261. The Fourier transform of a function x(t) is X(f).
     

     The Fourier transform of	dx(t)	will be—
     	dt

1. 1. dx(t)

      (df)

   
   
   

   2. j2πf X(f)

   
   
   

   3. jt X(t)

   
   
   

   4. x(f)

      if

   
   
   

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1. View Hint View Answer Discuss in Forum

   If x(t) ↔ X(jω)
   

   then	d	x(t) ↔ (jω) X(jω)
   	dt

   
   

   or	d	x(t) ↔ j2πf·X(f)
   	dt

   Correct Option: B

   If x(t) ↔ X(jω)
   

   then	d	x(t) ↔ (jω) X(jω)
   	dt

   
   

   or	d	x(t) ↔ j2πf·X(f)
   	dt

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262. The Fourier transform of a voltage signal x(t) is x(f). The unit of |X(f)| is—

1. 1. volt

   
   
   

   2. volt-sec

   
   
   

   3. volt/sec

   
   
   

   4. volt²

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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263. The spectral density of a real valued random process has—

1. 1. an even symmetry

   
   
   

   2. an odd symmetry

   
   
   

   3. a conjugate symmetry

   
   
   

   4. no symmetry

   
   
   

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1. View Hint View Answer Discuss in Forum

   The spectral density of a real valued random process has an even symmetry.

   Correct Option: A

   The spectral density of a real valued random process has an even symmetry.

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264. The probability density function of the envelope of narrow-band Gaussian noise is—

1. 1. Poisson

   
   
   

   2. Gaussian

   
   
   

   3. Rayleigh

   
   
   

   4. Rician

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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265. The z-transform F(z) of the function f(nT) = a^nT is—

1. 1. z

      z – aT

   
   
   

   2. z

      z + aT

   
   
   

   3. z

      z – a– T

   
   
   

   4. z

      z + a– T

   
   
   

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1. View Hint View Answer Discuss in Forum

   The z-transform of function f(n) is given by relation
   

   	∞
   z[f(n)] =	∑	f(n)·z– n
   	n = – ∞

   
   

   	∞
   z[f(nT)] =	∑	ant·z – n
   	n = – ∞

   
   = 1 + a^T z^{– 1} + a^2T z ^{– 2} + …
   

   =	1
   	1 – aT z– 1

   
   

   =	z
   	z – aT

   
   Hence, alternative (A) is the correct choice.

   Correct Option: A

   The z-transform of function f(n) is given by relation
   

   	∞
   z[f(n)] =	∑	f(n)·z– n
   	n = – ∞

   
   

   	∞
   z[f(nT)] =	∑	ant·z – n
   	n = – ∞

   
   = 1 + a^T z^{– 1} + a^2T z ^{– 2} + …
   

   =	1
   	1 – aT z– 1

   
   

   =	z
   	z – aT

   
   Hence, alternative (A) is the correct choice.

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