Signals and Systems - Electrical Engineering

604 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems FIGURE 10.9 Computation of Fourier series coefficien ...

10.3 Fourier Series of Discrete-Time Periodic Signals 605 then according to the eigenfunction property of LTI systems, the outpu ...

606 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems corresponding outputsy 1 [n],y 2 [n], andy 3 [n]. Th ...

10.3 Fourier Series of Discrete-Time Periodic Signals 607 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Example 10.16---Filtering of a ...

608 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems nExample 10.17 To visualize the difference between a ...

10.3 Fourier Series of Discrete-Time Periodic Signals 609 For the circular representation ofx[n−1] we shift the termx[0] from th ...

610 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems Remarks n As before, multiplication in one domain ca ...

10.3 Fourier Series of Discrete-Time Periodic Signals 611 FIGURE 10.12 Periodic convolution of the Fourier series coefficientsX[ ...

612 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems nExample 10.19 A periodic signalx 1 [n] of periodN=4 ...

10.3 Fourier Series of Discrete-Time Periodic Signals 613 (a) 01 1 2345 n x[n] ...... (b) 0 1 1 2 2 3 n v[n] 1 ...... 1 0, 0, 1, ...

614 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems which coincides with theZ[k] obtained by the periodi ...

10.4 Discrete Fourier Transform 615 coefficients can be calculated using the Z-transform as X ̃[k]=^1 N Z[ ̃x 1 [n]] ∣ ∣ z=ejkω^ ...

616 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems 10.4.2 DFT of Aperiodic Discrete-Time Signals We obt ...

10.4 Discrete Fourier Transform 617 Therefore, by the linearity of the DFT, we have the DFT ofy[n] is Y[k]= ∑ m DFT(ym[n])= ∑ m ...

618 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems above sequence and obtainLvalues corresponding to th ...

10.4 Discrete Fourier Transform 619 n On the other hand, the harmonic frequencies of a periodic signal of periodNare fixed to 2 ...

620 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems from 0 to 2π(N− 1 )/Nrad (notice that this value is ...

10.4 Discrete Fourier Transform 621 FIGURE 10.14 Computation of the FFT of (a) a causal signal and (b) a noncausal signal. Notic ...

622 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems where fs= 1 /Ts is the sampling rate given in sample ...

10.4 Discrete Fourier Transform 623 FIGURE 10.15 Computation of the FFT of a periodic signal using (a) 4 and (b) 12 periods to i ...