Digital signal processing: Difference between revisions
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(Quantisation noise discussion - first draft) |
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=== Sampling and Quantisation Considerations === |
=== Sampling and Quantisation Considerations === |
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When selecting an ADC (Analog to Digital Converter), there are two main dimensions to consider. |
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The first is the resolution of your conversion - the number of bits you want to represent. The choice here will affect the amount of quantisation noise introduced into your signal. For example, let's assume you have a bipolar input signal that varies between -1V and 1V. With an 8-bit converter, that means that a range of width 2V is represented by values of anything from -127 to 127 (or 255 steps). That means that the input voltage represented by 1 bit of the converted signal is equivalent to 7.84 mV. Assuming a perfectly linear, this means that when an input signal |
The first is the resolution of your conversion - the number of bits you want to represent. The choice here will affect the amount of [https://en.wikipedia.org/wiki/Quantization_(signal_processing) quantisation] noise introduced into your signal. For example, let's assume you have a bipolar input signal that varies between -1V and 1V. With an 8-bit converter, that means that a range of width 2V is represented by values of anything from -127 to 127 (or 255 steps). That means that the input voltage represented by 1 bit of the converted signal is equivalent to 7.84 mV. Assuming a perfectly linear converter, where the quantisation error is uniformly distributed between -1/2 LSB (Least Significant Bit) and 1/2 LSB, this means that when an input signal increases from one sample to the next by 3.92 mV or less, its digital representation will not appear to change, whereas if it moves 3.93 mV or more, it will change by 1 bit (and similarly for decreases). This can be considered to be like a rounding error that gets injected, as noise, into the input stream as a consequence of conversion. |
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For an "ideal" ADC, the signal to quantisation noise ratio (SQNR) is calculated as: |
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'''SQNR = 20 log<sub>10</sub>(2<sup>Q</sup>)''' dB |
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where Q is the number of quantisation bits. |
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[[File:Sampling-illustration.png|frameless|1000x800px]] |
[[File:Sampling-illustration.png|frameless|1000x800px]] |
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