Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W.

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Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.1 Even and odd parts of a real causal sequence.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.2 Interpretation of the Hilbert transform as a periodic convolution.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.3 Even and odd parts of a periodically causal, real, periodic sequence of period N = 8.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.4 Illustration of decomposition of a one-sided Fourier transform. (Solid curves are real parts and dashed curves are imaginary parts.)

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.5 Impulse response of an ideal Hilbert transformer or 90-degree phase shifter.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.6 Block diagram representation of the creation of a complex sequence whose Fourier transform is one- sided.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.7 (a) Impulse response and (b) magnitude response of an FIR Hilbert transformer designed using the Kaiser window. (M = 18 and β = )

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.8 (a) Impulse response and (b) magnitude response of an FIR Hilbert transformer designed using the Kaiser window. (M = 17 and β = 2.44.)

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure 12.9 Block diagram representation of the allpass phase splitter method for the creation of a complex sequence whose Fourier transform is one-sided.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure Fourier transforms for representation of bandpass signals. (Solid curves are real parts and dashed curves are imaginary parts.) (Note that in parts (b) and (f) the functions j X i (e jω ) and j S i (e jω ) are plotted, where X i (e jω ) and S i (e jω ) are the Fourier transforms of x i [n] and s i [n], respectively.)

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure Block diagram representation of Eqs. (12.75a) and (12.76a) for obtaining a single-sideband signal.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure System for reduced-rate sampling of a real bandpass signal by decimation of the equivalent complex bandpass signal.

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure Example of reduced-rate sampling of a bandpass signal using the system of Figure (a) Fourier transform of continuous-time bandpass signal. (b) Fourier transform of sampled signal. (c) Fourier transform of complex bandpass discrete-time signal derived from the signal of part (a). (d) Fourier transform of decimated complex bandpass of part (c). (Solid curves are real parts and dashed curves are imaginary parts.)

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P12.18

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P12.19

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P12.20

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P12.26 System for obtaining y[n] from yr[n].

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P

Copyright ©2010, ©1999, ©1989 by Pearson Education, Inc. All rights reserved. Discrete-Time Signal Processing, Third Edition Alan V. Oppenheim Ronald W. Schafer Figure P