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Latest Condition For Existence of Fourier Transform MCQ Objective Questions

Condition For Existence of Fourier Transform Question 1:

The Fourier Transform of an real and even function results in:

a purely real and odd function
a purely imaginary and even function
an imaginary and odd function
a purely real and even function

Answer (Detailed Solution Below)

Option 4 : a purely real and even function

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Let’s take: f(t) = cos(ω0t)

It is real.
It is even, because $cos (- ω_{0} t) = cos (ω_{0} t)$

Fourier Transform of $cos (ω_{0} t)$ is: F(ω)=π [δ(ω−ω₀)+δ(ω+ω₀)]

This result is:

Purely real (involves delta functions, no imaginary component)
Even since it's symmetric around $ω = 0$

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Condition For Existence of Fourier Transform Question 2:

A signal x(t) has a fourier transform x(ω). If x(t) is a real and even function the x(ω) is Even

Real and Even
Imaginary and odd
Real and odd
Imaginary and Even

Answer (Detailed Solution Below)

Option 1 : Real and Even

x(t) – x(ω) pairs

X(t)	X(ω)
R	C.S
C.S	R
I	C.A.S
C.A.S	I
R + E	R + E
R + O	I + O
I + E	I + E
I + O	R + 0

R → Real, C.S → Conjugate Symmetry.

I – Imaginary, CAS → Conjugate Any Symmetry

E → Even, O → Odd

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Top Condition For Existence of Fourier Transform MCQ Objective Questions

Condition For Existence of Fourier Transform Question 3

Download Solution PDF

The Fourier Transform of an real and even function results in:

a purely real and odd function
a purely imaginary and even function
an imaginary and odd function
a purely real and even function

Answer (Detailed Solution Below)

Option 4 : a purely real and even function

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Let’s take: f(t) = cos(ω0t)

It is real.
It is even, because $cos (- ω_{0} t) = cos (ω_{0} t)$

Fourier Transform of $cos (ω_{0} t)$ is: F(ω)=π [δ(ω−ω₀)+δ(ω+ω₀)]

This result is:

Purely real (involves delta functions, no imaginary component)
Even since it's symmetric around $ω = 0$

Download Solution PDF

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Condition For Existence of Fourier Transform Question 4:

A signal x(t) has a fourier transform x(ω). If x(t) is a real and even function the x(ω) is Even

Real and Even
Imaginary and odd
Real and odd
Imaginary and Even

Answer (Detailed Solution Below)

Option 1 : Real and Even

x(t) – x(ω) pairs

X(t)	X(ω)
R	C.S
C.S	R
I	C.A.S
C.A.S	I
R + E	R + E
R + O	I + O
I + E	I + E
I + O	R + 0

R → Real, C.S → Conjugate Symmetry.

I – Imaginary, CAS → Conjugate Any Symmetry

E → Even, O → Odd

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Condition For Existence of Fourier Transform Question 5:

The Fourier Transform of an real and even function results in:

a purely real and odd function
a purely imaginary and even function
an imaginary and odd function
a purely real and even function

Answer (Detailed Solution Below)

Option 4 : a purely real and even function

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Let’s take: f(t) = cos(ω0t)

It is real.
It is even, because $cos (- ω_{0} t) = cos (ω_{0} t)$

Fourier Transform of $cos (ω_{0} t)$ is: F(ω)=π [δ(ω−ω₀)+δ(ω+ω₀)]

This result is:

Purely real (involves delta functions, no imaginary component)
Even since it's symmetric around $ω = 0$

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Condition For Existence of Fourier Transform Question 6:

A signal x(t) has a fourier transform x(ω). If x(t) is a real and even function the x(ω) is Even

Real and Even
Imaginary and odd
Real and odd
Imaginary and Even
complex Always

Answer (Detailed Solution Below)

Option 1 : Real and Even

x(t) – x(ω) pairs

X(t)	X(ω)
R	C.S
C.S	R
I	C.A.S
C.A.S	I
R + E	R + E
R + O	I + O
I + E	I + E
I + O	R + 0

R → Real, C.S → Conjugate Symmetry.

I – Imaginary, CAS → Conjugate Any Symmetry

E → Even, O → Odd

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Condition For Existence of Fourier Transform Question 7:

Consider the single x[n] = 2ⁿu[n]. The given signal does not coverage. To make the signal converge. The signal is multiplied by r^-n i.e. now the modified signal is x’[n] = r^-nx[n]. The range of r for which the signal will converge is

|r| > 2
0 < r < 2
-2 < r < 0
|r| < 2

Answer (Detailed Solution Below)

Option 1 : |r| > 2

For convergence the signal should be absolutely summable.

is finite if |r| > 2.

Therefore, the Fourier transform of r^-nx[n] converges for |r| > 2

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Condition For Existence of Fourier Transform Question 8:

For the given signal f(t), what is the amplitude of Fourier transform of f(t)?

Answer (Detailed Solution Below)

Option 2 : 150

we know that Fourier transform of pulse is a sampling function

If F(ω) is the Fourier transform, then

A → Amplitude

τ → pulse width

Amplitude of sampling function = Area of pulse in time domain

= 10 × {10 - (- 5)}

= 150

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Condition For Existence of Fourier Transform MCQ Quiz - Objective Question with Answer for Condition For Existence of Fourier Transform - Download Free PDF

Latest Condition For Existence of Fourier Transform MCQ Objective Questions

Condition For Existence of Fourier Transform Question 1:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 1 Detailed Solution

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Condition For Existence of Fourier Transform Question 2:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 2 Detailed Solution

Top Condition For Existence of Fourier Transform MCQ Objective Questions

Condition For Existence of Fourier Transform Question 3

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 3 Detailed Solution

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Condition For Existence of Fourier Transform Question 4:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 4 Detailed Solution

Condition For Existence of Fourier Transform Question 5:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 5 Detailed Solution

Concept: Fourier Transform Symmetry Property
If a time-domain function $f (t)$ is:

Real: It has no imaginary part

Even: $f (t) = f (- t)$

Then it's Fourier Transform $F (ω)$ will be:

Purely real

Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Condition For Existence of Fourier Transform Question 6:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 6 Detailed Solution

Condition For Existence of Fourier Transform Question 7:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 7 Detailed Solution

Condition For Existence of Fourier Transform Question 8:

Answer (Detailed Solution Below)

Condition For Existence of Fourier Transform Question 8 Detailed Solution