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Proper and Under-Sampled Sinusoids in ADC to DAC Conversion

This document explores the characteristics and behaviors of properly sampled and under-sampled sinusoids at the input to an ADC (Analog-to-Digital Converter) and their subsequent output after passing through a DAC (Digital-to-Analog Converter). The study examines sampling frequencies represented as multiples and fractions of Fs, particularly focusing on the outputs from the DAC based on properly and under-sampled input signals. The analysis provides insights into the implications of sampling rates on signal reconstruction and data integrity.

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Proper and Under-Sampled Sinusoids in ADC to DAC Conversion

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  1. X( f ) f f f Fs/2 Fs Properly Sampled Sinusoid At Input to ADC Inside DAC -2Fs -Fs -Fs/2 Fs/2 Fs 2Fs Output of DAC Fs/2

  2. X( f ) f f f Under-Sampled Sinusoid At Input to ADC Fs/2 Fs Inside DAC -2Fs -Fs -Fs/2 Fs/2 Fs 2Fs Output of DAC Fs/2

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