Question
Download Solution PDFएक वास्तविक और सम फलन का फूरियर रूपांतरण परिणामस्वरूप क्या होता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा: फूरियर रूपांतरण सममिती गुण
यदि एक समय-डोमेन फलन है:
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वास्तविक: इसका कोई काल्पनिक भाग नहीं है
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सम:
तब इसका फूरियर रूपांतरण होगा:
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पूर्णतः वास्तविक
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सम: F(ω)=F(−ω)
🔍 उदाहरण: कोसाइन तरंग
मान लीजिये: f(t) = cos(ω0t)
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यह वास्तविक है।
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यह सम है, क्योंकि
फूरियर रूपांतरण का है: F(ω)=π [δ(ω−ω0)+δ(ω+ω0)]
यह परिणाम है:
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पूर्णतः वास्तविक (डेल्टा फलनों को शामिल करता है, कोई काल्पनिक घटक नहीं)
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सम क्योंकि यह के आसपास सममित है
Last updated on Jun 7, 2025
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