નીચેનાં વિધાનો આપેલ છે:
વિધાન 1: આવર્તી સંકેત પ્રતિકારણાત્મક (anticausal) હોઈ શકે નહીં.
વિધાન 2: ઊર્જા સંકેત મર્યાદિત અવધિનો હોવો જોઈએ.
ઉપરોક્ત વિધાનો માટે સાચો વિકલ્પ પસંદ કરો
જવાબ અને પગલાવાર ઉકેલ
A — વિધાન 1 સાચું, વિધાન 2 ખોટું. શૂન્યેતર આવર્તી સંકેત અનિશ્ચિત સમય સુધી પુનરાવર્તિત થાય છે; જો તે તમામ ધન સમય માટે શૂન્ય હોય તો આવર્તિતા તેને બધે શૂન્ય કરી દે. ઊર્જા સંકેત અનંત અવધિનો પણ હોઈ શકે, જેમ કે e^(−t)u(t).
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept and Reasoning
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Calculation / Key Relation
Energy E=∫|x(t)|²dt <∞
Exam Takeaway
Finite energy does not imply finite duration.
Common Mistake
Do not confuse time support with convergence of the energy integral.
Quick Trick
Finite energy does not imply finite duration.
Given the following statements:
Statement 1:A periodic signal cannot be anticausal.
Statement 2:An energy signal must be of finite duration.
Choose the correct option for the above statements
Answer & step-by-step solution
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Concept and Reasoning
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Calculation / Key Relation
Energy E=∫|x(t)|²dt <∞
Exam Takeaway
Finite energy does not imply finite duration.
Common Mistake
Do not confuse time support with convergence of the energy integral.
Quick Trick
Finite energy does not imply finite duration.
निम्नलिखित कथन दिए गए हैं:
कथन 1: एक आवर्ती संकेत प्रतिकारणात्मक (anticausal) नहीं हो सकता।
कथन 2: एक ऊर्जा संकेत परिमित अवधि का होना चाहिए।
उपरोक्त कथनों के लिए सही विकल्प चुनिए
उत्तर और चरणबद्ध हल
A — कथन 1 सत्य, कथन 2 असत्य। शून्येतर आवर्ती संकेत अनिश्चित काल तक दोहराता है; यदि वह सभी धनात्मक समय पर शून्य हो तो आवर्तिता उसे हर जगह शून्य कर देगी। ऊर्जा संकेत अनंत अवधि का भी हो सकता है, जैसे e^(−t)u(t)।
विस्तृत हल (मूल भाषा में)
Concept and Reasoning
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Calculation / Key Relation
Energy E=∫|x(t)|²dt <∞
Exam Takeaway
Finite energy does not imply finite duration.
Common Mistake
Do not confuse time support with convergence of the energy integral.
Quick Trick
Finite energy does not imply finite duration.
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