Digital Coding of Analog Signal

1. Digital Coding of Analog Signal Electronics Engineering Department, Sardar Vallabhbhai National Institute of Technology, Surat-395007. Prepared By: Amit Degada Teaching Assistant

2. Goal of Today’s lecture. • Something More about the practical Approach • Delta Modulation De-merits • SNR Calculation for DM • Comparison of DM, DPCM and PCM • Adaptive delta Modulation

3. Integrator • Integrator is nothing but a RC Low Pass filter.

4. Characteristic of Quantizer • Quantizer is 1 bit Quantizer. • Its simply a Voltage Comparator. If the Difference is positive increase the Voltage by step-size σ, Vice-Versa.

5. Noise in DM • The key to effective use of DM is proper selection of step size σ and sampling Freq/Sampling Time. • They must be chosen in a such a way that stair-case approximation is close to message signal. • We can know he max frequency at which the signal is changing

6. Noise in DM • To account fastest possible change we have to increase the sampling frequency as well as step size. • But Sampling Freq  Bandwidth & Larger the step Size  Quantization Error

7. Noise in DM • Ideally the slope of both Quantized signal and Message signal must match. • It requires that ………..(7) Suppose Hence, ………..(8) So ………..(9)

8. Noise in DM The maximum Amplitude that we can follow for message signal can be given by * ………..(10) Where, Rad * This equation is proved by de jagger. U may see, F. De. Jagger, “ Delta Modulation, a method of PCM transmission by 1 bit code”, Phillips Res. Rep. No 7 pp 442-466, 1952

9. Noise in DM Thus the maximum Amplitude that we can use without causing the slope overload can be found at frequency 800Hz. • Fortunately, Voice signal spectrum decays with frequency. • Decreases as 1/ω up to 2000 Hz and beyond that by 1/ω2 • Hence Single Integration up to 2000Hz and Double for Beyond it • Double Integrator Can be Built By 2 Cascade RC with time constant 1/200Pi (100 Hz to 2KHz) and 1/4000pi(>2KHz) respectively.

10. Noise in DM Slope overload The name slope overload comes due to quantized signals fails to follow the slop of message signal. The DM With Fixed step size is Linear Delta Modulation (LDM)

11. Noise in DM • What would happen if we keep the step size larger? This would results into considerable Overshoot. This is Known as Hunting or Granular Noise. It is analogous to Quantization Noise.

12. Noise in DM • The error d(t) caused by Hunting Lies in the range of (-σ,+σ). where, σ=Step-Size. • So Finding the Granular Noise Power,

13. Signal To Noise Ratio • Granular Noise has Power Spectral Density in the range of well-beyond the fs. • Band-limiting LPF can remove it. • Ideally Noise Power will be well-below the above equation. • To Compute Noise power we assume that PSD is uniform and in the range of 0 to fs Hz. (Experimentally Proved) • σ3/3 is total noise power, which is uniformly distributed over the range of fs, the Power within Signal Bandwidth B is, And

14. Signal To Noise Ratio Suppose mp is the Signal Peak ………..(11) Hence, ………..(12) So SNR becomes ………..(13) Manipulating all equations * For Double Integration For Single Integration Where,

15. Signal To Noise Ratio (PCM) In General, ………..(14) Where, Uncompressed ………..(15) Compressed ………..(16) But & Finally ………..(17)

16. Comparison Between DM and PCM

17. Thank You