻠﻴﺪ ‪ 8‬ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
‫ﺭﻭﺵﻫﺎﻱ ﻣﺨﺘﻠﻔﻲ ﺑﺮﺍﻱ ﺩﻳﮑﻮﺩ ﮐﺮﺩﻥ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﺩﺭ ﮔﻴﺮﻧﺪﻩ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪ ،‬ﺍﺯ ﺟﻤﻠﻪ ﺍﻟﮕﻮﺭﻳﺘﻢ ‪ ، Goertzel‬ﺑﻪ ﮐﺎﺭﺑﺮﺩﻥ ‪ match-filter‬ﻭ‬
‫ﻏﻴﺮﻩ‪ .‬ﺩﺭ ﺍﻳﻨﺤﺎ ﻣﻲﺧﻮﺍﻫﻴﻢ ﺍﺯ ﺭﻭﺵ ‪ FFT‬ﮔﺮﻓﺘﻦ ﺑﺮﺍﻱ ﺗﺸﺨﻴﺺ ﻓﺮﮐﺎﻧﺲﻫﺎﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﺳﻄﺮ ﻭ ﺳﺘﻮﻥ ﮐﻠﻴﺪﻫﺎﻱ ﻓﺸﺮﺩﻩ ﺷﺪﻩ ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻴﻢ‪.‬‬
‫‪FFT‬‬
‫‪2‬‬
‫ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﺳﺮﻳﻊ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﺳﻴﮕﻨﺎﻝﻫﺎﻱ ﮔﺴﺴﺘﻪ ﺍﺳﺖ )ﺑﺮﺍﻱ ﺁﺷﻨﺎﻳﻲ ﺑﻴﺸﺘﺮ ﺩﺭ ‪ Matlab‬ﺍﺯ‪ help ،FFT‬ﺑﮕﻴﺮﻳﺪ(‪.‬‬
‫ﺩﻗﺖ ﮐﻨﻴﺪ ﮐﻪ ﺑﺮﺍﻱ ‪ FFT‬ﮔﺮﻓﺘﻦ ﺑﺎﻳﺪ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﺭﺍ ﺑﺎ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮔﺴﺴﺘﻪ ﮐﻨﻴﺪ‪ .‬ﻓﺮﮐﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ‬
‫ﺩﺭ ﻧﻈﺮ‬
‫ﺑﮕﻴﺮﻳﺪ‪ .‬ﺑﺪﻳﻦ ﺗﺮﺗﻴﺐ ﺩﺭ ﻣﺜﺎﻝ ﻗﺒﻞ ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ‪:‬‬
‫ﺍﻟﻒ( ﺑﺮﻧﺎﻣﻪﺍﻱ ﺑﻨﻮﻳﺴﻴﺪ ﮐﻪ ﺑﺮﺩﺍﺭ ﻣﺮﺑﻮﻁ ﺑﻪ ﺷﻤﺎﺭﻩﻫﺎﻱ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﻭﺭﻭﺩﻱ ﮔﺮﻓﺘﻪ ﻭ ﺑﺮﺩﺍﺭ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﻣﺮﺑﻮﻁ ﺑﻪ ﺁﻥﻫﺎ ﺭﺍ‬
