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

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RRB JE ECE 22 Apr 2025 Shift 2 CBT 2 Official Paper
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  1. a purely real and odd function
  2. a purely imaginary and even function
  3. an imaginary and odd function
  4. a purely real and even function

Answer (Detailed Solution Below)

Option 4 : a purely real and even function
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Detailed Solution

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Concept: Fourier Transform Symmetry Property

If a time-domain function is:

  • Real: It has no imaginary part

  • Even: f(t) = f(-t)

Then it's  Fourier Transform will be:

  • Purely real

  • Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Let’s take: f(t) = cos(ω0​t)

  • It is real.

  • It is even, because

Fourier Transform of 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

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Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.What type of distortion occurs if a signal that contains frequency components up to 15 kHz is sampled using 20 kHz?
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Q6.A continuous-time signal x(t) is defined as : \(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\) The energy of signal x(t) is : 
Q7.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q8.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q9.Which one of the following is the correct relation ? (a > 0) 
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