Time Differentiation MCQ Quiz - Objective Question with Answer for Time Differentiation - Download Free PDF
Last updated on May 16, 2025
Latest Time Differentiation MCQ Objective Questions
Time Differentiation Question 1:
Fourier transform of
Answer (Detailed Solution Below)
Time Differentiation Question 1 Detailed Solution
Concept:
Fourier Transform:
- The Fourier transform of a function converts it from time domain to frequency domain.
- If f(t) is a time-domain function, its Fourier Transform is defined as:
- For Gaussian functions like
, their Fourier transform is also Gaussian. - The Fourier transform of
is . - Multiplying by t in time domain corresponds to taking derivative with respect to p in frequency domain:
Calculation:
Given,
Let f(t) = t e−t²⁄2
Let F(p) = Fourier transform of e−t²⁄2 = e−p²⁄2
⇒ Fourier transform of t f(t) = i × d/dp (e−p²⁄2)
⇒ = i × (−p e−p²⁄2) = −i p e−p²⁄2
⇒ Now t e−t²⁄2 = f(t),
so full FT is i × d/dp (F(p))
⇒ Add F(p) itself:
Final result = (1 + i p) e−(p² − 1)/2
∴ The correct Fourier transform is:
Top Time Differentiation MCQ Objective Questions
Time Differentiation Question 2:
The Fourier transform of
Answer (Detailed Solution Below)
Time Differentiation Question 2 Detailed Solution
Let
The
Now,
Let
Taking Fourier transform
Thus,
Time Differentiation Question 3:
Fourier transform of
Answer (Detailed Solution Below)
Time Differentiation Question 3 Detailed Solution
Concept:
Fourier Transform:
- The Fourier transform of a function converts it from time domain to frequency domain.
- If f(t) is a time-domain function, its Fourier Transform is defined as:
- For Gaussian functions like
, their Fourier transform is also Gaussian. - The Fourier transform of
is . - Multiplying by t in time domain corresponds to taking derivative with respect to p in frequency domain:
Calculation:
Given,
Let f(t) = t e−t²⁄2
Let F(p) = Fourier transform of e−t²⁄2 = e−p²⁄2
⇒ Fourier transform of t f(t) = i × d/dp (e−p²⁄2)
⇒ = i × (−p e−p²⁄2) = −i p e−p²⁄2
⇒ Now t e−t²⁄2 = f(t),
so full FT is i × d/dp (F(p))
⇒ Add F(p) itself:
Final result = (1 + i p) e−(p² − 1)/2
∴ The correct Fourier transform is:
Time Differentiation Question 4:
If x(t) is real valued signal whose Fourier transform is defined as
Answer (Detailed Solution Below) 0
Time Differentiation Question 4 Detailed Solution
at t = 1/3, δ(t) = 0
Time Differentiation Question 5:
Find the inverse Fourier transform of
Answer (Detailed Solution Below)
Time Differentiation Question 5 Detailed Solution
We know that,
From the property of delta function
F (t) δ (t – t0) = f (t0) δ (t – t0)
⇒ t e-4t δ (t) = 0 e-4(0) δ (t) = 0
⇒ x (t) = -4te-4t u(t) + e-4t u(t)
Time Differentiation Question 6:
The Fourier transfer of the signal x(t) given below be x(ω) then the value of
Answer (Detailed Solution Below) 0.2 - 0.3
Time Differentiation Question 6 Detailed Solution
Differentiating given signal w.r.t time
Again differentiating w.r.t time we get
The Fourier transform of above signal is
≃ 0.26
Time Differentiation Question 7:
The Fourier transform of
Answer (Detailed Solution Below)
Time Differentiation Question 7 Detailed Solution
Let
The
Now,
Let
Taking Fourier transform
Thus,
Time Differentiation Question 8:
The input x(t)and output y(t) of causal LTI system are related by:-
Then, the impulse response of the system is
Answer (Detailed Solution Below)
Time Differentiation Question 8 Detailed Solution
We have
Taking Fourier transform we have,