Digital signal processing: Difference between revisions
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=== Input Sampling and Quantisation Considerations ===
When selecting an ADC (Analog to Digital Converter), there are two main dimensions to consider.
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The first thing you need to consider is what is the bandwidth of the signal you wish to process on the input. For example, if you are processing audio signals, what sort of quality are you satisfied with? For telephony quality audio, for example, the input signal is band-limited to about 4 kHz, where the economics of [https://en.wikipedia.org/wiki/Frequency-division_multiplexing#Group_and_supergroup higher-level grouping and super-grouping of FDM channels] result in a compromise where any frequency components above 4 kHz are redundant and all the necessary speech information can be represented sufficiently clearly below that threshold. For CD quality audio, the bandwidth is extended out beyond 20 kHz, as being better than the average healthy human's auditory bandwidth.
One of the features of sampled signals is the idea of [https://en.wikipedia.org/wiki/Aliasing aliasing]. This is a form of distortion where higher frequency components, when sampled, appear "folded" (in the frequency domain) into lower frequency artefacts. In order to minimise this distortion the designer has to decide the effective bandwidth of their system and enforce it. That is done in two ways. The first is to place a low-pass filter on the input signal, commonly known as an anti-aliasing filter, and the second is to select the sampling frequency correctly. This is done by calculating the [https://en.wikipedia.org/wiki/Nyquist_rate Nyquist Rate], which is twice the highest frequency component required in the input signal.
So, for CD-quality audio, the standard sample rate is 44.1 kHz. This means that the [https://en.wikipedia.org/wiki/Nyquist_frequency Nyquist Frequency] (the upper limit for input frequency components that don't produce aliasing effects) is 22.05 kHz. Since the upper threshold for a normal adult with healthy hearing tops out at around 15 kHz, this means that an economical linear anti-aliasing filter can be produced to eliminate sufficient aliasing components for good listening quality.
Therefore, the design goals for any chosen ADC would appear to be very simple - maximise the sample rate and the number of bits and you can't go wrong. But ...
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Of course, having seen how easy it is to design a simple quantiser, it should be possible to see that, given 10- or 12-bits to play with, a more complex quantiser, supporting portamento and microtonal scale mappings, could be built without incurring any significant additional hardware cost.
=== Output stage design ===
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