Determine the discrete−time signal: x(n) = 1 for n ≥ 0 and x(n) = 0 for n < 0.
Answer & step-by-step solution
The sequence defined as 1 for n≥0 and 0 for n<0 is the discrete-time unit step u[n]. It switches from 0 to 1 at n=0 and remains at 1 thereafter.
Concept & Reasoning
The unit impulse δ[n] is nonzero only at n=0, whereas the unit step u[n] remains one for all nonnegative n. A unit ramp grows with n. These distinctions are fundamental in convolution and system-response problems.
How to Solve It in the Exam
One at and after zero → unit step.
Important Exam Point
Use δ[n] only for a single non-zero sample at n=0.
Quick Trick
One at and after zero → unit step.
Common Mistake
Confusing unit step with unit impulse.
असतत-समय संकेत पहचानिए: x(n) = 1, n ≥ 0 के लिए और x(n) = 0, n < 0 के लिए।
उत्तर और चरणबद्ध हल
D — इकाई स्टेप अनुक्रम u[n]। यह n = 0 पर 0 से 1 पर जाता है और उसके बाद 1 ही रहता है।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
The unit impulse δ[n] is nonzero only at n=0, whereas the unit step u[n] remains one for all nonnegative n. A unit ramp grows with n. These distinctions are fundamental in convolution and system-response problems.
How to Solve It in the Exam
One at and after zero → unit step.
Important Exam Point
Use δ[n] only for a single non-zero sample at n=0.
Quick Trick
One at and after zero → unit step.
Common Mistake
Confusing unit step with unit impulse.
અસતત-સમય સંકેત ઓળખો: x(n) = 1, n ≥ 0 માટે અને x(n) = 0, n < 0 માટે.
જવાબ અને પગલાવાર ઉકેલ
D — એકમ સ્ટેપ અનુક્રમ u[n]. તે n = 0 પર 0 થી 1 થાય છે અને પછી 1 જ રહે છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
The unit impulse δ[n] is nonzero only at n=0, whereas the unit step u[n] remains one for all nonnegative n. A unit ramp grows with n. These distinctions are fundamental in convolution and system-response problems.
How to Solve It in the Exam
One at and after zero → unit step.
Important Exam Point
Use δ[n] only for a single non-zero sample at n=0.
Quick Trick
One at and after zero → unit step.
Common Mistake
Confusing unit step with unit impulse.
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