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The response of system to complex exponentials

The response of system to complex exponentials. z - transform. The response of system to complex exponentials. Laplace transform. The response of system to complex exponentials. Fourier series representation of continuous-time periodical signal. Periodic signal. for all t. e.g.

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The response of system to complex exponentials

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  1. The response of system to complex exponentials z - transform

  2. The response of system to complex exponentials Laplace transform

  3. The response of system to complex exponentials

  4. Fourier series representation of continuous-time periodical signal Periodic signal for all t e.g.

  5. 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. Kronecker Delta Orthogonal: Orthogonal:

  6. Fourier series representation of continuous-time periodical signal Periodic signal for all t k is an integer

  7. Fourier series representation of continuous-time periodical signal Periodic signal for all t k is an integer e.g.

  8. Fourier series representation of continuous-time periodical signal 0

  9. Fourier series representation of continuous-time periodical signal 0

  10. Fourier series representation of continuous-time periodical signal 0

  11. The response of system to complex exponentials Band limited channel Bandwidth Bandwidth

  12. The response of system to complex exponentials Matlab code Band limited channel clear; clf; T = 1; T1 = 0.2; omg0 = 2*pi/T; N = 10; for k = -N:1:N x(k+N+1) = k; if k==0 a(N+1) = 2*T1/T; else a(k+N+1) = sin(k.*omg0.*T1)./(k.*pi); end 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*omg0.*t(m)); yt(m) = yt(m) + yk; end end figure(2) plot(t,abs(yt)); zoom on; Bandwidth

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