lecture2

# lecture2 - &amp;amp;lt;-----------&amp;amp;gt; Discrete...

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Lecture Outline Fourier Analysis – A Review Reading: Sections 2.1 and 2.2 of Principles. Focus on 2.2 Material covered: 1. Frequencies. What are they? Why focus on frequency? Telecom real estate Example: Transform of a rectangular function: Richness in frequency (broadband) allows signal to change rapidly, i.e. higher data rate. Consider a shorter baud/symbol of a rectangular function: Ease of moving signals in frequency by modulation.

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2. Fourier Series versus Fourier Transforms Fourier series pair: (For discrete signals) Fourier transform pair: (For continuous signals) Signals in time: Are they periodic (time limited)? Are they discrete? Signals in frequency: Are they discrete? Are they bandlimited? Time Domain Frequency Domain Discrete & periodic

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Unformatted text preview: &lt;-----------&gt; Discrete &amp; bandlimited Discrete &amp; aperiodic &lt;-----------&gt; Continuous &amp; bandlimited Continuous &amp; periodic &lt;-----------&gt; Discrete &amp; infinite band Continuous &amp; aperiodic &lt;-----------&gt; Continuous &amp; infinite band 3. Short Review of Fourier Transforms Basic Functions: Laplace Transforms: Delta function: Complex exponential functions: Sinusoidal functions: Rectangular and Sinc Functions Elementary identities (should be remembered): 4. Basic Operations: Linearity Duality Shift in time domain Scaling Convolution Modulation Parsevals theorem Differentiation Differentiation in frequency domain Integration Zeroes Signal multiplication...
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## lecture2 - &amp;amp;lt;-----------&amp;amp;gt; Discrete...

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