Question

(a) The MATLAB command trapz(x,y) computes the integral of the function y with respect to the 'variable of integration' r, i.e J ydr. Use MATLAB help to understand how trapz works. (b) Consider r(t) 1 for -1 t1, and r(t) 0 otherwise. Use the trapz command to compute and plot the Fourier transform of r (t). Denote this by X (jw). compute and plot the inverse Fourier transform of 2πX(jw). in part b)? Why, or why not? This is called the duality property (c) Now consider the X(ju) of part b). Use the trapz command to (d) Is the result you got in part c) above consistent with r(t) defined of the Fourier transform (Section 4.3.6).

Answer 1

"1 trapz (x,y) computers the integral of the fuction y with respect to the variable of integration""x"" ie integral y dx Q = trapz(x,y) integrates y with spacing increment x trapz operater on the first dimension of y whose size does not eqaul 1 length (x) must be equal to the size of the dimension if x in scalar then trapz(x,y) in equivalent to x * trapz(x,y) x = 0: pi/100: pi y = sin x Q = trapz = (x,y) these integrate function values contained in y usoing trap z the Q c = 1.998 when the spacing between points is constant but not equal to 1 you can multyply by the spacing value in this case pi/100 * trapz(y)_ the answer is the same if you pan value directly to the function trapz(x,y) trapz perform numerical integration Via the trapezodial method this methodapproximation the integration over an integral by breaking the area down into "