Notions on Digital Signals
Digital signals are sequences of numbers. The index in the sequence acts as time. Digital signals may be purely synthetic (calculated algorithmically) or result from the conversion of analog signals by Analog/Digital converters. Digital signals possess se
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Notions on Digital Signals
Digital signals are sequences of numbers. The index in the sequence acts as the time. We say that time is discrete (or discontinuous). Digital signals may be purely synthetic (calculated algorithmically) or result from the conversion of analog signals by Analog/Digital converters (abbreviated ADC). Digital signals have nowadays become prominent, driven by continuing advances in microelectronics (Moore’s Law, which has been verified for over thirty years, states that the ability to integrate electronic circuits doubles every 18 months). Digital signals possess several advantages compared to analog signals: First, their treatment is more flexible. Processes on digital signals can be achieved that are impossible for analog signals. For example, one can easily change the parameters in a rule of calculation to improve filtering. Second, the signal-to-noise ratio of digital signals can be large. For example, it can be maintained intact during propagation on a transmission channel unlike the situation for an analog signal that is always negatively affected during propagation. Indeed, the use of error-correcting codes allows finding back exactly the original digital signal at the output of the transmission channel. In this chapter, we first give some idea of the analog to digital signal conversion and the error committed during this operation conditioned by the limited resolution of the converter. We show with a simple example the necessity of using a sampling frequency of the analog signal that is sufficiently high so that rapid variations of a signal can be correctly rendered in the digital signal. We also show with the simple example of digitizing a sine function how a frequency component higher than the sampling frequency can have the same digital image as a low-frequency signal caused by a stroboscopic effect (aliasing). These facts will be demonstrated mathematically in Chap. 19. We give at the end of this chapter, the expression of simple digital signals. We emphasize the fact that they appear as weighted sequences of Kronecker unit pulses.
© Springer International Publishing Switzerland 2016 F. Cohen Tenoudji, Analog and Digital Signal Analysis, Modern Acoustics and Signal Processing, DOI 10.1007/978-3-319-42382-1_13
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Notions on Digital Signals
Analog to Digital Conversion
An Analog to Digital Converter (ADC) has two main characteristics: – Its sampling frequency fe which is the number of conversions per second. – Its resolution (given by the number of possible levels at the converter output). While the values of the signal to be sampled are real numbers, their coding by the converter is in integer values. The conversion operation requires the comparison of the value of the signal to different reference levels values. It requires a certain time which generally increases with the number of levels of comparison. It is conditioned by the speed of electronic circuits that are used. Increasing the accuracy of the conversion may require a change of technology and the decreas
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