1. Consider the Gaussian function ...Using Eq.(21 ) show that ....
Plot ...for a = 2 and σ = 1.0, 5.0 and 10.0. Hence show
that ... (46)which is the Gaussian representation of the delta
function. Get solution
2. Consider the ramp function defined by the following equation ... (47)Show that ..., where ...is the rectangle function defined by Eq.(4).Taking the limit ...show that ...where ...is the unit step function. Thus we get the following important result:If a function has a discontinuity of ...then its derivative (at x = a) is .... Get solution
3. Consider the symmetric function...Show that... Get solution
4. Consider the function ... Calculate its Fourier spectrum ...and evaluate approximately ... Evaluate f(t)using the expression for F(ω). Get solution
5. Calculate the Fourier transform of the following functions(a) ...(b) ...In each case make an estimate of ...and interpret physically. Get solution
6. Show that the convolution of two Gaussian functions is another Gaussian function:... Get solution
2. Consider the ramp function defined by the following equation ... (47)Show that ..., where ...is the rectangle function defined by Eq.(4).Taking the limit ...show that ...where ...is the unit step function. Thus we get the following important result:If a function has a discontinuity of ...then its derivative (at x = a) is .... Get solution
3. Consider the symmetric function...Show that... Get solution
4. Consider the function ... Calculate its Fourier spectrum ...and evaluate approximately ... Evaluate f(t)using the expression for F(ω). Get solution
5. Calculate the Fourier transform of the following functions(a) ...(b) ...In each case make an estimate of ...and interpret physically. Get solution
6. Show that the convolution of two Gaussian functions is another Gaussian function:... Get solution
