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Digital to Analogue Conversion

Digital to Analogue Conversion. Natural signals tend to be analogue Need to convert to digital. Sample and Hold. Analogue To digital converter. Sampling. Need to hold the signal steady for long enough to enable the A to D converter to generate an output.

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Digital to Analogue Conversion

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  1. Digital to Analogue Conversion • Natural signals tend to be analogue • Need to convert to digital

  2. Sample and Hold Analogue To digital converter Sampling • Need to hold the signal steady for long enough to enable the A to D converter to generate an output

  3. Quantization converts continuous value to a discrete (usually integer) value • Output value is rounded so accuracy lost • Maximum quantization error of ±0.5 lsb • Error is combined with signal as noise

  4. Quantization accuracy • Least significant bit determines accuracy. So for a 2 Volt peak to peak signal, an 8 bit converter can accurately represent multiples of 7.81mV but anything in between will be rounded

  5. Quantization error Error is at most ±1/2 an lsb, or ±3.905 mV for the 8 bit converter or ±15.25µV in the 16 bit case

  6. Quantization error • Relatively small signal changes are subject to severe quantization errors

  7. Quantization error creates steps • Steps create distortion which is visible in the frequency domain • Noise shown on dB scale as it is relatively small compared to the signal

  8. Sampling theory • Signal needs to be sampled at twice the speed of the fastest change to be captured • Shannon or the Nyquist sampling theorem, (authors of 1940s papers) • Theorem states that a continuous signal can be properly sampled, only if it does not contain frequency components above one-half of the sampling rate

  9. Correctly sampled signal • Signal frequency is 0.09 of the sample rate (i.e. sample rate is about 11x signal freq) • e.g. 90Hz signal sampled at 1kHz

  10. Sample rate still ok • Signal frequency is 0.31 of the sample rate (i.e. sample rate about 3x signal freq) • 3.2 samples / cycle but freq still preserved

  11. Improper Sampling • Signal frequency is 0.95 of the sample rate (i.e. sample rate only slightly higher than signal freq) • Only 1.05 samples per cycle. Produces a 0.05Hz alias signal which is mixed with the original

  12. Sidebands • Sampling a signal is effectively multiplication of signals in the time domain • Multiples of the sample frequency are produced as well as sum and difference frequencies (sidebands)

  13. No sampling no sidebands • Time domain to frequency domain of an analogue signal

  14. Sampled signal produces sidebands

  15. Incorrectly sampled signal • Breaching Nyquist causes aliasing with overlapping sidebands

  16. Simulated sampling • Using a sample rate of 1kHz, the frequency spectrum with noise was calculated from: • Then modified to illustrate aliasing by changing 300Hz signal to 800Hz:

  17. Correct sample rate

  18. Aliasing at 200Hz

  19. Anti-alias filter • Frequencies higher than those of interest (such as noise) need to be blocked before sampling. Use an analogue low pass filter

  20. Analogue Anti-alias Filter Sample and Hold Analogue to digital converter Digital to analogue converter Analogue Reconstruction Filter DSP DSP system • Low pass input filter removes F > 0.5F(S) • Reconstruction filter removes high frequency F(S) multiples

  21. Sound Blaster block diagram

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