‫ﺑﺎﺯﮔﺮﺩﺍﻧﺪ‪ .‬ﺑﺮﺍﻱ ﺍﻳﻦ ﮐﺎﺭ ﻣﺪﺕ ﺳﻴﮕﻨﺎﻝ ﻣﺮﺑﻮﻁ ﺑﻪ ﻫﺮ ﺭﻗﻢ ﻭ ﻫﻤﭽﻨﻴﻦ ﺳﮑﻮﺕ ﺑﻴﻦ ﺍﺭﻗﺎﻡ ﻣﺘﻮﺍﻟﻲ ﺭﺍ ‪ 0.5s‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪(DTMF_gen.m) .‬‬
‫ﻓﺮﺽ ﮐﻨﻴﺪ ﻓﻘﻂ ‪ 0‬ﺗﺎ ‪ 9‬ﺍﺭﺳﺎﻝ ﻣﻲﺷﻮﻧﺪ‪.‬‬
‫ﺏ( ‪ 4‬ﺭﻗﻢ ﺁﺧﺮ ﺷﻤﺎﺭﻩ ﺩﺍﻧﺸﺠﻮﻳﻲ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﻭﺭﻭﺩﻱ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻭ ﭘﺲ ﺍﺯ ﭘﺨﺶ ﺳﻴﮕﻨﺎﻝ ﺻﻮﺗﻲ ‪ DTMF‬ﺑﻪ ﮐﻤﮏ ﺑﺮﻧﺎﻣﻪ ﻗﺴﻤﺖ ﻗﺒﻞ‪،‬‬
‫ﻧﻤﻮﺩﺍﺭ ‪ FFT‬ﺳﻴﮕﻨﺎﻝ ﻣﺮﺑﻮﻁ ﺑﻪ ﺍﻳﻦ ﺭﻗﻢﻫﺎ ﺭﺍ ﺑﺎ ‪ subplot‬ﺩﺭ ﻳﮏ ﺷﮑﻞ ﺭﺳﻢ ﮐﻨﻴﺪ‪ .‬ﺩﺭ ﺗﻤﺎﻣﻲ ﻣﺮﺍﺣﻞ ﻓﺮﮐﺎﻧﺲ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺍ ‪ 8KHz‬ﺩﺭ ﻧﻈﺮ‬
‫ﺑﮕﻴﺮﻳﺪ‪(DTMF_id.m) .‬‬
‫ﺝ( ﺑﺮﻧﺎﻣﻪﺍﻱ ﺑﺮﺍﻱ ﺩﻳﮑﻮﺩ ﮐﺮﺩﻥ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﺑﻨﻮﻳﺴﻴﺪ ﮐﻪ ﺑﺮﺩﺍﺭ ﻣﺮﺑﻮﻁ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﻭﺭﻭﺩﻱ ﺭﺍ ﮔﺮﻓﺘﻪ ﻭ ﺑﺮﺩﺍﺭ ﺷﻤﺎﺭﻩﻫﺎﻱ ﺩﻳﮑﻮﺩ ﺷﺪﻩ ﺭﺍ‬
‫ﺑﺎﺯﮔﺮﺩﺍﻧﺪ‪ .‬ﻣﺪﺕ ﺯﻣﺎﻥ ﻣﺮﺑﻮﻁ ﺑﻪ ﻫﺮ ﺭﻗﻢ ﻭ ﺳﮑﻮﺕ ﺑﻴﻦ ﺍﺭﻗﺎﻡ ﻣﺘﻮﺍﻟﻲ ﺭﺍ ﻫﻤﺎﻥ ‪ 0.5s‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪(DTMF_detect.m).‬‬
‫ﻗﺴﻤﺖ ﺍﺧﺘﻴﺎﺭﻱ‪:‬‬
