16 362 Signal and System I The response
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16. 362 Signal and System I • The response of system to complex exponentials z - transform
16. 362 Signal and System I • The response of system to complex exponentials Laplace transform
16. 362 Signal and System I • The response of system to complex exponentials
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal Periodic signal e. g. for all t
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal Periodic signal for all t k is an integer Fourier series form a complete and orthogonal bases Complete: no other basis is needed. Orthogonal: Kronecker Delta Orthogonal:
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal Periodic signal for all t k is an integer
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal Periodic signal for all t k is an integer e. g.
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal 0
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal 0
16. 362 Signal and System I • Fourier series representation of continuous-time periodical signal 0
16. 362 Signal and System I • The response of system to complex exponentials Band limited channel Bandwidth
16. 362 Signal and System I • The response of system to complex exponentials Band limited channel Bandwidth Matlab code clear; clf; T = 1; T 1 = 0. 2; omg 0 = 2*pi/T; N = 10; for k = -N: 1: N x(k+N+1) = k; if k==0 a(N+1) = 2*T 1/T; else a(k+N+1) = sin(k. *omg 0. *T 1). /(k. *pi); end stem(x, a); zoom on; t = -2: 0. 001: 2; for m =1: length(t) yt(m) = 0; for k = -N: 1: N yk = a(k+N+1)*exp(j*k*omg 0. *t(m)); yt(m) = yt(m) + yk; end figure(2) plot(t, abs(yt)); zoom on;
