1. ADC AND DAC Sub-topics: Analog-to-Digital Converter -. Sampling
-. Quantizing
-. Coding
Digital-to-Analog Converter
-. Teknik Sample and Hold.
-. Teknik First-Order Hold
-. Teknik Linear Interpolation with Delay

2. Analog-to-Digital Converter
Most signals are analog
e.g. speech, biological signals, seismic signals, radar signals, sonar signals, etc.
ADC is applied to process analog signals by digital means
ADC has a three-step process
Sampling
Quantization
Coding
Sampler
Quantizer
Coder
A/D Converter
Xa(t)
X(n)
Xq(n)
01011 …
Analog Signal
Discrete-Time
Signal
Quantized
Digital Sinyal

3. Sampling X(n) = xa(nT); -∞< n < ∞ t = nT = n/Fs
Fs = Sampling rate
T = Sampling period

4. Continuous-Time Signals Discrete-Time Signals
Relationship Among Frequency Variables
Continuous-Time Signals
Discrete-Time Signals
Ω = 2F
 = 2f
(radians/sec) Hz
(radians/sample) (cycles/sample)
 = ΩT, f = F/Fs
-    
Ω = /T, F = f ∙ Fs
-½  f  ½
-∞ < Ω < ∞
-π  Ω  π
-∞ < F < ∞
-Fs/2  F  Fs/2

5. Sampling Theorem
If the highest freq. contained in an analog signal xa(t) is Fmax = B and the signal is sampled at a rate Fs > 2 Fmax  2B, then xa(t) can be exactly recovered from its sample values using the interpolation function
g(t) = (sin 2Bt)/(2Bt)

6. Aliasing effect in sampling process
If x1(n) and x2(n) have the same output, i.e. sampling of high freq. analog signal is the same as sampling of low freq. analog signal

7. Signal x(t) must a bandlimited signal
Therefore to solve the aliasing problem, sampling process should meet 2 requirements:
Signal x(t) must a bandlimited signal
The sampling rate fs must be min. 2fmax, i.e. fs  2 fmax or T  1/(2 fmax)
Spectrum of Bandlimited Signal

8. NYQUIST RATE Minimum sampling rate to avoid aliasing problem
fs = 2 fmax -> Nyquist rate
fs/2 is Nyquist frequency or folding frequency or cutoff frequency
[-fs/2, fs/2] = Nyquist Interval
Antialiasing Prefilter

9. Aplikasi fmax fs Sampling Rate of DSP Applications Geophysical 500 Hz
1 kHz
Biomedical
2 kHz
Mechanical
4 kHz
Speech
8 kHz
Audio
20 kHz
40 kHz
Video
4 MHz
8 MHz

10. Quantizing
Quantization sample XQ(nT) that is B bits, has quantization levels 2B
R = Range
L=2B = quantization level
Q = the width between quantization level

11. The difference between the quantized value and the actual sample value
Quantization error:
The difference between the quantized value and the actual sample value
eq(n) = xq(n) – x(n)
To eliminate the excess digits in quantization process, there are two techniques:
Truncation
Rounding: emax=Q/2

12. Coding To assign a unique binary number to each quantization level
For L levels, at least L different binary numbers are required
With a word length of b bits, 2b different binary numbers is created
Therefore blog2L
If word length is B+1 bit, therefore binary code combination is 2B+1, is equivalent to B+1log2L.
Binary code is 012 … B with sequence as
-   … + b . 2-b
0 is the MSB (Most Significant Bit) and b is the LSB (Least Significant Bit)

13. Digital-to-Analog Converter
Sample and Hold Technique
First-Order Hold Technique
Linear Interpolation with Delay Technique

14. Sample and Hold Technique
Digital
Input
Signal
Digital-to-analog converter
Sample and Hold
Lowpass smoothing filter
Analog output

15. First-order-Hold

16. Linear Interpolation with Delay technique