‫ﺩ( ﻭﺍﺿﺢ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﻋﻤﻞ ﺍﻃﻼﻋﻲ ﺍﺯ ﻣﺪﺕ ﺯﻣﺎﻥ ﻣﺮﺑﻮﻁ ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﻫﺮ ﺭﻗﻢ ﻭ ﻫﻤﭽﻨﻴﻦ ﻣﺪﺕ ﺳﮑﻮﺕ ﺑﻴﻦ ﺍﺭﺳﺎﻝ ﺭﻗﻢﻫﺎﻱ ﻣﺘﻮﺍﻟﻲ ﻧﺪﺍﺭﻳﻢ‪.‬‬
‫ﻫﻤﭽﻨﻴﻦ ﻭﺟﻮﺩ ﻧﻮﻳﺰ ﺩﺭ ﻣﺴﻴﺮ ﻣﻮﺟﺐ ﻣﻲﺷﻮﺩ ﺗﺎ ﻧﺘﻮﺍﻥ ﺳﻴﮕﻨﺎﻝ ﺩﺭﻳﺎﻓﺘﻲ ﺑﻴﻦ ﺳﻴﮕﻨﺎﻝ ﺍﺭﻗﺎﻡ ﻣﺘﻮﺍﻟﻲ ﺭﺍ ﺻﻔﺮ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ‪ .‬ﺑﺮﻧﺎﻣﻪ ﻗﺴﻤﺖ ﻗﺒﻞ ﺭﺍ‬
‫ﻃﻮﺭﻱ ﺍﺻﻼﺡ ﮐﻨﻴﺪ ﺗﺎ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﺑﺘﻮﺍﻧﺪ ﺳﻴﮕﻨﺎﻝ ‪ DTMF‬ﻭﺭﻭﺩﻱ ﺭﺍ ﺩﻳﮑﻮﺩ ﮐﻨﺪ‪) .‬ﺭﺍﻫﻨﻤﺎﻳﻲ‪ :‬ﻣﻲﺗﻮﺍﻧﻴﺪ ﺍﺯ ﺍﻧﺮﮊﻱ ﻣﺘﻮﺳﻂ ﺑﺮﺍﻱ ﺗﺸﺨﻴﺺ ﺯﻣﺎﻥ‬
‫ﻫﺎﻱ ﺳﮑﻮﺕ ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻴﺪ( )‪(DTMF_bonus.m‬‬
‫ﻣﺴﺎﻟﻪ ﺩﻭﻡ ‪. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .‬‬
‫ﻓﻴﻠﺘﺮ ﭘﺎﻳﻴﻦ ﮔﺬﺭ ‪Butterworth‬‬
‫ﺍﻳﻦ ﻓﻴﻠﺘﺮ ﻳﮑﻲ ﺍﺯ ﻓﻴﻠﺘﺮﻫﺎﻱ ﭘﺎﻳﻴﻦ ﮔﺬﺭﻱ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﻋﻤﻞ ﺑﻪ ﮐﺎﺭ ﻣﻲﺭﻭﺩ‪ .‬ﺍﻧﺪﺍﺯﻩ ﺗﺒﺪﻳﻞ ﻓﻮﺭﻳﻪ ﻓﻴﻠﺘﺮ ‪ Butterworth‬ﻣﺮﺗﺒﻪ ‪ N‬ﺍﻡ ﺍﺯ ﺭﺍﺑﻄﻪ ﺯﻳﺮ‬
‫ﺑﺪﺳﺖ ﻣﻲﺁﻳﺪ‪:‬‬
‫ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺭﺍﺑﻄﻪ‬
‫ﻓﺮﮐﺎﻧﺲ ﻗﻄﻊ ﻓﻴﻠﺘﺮ ﺍﺳﺖ‪.‬‬
‫‪Fast Fourier Transform‬‬
‫‪2‬‬
‫ﺍﻟﻒ( ﺑﺎ ﻓﺮﺽ ﺣﻘﻴﻘﻲ ﺑﻮﺩﻥ ﭘﺎﺳﺦ ﺿﺮﺑﻪ ﻭ ﭘﺎﻳﺪﺍﺭﻱ ﻭ ﺳﺒﺒﻲ ﺑﻮﺩﻥ ﺳﻴﺴﺘﻢ‪ ،‬ﻣﻲﺗﻮﺍﻥ ﻣﮑﺎﻥ ﺻﻔﺮ ﻭ ﻗﻄﺐﻫﺎﻱ‬
‫ﺗﺎﺑﻊ ﺗﺒﺪﻳﻞ‬
‫ﺭﺍ ﺗﻌﻴﻴﻦ ﮐﺮﺩ‪ .‬ﺑﺮﺍﻱ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ‬
