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This lecture covers the Fourier representation for discrete-time signals, including Fourier series for periodic discrete signals and Fourier Transform for nonperiodic discrete signals. It also discusses the Sampling Theorem and its application in signal reconstruction.
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Lecture #05 Fourier representation for discrete-time signals And Sampling Theorem signals & systems
Fourier series for periodic discrete signals Fourier Transform for nonperiodic discrete signals signals & systems
Example 3.2 signals & systems
Example 3.5 Inverse DTFS signals & systems
Example 3.17 Find DTFT of the sequence signals & systems
Example 3.18 Find DTFT of the sequence signals & systems
Example 3.17 Find DTFT of a unit impulse spectrum Example 3.18 Find Inverse DTFT of a unit impulse spectrum signals & systems
Sampling • Sampling is a process of converting a signal into a numeric sequence (a function of discrete time or space). • The sampling theorem states that exact reconstruction of a continuous time baseband signal from its samples is possible if the signal is bandlimited and the sample frequency is greater than twice the signal bandwidth. signals & systems
Take Fourier transform Fourier transform For example signals & systems
Example 4.2 Fourier series of p(t) Fourier transform of p(t) signals & systems
(v) Frequency shifting modulation Fourier series Fourier Transform signals & systems
Case I: Case II: Aliasing signals & systems
Sampling theorem : Let represent a band-limited signal, so that for . If , where Is the sampling frequency, then is uniquely determined by its samples The minimum sampling frequency, Nyquist sampling rate. signals & systems
