Question

Find the complex Fourier integral transform (or Fourier transform, hat{f}(k) = 1/sqrt{2pi}int_{-infty}^{infty} f(x)e^{ikx},dx) of the following aperiodic time pulse g(t) = egin{cases}0 & t<0,\1 & 0le t< T,\0 & t> T,end{cases} and sketch the variation of the modulus of hat{g}(k) in Fourier space.

          Find the complex Fourier integral transform (or Fourier transform, hat{f}(k) = 1/sqrt{2pi}int_{-infty}^{infty} f(x)e^{ikx},dx) of the following aperiodic time pulse

g(t) = egin{cases}0 & t<0,\1 & 0le t< T,\0 & t> T,end{cases}

and sketch the variation of the modulus of hat{g}(k) in Fourier space.

Find the complex Fourier integral transform (or Fourier transform, hatf(k) = 1/sqrt2piint-infty^infty f(x)e^ikx,dx) of the following aperiodic time pulse

g(t) = egincases0 t<0, 0le t< T, t> T,endcases

and sketch the variation of the modulus of hatg(k) in Fourier space.

Added by Rachel B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/15/2023

Step 1

The function is defined as: V(t) = 0, for t < 0 V(t) = V_0, for 0 < t < T V(t) = 0, for t > T The Fourier transform of V(t) is given by: G(k) = \int_{-\infty}^{\infty} V(t) e^{-i k t} dt Since V(t) is non-zero only in the interval (0, T), we can rewrite the Show more…

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Find the complex Fourier integral transform (or Fourier transform; f̂(k) = 1/√(2π) ∫_{-∞}^{∞} f(x)e^{ikx} dx) of the following aperiodic time pulse (0 < t < T, v(t) = 0 for t < 0 and t > T), and sketch the variation of the modulus of ĝ(k) in Fourier space.