Differentially Encoding Method used to encode information in terms of signal transition The original binary information is recovered simply by comparing the polarity of adjacent binary symbols to establish whether or not a transition has occured

0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 Original data Dif.enc. data 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 Dif.enc. data A transition is used to designate symbol ‘0’ in the incoming data stream, no transition means ‘1’. A reference bit is needed at the beginning

Modifications of PCM Most favorite transmission scheme for transmission of analog signals Advantages : 1- Same as digital ( easy to correct once the error is detected, secure communication use of encryption ) 2- A uniform format for the transmission of different kinds of baseband signals ( can integrate different services in one network)

Disadvantages 1- System complexity ( use of DM) 2- Increase bandwidth ( availability of wide bandwidth common channels such as satellites and optical fibers(

Delta Modulator The aim is to use simple quantizing strategy for constructing the encoded signal The sample will be encoded using only one bit ( the difference will be encoded instead of the sample itself) Use of fewer bits

In delta modulation (DM), the incoming signal is over sampled. i. e In delta modulation (DM), the incoming signal is over sampled. i.e., the sampling rate is much higher than the Nyquist rate DM provides a staircase approximation to the oversampled version of the message signal The difference between the I/P m(t) and the approximation mq(t) is quantized into only two levels ±S

m(t) S Ts mq(t)

Delta modulator includes a DM demodulator that generates a staircase approximation mq(t) of the analog message signal m(t) by an accumulator if the staircase approximation mq(t) falls below the message signal m(t) at any sampling time instant then the DM modulator emits a bit 1 which means that the value of mq(t) has to be increased by S

If mq(t) lies above m(t) then the DM modulator emits a bit 0 which means that the value of staircase approximation mq(t) has to be reduced by S DM wave is the binary sequence that shows if the actual value of message signal m(t) is above or below the previous reconstructed signal value mq(t)

Delta Modulator Block Diagram So(t) m(t)-mq(t) So(t) m(t) mq(t) Ts Delta Modulator Block Diagram

m(t) = The Base-band Signal mq(t) = The quantized approximation of m(t) If m(t) > mq(t) The comparator output = V(H) If m(t) < mq(t) The comparator output = V(L) If So(t) level is V(H), The Counter counts up If So(t) level is V(L), The Counter counts down

Problems in delta modulation Slope overload distortion If the step size S is too small then the staircase approximation mq(t) cannot follow the fast variations in the input waveform m(t) m(t) Ts S mq(t)

To avoid slope overload, i. e To avoid slope overload, i.e. in order for the sequence of samples mq[n] to increase as fast as the input sequence of samples m[n] [ S / Ts ] ≥ max | m’ (t) |

2. Start up response in DM: m(t) mq(t)

3. Granular noise If the step size S is too large then the staircase approximation oscillates around the relatively flat segments of input waveform. Granular noise is analogous to quantization noise in a PCM system The choice of S compromises between the two problems When the change in the I/P is too large choose large S and vice versa We can use an adaptive DM to solve these problems

Figure 3–32 DM system waveforms. Couch, Digital and Analog Communication Systems, Seventh Edition ©2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

Signal-to-noise ratio out of a DM system as a function of step size. Couch, Digital and Analog Communication Systems, Seventh Edition ©2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0

Comparison OF PCM and DM Systems

Differential PCM We transmit the difference between the sample value m(k) at time k, and the sample value m(k-1) at time (k-1) So, by adding up (accumulating) these changes, we shall generate at the receiver a waveform identical to m(t) We transmit these differences by PCM Since [m(k)-m(k-1)]<m(k), then we’ll need fewer levels, and fewer bits

Differential PCM Transmitter d[k] dq [k] to channel m[k] Quantizer mq [k] m1q [k]

Differential PCM Transmitter So, mq[k] is the quantized version of m[k] dq[k] is transmitted over the channel.

Differential PCM Receiver From channel dq [k] The output q[k] Predictor m1q [k] Since the receiver is the same as the feed back portion of the transmitter, then: The predictor output is the same (m1q[k]) The receiver output = The predictor input = mq[k]=m[k]+q[k] So the added quantization noise is q[k], associated with the difference signal d[k] which is << m[k]

Adaptive Delta-Modulation Adaptive Delta Modulation (ADM) Adaptive Delta-Modulation

Adaptive Delta Modulation (ADM) The step size S(k) is not kept fixed and always multiple of basic step So When slope overload occurs, the step size becomes larger mqa(t) will catch m(t) more rapidly Step size: The output e(k) = 1 if m(t)> mq(t) The output e(k) =-1 if m(t)<

Adaptive Delta Modulator Block Diagram

Waveforms comparing Adaptive DM & linear DM m(t) mqa(t) mq(t) Waveforms comparing Adaptive DM & linear DM mqa(t) will catch m(t) more rapidly ADM has large quantization error ADM has very low slop overload error