ADC AND DAC

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. A/D Converter Xa(t) Sampler X(n) Quantizer Coder Xq(n) 01011 … Analog Signal Discrete-Time Signal Quantized Signal Digital Sinyal 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

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

4. Relationship Among Frequency Variables

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. 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. Sampling Rate of DSP Applications

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. 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 -0 . 20 + 1 . 2-1 + 2 . 2-2 + … + 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. Lowpass smoothing filter Analog output Signal Sample and Hold Digital Input Signal Digital-to-analog converter • Sample and Hold Technique

15. First-order-Hold

16. Linear Interpolation with Delay technique