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Convergence of the Fourier Series Used in Example 2.3 (and why analysis of the harmonics is important in communication systems)
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Let’s see how the stairstep signal of Example 2.3 converges as we add more harmonics to its Fourier Series summation
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Summation of dc term plus first five harmonics
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Summation of dc term plus first ten harmonics
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Summation of dc term plus first fifteen harmonics
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Summation of dc term plus first twenty-five harmonics
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Summation of dc term plus all harmonics
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Let’s pass the stairstep function from Example 2.3 through channels with various bandwidths and evaluate the distortion in the received signal.
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The importance of analyzing harmonics in communication systems
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Channel with1 Hz bandwidth
Channel with 1 Hz bandwidth passes the first five harmonics
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Channel with2 Hz bandwidth
Channel with 2 Hz bandwidth passes the first ten harmonics
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Channel with3 Hz bandwidth
Channel with 3 Hz bandwidth passes the first fifteen harmonics
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Channel with5 Hz bandwidth
Channel with 5 Hz bandwidth passes the first twenty-five harmonics
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Channel with infinite bandwidth passes all harmonics
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Channel withinfinite bandwidth
For the stairstep function, we now see how channel bandwidth and accuracy of the received signal are related.