1. Chapter 2 Signal Sampling and Quantization

2. Sampling of Continuous Signals
The ADC unit samples an analog signal, quantizes the sampled signal, and encodes the quantized signal level to a digital signal

4. Sampling theorem:
An analog signal can be in theory perfectly recovered as long as the sampling rate is at least twice larger than the highest frequency of the analog signal to be sampled
Examples:
To sample a speech signal containing frequencies up to 4 kHz, the minimum sampling rate is chosen to be at least 8 kHz, or 8,000 samples per second
For an audio signal with frequencies up to 20 kHz, sample the audio signal at the sampling rate of at least 40,000 samples per second, or 40 kHz

5. Sampling condition is satisfied.
fmax=40Hz, fs=100 Hz
Undersampling:
Signal aliasing would occur when the sampling condition is not satisfied.
fmax=90 Hz, fs=100 Hz

6. View of sampling in frequency domain

8. 1. Sampling theorem establishes a minimum sampling rate for sampling a given band-limited analog signal with the highest frequency component of fmax
If the sampling condition is satisfied, then the analog signal can be recovered via its sampled values
2. The half of the sampling frequency = Nyquist frequency (Nyquist limit) = folding frequency

9. Signal Reconstruction

10. Anti-aliasing Lowpass Filter

11. Anti-aliasing filter (Butterworth type)

12. Distortion due to the hold circuit and
anti-image filter

13. ADC, DAC, and Quantization

14. 3-bit unipolar quantizer

16. 3-bit bipolar quantizer

18. DAC

19. Quantization error:
Quantization bound:
Signal to noise power ratio:

20. Example 1: a 4-bit bipolar quantizer

21. Example 2: Speech, a 4-bit bipolar quantizer