Multiplexing and more More bandwidth to carry information at a higher carrier

Multiplexing and more more bandwidth to carry

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Multiplexing, and more… More bandwidth to carry information at a higher carrier frequency Transmit different signals simultaneously (frequency division multiplexing, FDM) Filter design 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 19
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Complex Exponential Carrier 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 20 As we will see later, knowing the phase of the carrier signal is important for demodulation, and that is why we explicitly express it in the notation.
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Spectrum of the Modulation Step 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 21
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Demodulation Step 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 22
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Implementation using Only Real Signals 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 23
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Design a Bandpass Filter using Exponential Carrier Modulation 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 24 passband ¾ We wish to extract only the portion of the signal fallen within the red window (in frequency domain) ¾ Challenge: Sometimes difficult to design bandpass filter given arbitrary specification Could be difficult to adjust the filter if we change the filter requirement It is often easier to build a fixed filter (fixed center frequency, passband, etc.)
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Design a Bandpass Filter using Exponential Carrier Modulation 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 25 passband
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Frequency Response of the Equivalent Filter ¾ Given the original input x ( t ) is real, is the filtered signal f ( t ) real? Since the spectrum is not conjugate symmetric, the corresponding signal is not real A simple remedy is to extract the real part of the output Equivalently, this corresponds to taking the even part of the spectrum of the complex signal f ( t ). 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 26 Equivalent filter for f ( t ) Equivalent filter for Re{ f ( t )}
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Sinusoidal Carrier 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 27 Multiplication with a sinusoidal signal in the time domain is equivalent to move the spectrum to the right and to the left in the frequency domain.
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Sinusoidal Carrier To extract the original signal, we need to apply a lowpass filter Some simple algebra: 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 28
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Implementation 27-Mar-19 EIE3001 Sig & Sys, Spring 2019 29 The cutoff frequency w of the lowpass filter need to chosen to retain spectrum of the original signal while rejecting the portion that is moved to the high frequency.
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What If There Is a Phase Error? ¾ We have assumed that the demodulator perfectly knows the phase of the modulator How?
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