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**Fourier representation for discrete-time signals And Sampling Theorem**

Lecture #05 Fourier representation for discrete-time signals And Sampling Theorem meiling chen signals & systems

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**Fourier series for periodic discrete signals**

Fourier Transform for nonperiodic discrete signals meiling chen signals & systems

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Example 3.2 meiling chen signals & systems

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meiling chen signals & systems

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Example Inverse DTFS meiling chen signals & systems

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**Example 3.17 Find DTFT of the sequence**

meiling chen signals & systems

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meiling chen signals & systems

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**Example 3.18 Find DTFT of the sequence**

meiling chen signals & systems

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meiling chen signals & systems

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**Example 3.17 Find DTFT of a unit impulse spectrum**

Example Find Inverse DTFT of a unit impulse spectrum meiling chen signals & systems

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meiling chen signals & systems

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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. meiling chen signals & systems

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meiling chen signals & systems

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**Take Fourier transform**

For example meiling chen signals & systems

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**Fourier transform of p(t)**

Example 4.2 Fourier series of p(t) Fourier transform of p(t) meiling chen signals & systems

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**Fourier series Fourier Transform (v) Frequency shifting modulation**

meiling chen signals & systems

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Case I: Case II: Aliasing meiling chen signals & systems

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**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. meiling chen signals & systems

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meiling chen signals & systems

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