3. Basic Concepts
Analog To Digital Conversion
involves quantization of Input
and resulting a sequence of
digital values (called samples
and process is call Sampling)
A continuous-time and
continuous-amplitude analog
signal to a discrete-time and
discrete-amplitude digital signal.
Time
Amplitue
Analog signal
4. Sampling
The rate at which new digital values are sampled from the analog
signal is called the sampling rate or sampling frequency
A continuously varying band limited signal can be sampled and
then the original signal can be exactly reproduced from the
discrete-time values by an interpolation formula.
The accuracy is limited by quantization error.
Reproduction is only possible if the sampling rate is higher than
twice the highest frequency of the signal. This is Shannon-Nyquist
sampling theorem.
5. Quantization,
Is the process of mapping input
values to a smaller set and rounding
values to some unit of precision.
A device or algorithmic function that
performs quantization is called
a quantizer.
6. Quantization Error
The round-off error introduced by quantization is referred to as quantization
error.
Quantization Error increases the noise floor. In the example below the
spectrum of 6 bit vs 8 bit quantizer is compared and you will notice that the
6 bit quantizer noise floor is 12 db higher(-68db vs -80 db)
Note: Hence it is always better to Use Highest number of Bits possible Quantizer
As the number of levels is decreased, more square edges are introduced,
and higher frequency quantization noise appears.
7. Aliasing
Aliasing occurs whenever the use of discrete
elements to capture or produce a continuous
signal causes frequency ambiguity.
In the Example here.
Blue wave is low Frequency signal and Red
wave is High Frequency Signal
Black dots are the sampled points (we are using
low sampling frequency).
Using the sampling frequency for the Red (high
frequency) signal in A2D conversion causes
aliasing.
As During reconstruction ( Digital To analog
conversion) We will not be able to reproduce
the High Frequency at all.
8. Resolution
The resolution of the converter indicates the number of discrete values it
can produce over the range of analog values.
The resolution determines the magnitude of the quantization error
The maximum possible average signal to noise ratio for an ideal ADC.
The binary is called bits.
The number of discrete values available, or "levels", is power of two.
For Example if an analog signal
Full scale measurement range = -5 to 5 volts
ADC resolution is 8 bits
That is 28 = 256 quantization levels (codes)
ADC voltage resolution, Q = (10 V − 0 V) / 256 = 10 V / 256 ≈ 0.039 V ≈ 39 mV.