‫ﺭﺍ ﻳﺎﻓﺘﻪ ﻭ ﭘﺎﺳﺦ ﻓﺮﮐﺎﻧﺴﻲ )ﺑﺎ ﺩﺳﺘﻮﺭ ‪ ، (freqs‬ﻣﮑﺎﻥ ﺻﻔﺮ ﻭ ﻗﻄﺐﻫﺎ )ﺑﺎ ﺩﺳﺘﻮﺭ ‪ (pzmap‬ﻭ ﻧﻤﻮﺩﺍﺭ‬
‫‪) bode‬ﺑﺎ ﺩﺳﺘﻮﺭ ‪ ، (bode‬ﭘﺎﺳﺦ ﭘﻠﻪ )ﺑﺎ ﺩﺳﺘﻮﺭ ‪ (step‬ﻭ ﺿﺮﺑﻪ )ﺑﺎ ﺩﺳﺘﻮﺭ ‪ (impulse‬ﺭﺍ ﺭﺳﻢ ﮐﻨﻴﺪ‪(buttwerworth.m) .‬‬
‫ﺏ( ﺍﺯ ﺩﺳﺘﻮﺭ ‪ help ، lsim‬ﮔﺮﻓﺘﻪ ﻭ ﺑﺎ ﺁﻥ ﺁﺷﻨﺎ ﺷﻮﻳﺪ‪) .‬ﺍﺯ ﺍﻳﻦ ﺩﺳﺘﻮﺭ ﺑﺮﺍﻱ ﮔﺮﻓﺘﻦ ﺧﺮﻭﺟﻲ ﺍﺯ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﭘﻴﻮﺳﺘﻪ‪-‬ﺯﻣﺎﻥ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪(.‬‬
‫ﺣﺎﻝ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺩﺳﺘﻮﺭ ‪ ،gensig‬ﻳﮏ ﻭﺭﻭﺩﻱ ‪ square‬ﺑﺎ ﺩﻭﺭﻩ ﻱ ﺗﻨﺎﻭﺏ )‬
‫( ﺗﻮﻟﻴﺪ ﻧﻤﻮﺩﻩ ﻭﺧﺮﻭﺟﻲ ﺍﻳﻦ ﻓﻴﻠﺘﺮ ﺭﺍ ﺑﺮﺍﻱ ﺍﻳﻦ ﻭﺭﻭﺩﻱ‬
‫ﺑﺪﺳﺖ ﺁﻭﺭﺩﻩ ﻭ ﺭﺳﻢ ﮐﻨﻴﺪ‪(low_passed.m) .‬‬
‫) ﺭﺍﻫﻨﻤﺎﻳﻲ‪ :‬ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﺭﻳﺸﻪ ﻫﺎﻱ ﻳﮏ ﭼﻨﺪ ﺟﻤﻠﻪ ﺍﻱ ﻣﻲ ﺗﻮﺍﻧﻴﺪ ﺍﺯ ﺩﺳﺘﻮﺭ ‪ roots‬ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻴﺪ‪ .‬ﺩﺳﺘﻮﺭﺍﺕ ‪ pole‬ﻭ‪ zero‬ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﻗﻄﺐ‬
‫ﻭ ﺻﻔﺮ ﺑﻪ ﮐﺎﺭ ﻣﻲ ﺭﻭﻧﺪ‪ .‬ﺑﺮﺍﻱ ﺗﻮﻟﻴﺪ ﭼﻨﺪ ﺟﻤﻠﻪ ﺍﻱ ﮐﻪ ﺭﻳﺸﻪ ﻫﺎﻱ ﺁﻥ ﺭﺍ ﺩﺭ ﺍﺧﺘﻴﺎﺭ ﺩﺍﺭﻳﺪ ﺍﺯ ﺩﺳﺘﻮﺭ‪ poly‬ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻴﺪ‪ .‬ﺑﺮﺍﻱ ﺭﺳﻢ ﭘﺎﺳﺦ ﻓﺮﮐﺎﻧﺴﻲ‬
