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Fourier series representation of discrete-time periodical signal

Fourier series representation of discrete-time periodical signal. Periodic signal. for all t. Fourier series representation of discrete-time periodical signal. Periodic signal. for all t. Fourier series representation of discrete-time periodical signal. Periodic signal. for all t.

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Fourier series representation of discrete-time periodical signal

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  1. Fourier series representation of discrete-time periodical signal Periodic signal for all t

  2. Fourier series representation of discrete-time periodical signal Periodic signal for all t

  3. Fourier series representation of discrete-time periodical signal Periodic signal for all t

  4. Example #1

  5. Example #2

  6. Example #2 N = 40 clear; clf; N = 40; omg0 = 2*pi/N; N1 = 2; x(1:N)=0; x(N/2-N1:N/2+N1) = 1; stem(x); m = -N/2+1:1:N/2; for k = -N/2+1:N/2 a(k+N/2) = 0; for n = 1:length(x) a(k+N/2) = a(k+N/2) + x(n)*exp(-j*k*omg0*(n-N/2)); end a(k+N/2) = a(k+N/2)/N; end figure(2) stem(m, real(a)); zoom on;

  7. Properties of discrete-time Fourier series (1) Linearity

  8. (2) Time shifting (3) Time reversal

  9. (4) Time scaling (5) multiplication

  10. (6) Conjugation and conjugate symmetry Real signal Even Real & Even

  11. (7) Parseval’s relation

  12. (8) Time difference (9) Running sum

  13. Example N = 4 [1, 2, 2, 1] [1, 1, 1, 1]

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