2. Analog-to-digital Conversion and Digital-to-analog Conversion (with DSP) ES-3

3. A very simple (…too simple!) Digital-to-analog converter 8R 4R 2R R 8R V1V1 V2V2 V4V4 V8V8 V OUT

4. scitec.uwichill.edu.bb Analog Input A simple Analog-to-digital converter + -

5. scitec.uwichill.edu.bb Analog Input A simple Analog-to-digital converter + - 3.5v 0v 0 0 0 0 high 0 0 0 0 0 0 0 1 1v 0 0 0 0 0 0 1 0 2v 0 0 0 0 0 0 1 1 3v 0 0 0 0 0 1 0 0 4v low 0 0 0 0 0 0 1 1 3v 0 0 0 0 0 1 0 0 Improve accuracy: scale the DAC

6. Nyquist Sampling Rate The sampling of data must be at least twice the rate as the maximum frequency of the analog signal: f s >2f max V(t) Time, t Use a low pass filter with f c = f max to remove harmonics  sine

7. Nyquist Sampling Rate The sampling of data must be at least twice the rate as the maximum frequency of the analog signal : f s >2f max V(t) Time, t Aliasing

8. Digital Signal Processing

9. Running average of 10 pts

10. Digital Filtering Removing Noise and Interference from a Digital Signal Find the average of N points

11. sine + noise filtered noise FFT of a noisy sine wave and its digitally filtered signal

12. DSP Example

13. Simple Notch Filter to remove 60 Hz interference t (s) V in (n) f S = 1440 samples per second 1/60 s 60 Hz sine V out (n) = V in (n) + V in (n - f s / 2f notch ) = V in (n)+V in (n-12) V in (n) V in (n-12) This adds the sample that is 180 0 out of phase at 60 Hz

14. Matlab demo es3_60Hz.m