37 lines
2.7 KiB
TeX
37 lines
2.7 KiB
TeX
\contentsline {chapter}{\numberline {1}Discrete Time Signals}{3}{chapter.1}%
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\contentsline {section}{\numberline {1.1}Uniform Sampling}{3}{section.1.1}%
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\contentsline {section}{\numberline {1.2}Characterizing Discrete Signals in the Time Domain}{5}{section.1.2}%
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\contentsline {section}{\numberline {1.3}The Norm of a Discrete Signal}{6}{section.1.3}%
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\contentsline {subsection}{\numberline {1.3.1}Geometric Series}{8}{subsection.1.3.1}%
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\contentsline {section}{\numberline {1.4}Elementary Operations on Signals}{9}{section.1.4}%
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\contentsline {chapter}{\numberline {2}Discrete Systems}{11}{chapter.2}%
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\contentsline {section}{\numberline {2.1}Properties of Systems}{11}{section.2.1}%
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\contentsline {subsection}{\numberline {2.1.1}Linearity}{11}{subsection.2.1.1}%
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\contentsline {subsubsection}{Homogeneity}{11}{section*.2}%
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\contentsline {subsubsection}{Superposition}{11}{section*.3}%
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\contentsline {subsection}{\numberline {2.1.2}Time Invarience}{11}{subsection.2.1.2}%
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\contentsline {subsection}{\numberline {2.1.3}Causality}{11}{subsection.2.1.3}%
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\contentsline {subsection}{\numberline {2.1.4}Bounded Input, Bounded Output (BIBO) Stability}{12}{subsection.2.1.4}%
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\contentsline {subsubsection}{Homogeneity}{12}{section*.4}%
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\contentsline {subsubsection}{Superposition}{12}{section*.5}%
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\contentsline {subsubsection}{Time Invariance}{12}{section*.6}%
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\contentsline {subsubsection}{Causality}{12}{section*.7}%
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\contentsline {subsubsection}{BIBO Stability}{12}{section*.8}%
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\contentsline {section}{\numberline {2.2}LTI Systems}{12}{section.2.2}%
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\contentsline {paragraph}{Properties of the Discrete LTI Systems}{12}{section*.9}%
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\contentsline {subsubsection}{The Integral Test}{13}{section*.10}%
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\contentsline {subsubsection}{Convolution}{13}{section*.11}%
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\contentsline {section}{\numberline {2.3}Periodicity}{13}{section.2.3}%
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\contentsline {section}{\numberline {2.4}Energy and Power}{14}{section.2.4}%
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\contentsline {subsection}{\numberline {2.4.1}Energy}{14}{subsection.2.4.1}%
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\contentsline {subsection}{\numberline {2.4.2}Power}{14}{subsection.2.4.2}%
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\contentsline {chapter}{\numberline {3}}{16}{chapter.3}%
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\contentsline {section}{\numberline {3.1}The Discrete Time Fourier Transform}{16}{section.3.1}%
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\contentsline {subsection}{\numberline {3.1.1}Derivation of the Discrete Time Fourier Transform}{16}{subsection.3.1.1}%
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\contentsline {subsection}{\numberline {3.1.2}Properties of the Discrete Time Fourier Transform}{17}{subsection.3.1.2}%
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\contentsline {subsection}{\numberline {3.1.3}Special Cases}{18}{subsection.3.1.3}%
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\contentsline {chapter}{\numberline {4}The Z-Transform}{19}{chapter.4}%
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\contentsline {section}{\numberline {4.1}Z Transform Transfer Functions}{20}{section.4.1}%
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\contentsline {section}{\numberline {4.2}The Inverse Z-Transform}{22}{section.4.2}%
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\contentsfinish
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