‫ﻳﮏ ﺳﻴﺴﺘﻢ ﭘﻴﻮﺳﺘﻪ ﺍﺯ ﺩﺳﺘﻮﺭ ‪ freqs‬ﻭ ﺑﺮﺍﻱ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﮔﺴﺴﺘﻪ ﺍﺯ ﺩﺳﺘﻮﺭ ‪ freqz‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺩﺳﺘﻮﺭ ‪ tf‬ﺭﺍ ﺑﺮﺍﻱ ﻣﻌﻴﻦ ﮐﺮﺩﻥ‬
‫ﺗﺎﺑﻊ ﺗﺒﺪﻳﻞ ﺳﻴﺴﺘﻢ ﺑﻪ ﮐﺎﺭ ﺑﺒﺮﻳﺪ(‬
‫ﻣﺴﺎﻟﻪ ﺳﻮﻡ ‪. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .‬‬
‫ﺍﺛﺮ ‪Aliasing‬‬
‫ﺳﻴﮕﻨﺎﻝ ﺯﻳﺮ ﺭﺍ ﮐﻪ ‪ chirp‬ﻧﺎﻣﻴﺪﻩ ﻣﻲﺷﻮﺩ‪ ،‬ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ ‪:‬‬
‫ﻓﺮﮐﺎﻧﺲ ﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﻃﻮﺭ ﺧﻄﻲ ﻭ ﺑﺎ ﺷﻴﺐ‬
‫ﺍﻟﻒ( ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ‬
‫ﺩﺭ ﺯﻣﺎﻥ ﺗﻐﻴﻴﺮ ﻣﻲﮐﻨﺪ‪:‬‬
‫ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﮐﺮﺩﻩ ﻭ ﺑﺎ ﻓﺮﮐﺎﻧﺲ‬
‫ﻭ ﺑﻪ ﻣﺪﺕ ‪ 5sec‬ﺍﺯ ﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮐﺮﺩﻩ‬
‫ﺑﻪ ﺳﻴﮕﻨﺎﻝ ﮔﺴﺴﺘﻪ ﺣﺎﺻﻞ ﺍﺯ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﮔﻮﺵ ﺩﻫﻴﺪ‪ .‬ﺩﺭ ﻣﻮﺭﺩ ﺻﺪﺍﻱ ﺷﻨﻴﺪﻩ ﺷﺪﻩ ﻭ ﺍﺭﺗﺒﺎﻁ ﺁﻥ ﺑﺎ ﭘﺪﻳﺪﻩ ‪ aliasing‬ﺗﻮﺿﻴﺢ ﺩﻫﻴﺪ‪.‬‬
‫)‪(aliasing.m‬‬
‫ﺏ( ﻳﮏ ﺳﻴﮕﻨﺎﻝ ‪ chirp‬ﺑﺎ ﻓﺮﮐﺎﻧﺲ ﻣﺘﻐﻴﺮ ﺑﻴﻦ ‪ 0-2500Hz‬ﺳﺎﺧﺘﻪ‬
‫ﻭ ﺍﻳﻦ ﺳﻴﮕﻨﺎﻝ ﮔﺴﺴﺘﻪ ﺭﺍ ﺑﺎ ﻧﺮﺥ ﺩﻭ ﺑﺮﺍﺑﺮ ‪upsample‬‬
‫ﮐﻨﻴﺪ ‪:‬‬
‫ﺣﺎﻝ ﺑﻪ ﮐﻤﮏ ﻳﮏ ﻓﻴﻠﺘﺮ ‪ Butterworth‬ﻣﻨﺎﺳﺐ ﺳﻴﮕﻨﺎﻝ ﺍﻭﻟﻴﻪ ﺭﺍ ﺑﺎﺯﺳﺎﺯﻱ ﮐﺮﺩﻩ ﻭ ﺁﻥ ﺭﺍ ﭘﺨﺶ ﮐﻨﻴﺪ‪(reconstruct.m).‬‬