- Composition Fundamentals Of Problem 7 20pts Fourier Transform A Complete The Certification Process Of The Dirichlet 1 (125.87 KiB) Viewed 35 times
Composition fundamentals of PROBLEM 7 (20pts) (Fourier transform (a) Complete the certification Process of the dirichlet kernel. The impulse train (right side) with a period I is expressed as a linear Combination of sinusoidal function with an integer multiple of frequrcy 1/T as frequency. -nt Σ δ(t-nT)= Σ « Show that the linear coupling coefficient an is an = = a e 11=100 11=-00 ∞ 1 (b) Prove 8(t) = [e³²f¹ df elex do in the difichlet kernel equation = 2π 88 27 Obtained in this way by changing [8(1-nT) = 2 = to an integral equation with 1 jnt T -e T 11=-00 11=-00 the basic Period I as infinity. (c) Based on the above, explain the membership of Fourier transform and Inverse Fourier transform (See Lecture) Fourier transform X (jw)=√x(t)e¯jax dt 1 Inverse Fourier transform x(1) = x(j)edo 2π 00 (d) Find Fourier transform X(jw) of the Periodic function _x(t)= [ f(t-nT) k=-∞