Lecture Notes in Digital Communications: Sampling & Pulse Modulation, Study notes of Electrical Engineering

Download Lecture Notes in Digital Communications: Sampling & Pulse Modulation and more Study notes Electrical Engineering in PDF only on Docsity! Lecture Notes in “Digital Communications” Sampling & Pulse Modulation Electrical Engineering | University of Anbar by: Dr. Mohammed AlMahamdy -20- 1.7 PCM QUALITY VERSUS REQUIRED RATE In addition to the channel effects, PCM performance depends primarily on the quantization noise. To make the reconstructed signal like the original baseband signal we must reduce the quantizing noise by increasing 𝐿. Now, we learned that increasing the number of quantization levels requires more bits per sample to be transmitted. Large 𝑙 is not perfect for crowded channels and due to some channel’s limitations. So, beside the non-uniform quantization, several techniques are used to reduce the quantization noise at the same number of the L. 1.8 BANDWIDTH REDUCTION TECHNIQUES The channel bandwidth is limited, and it is a valuable resource. A frequent objective of the communications engineer is to transmit the maximum information rate via the minimum possible bandwidth. This is especially true for radio communications in which radio spectrum is a scarce, and therefore valuable, resource. The following systems are used to maintain the same coding fidelity using fewer bits per sample. 1.8.1 Delta PCM Because the samples of most of the baseband signals are highly correlated, it is possible to transmit the information about the changes between samples instead of sending the sample values themselves. A simple way for such systems is the Delta PCM. This method transmits the difference between adjacent samples through code words. This difference is significantly less than the actual sample values, hence it is coded using fewer binary symbols per word than the conventional PCM. However, Delta PCM systems cannot accommodate rapidly varying transient signals. + _ + Sampler Delay TS PCM Encoder Delta PCM + Delta PCM Delay TS PCM Decoder Output Signal Delta PCM Encoder Delta PCM Decoder Input Signal Sampling & Pulse Modulation Lecture Notes in “Digital Communications” by: Dr. Mohammed AlMahamdy Electrical Engineering | University of Anbar -21- 1.8.2 Deferential PCM Since neighbor samples within many information signals are highly correlated, Deferential PCM (DPCM) uses an algorithm to predict future values. Such algorithms monitor the trend of the baseband samples and use some models to predict the value of the incoming samples. Then DPCM waits until the actual value becomes available for examination and transmits the correction to the already predicted value. The correction signal represents the information signal’s unpredictable part. By this means, DPCM reduces the redundancy in signal and allows the information to be transmitted using fewer symbols, less spectrum, and shorter time. 1.9 DELTA MODULATION (DM) If the quantizer of the DPCM system is restricted to one bit (i.e. the two levels only: ±∆) and the predictor to one sample delay, then the resulting scheme is called DM. The information signal is represented by a stepped waveform. The resolution of this waveform depends on ∆ & 𝑇𝑠 values. + _ + Sampler Predictor Encoder DPCM signal + DPCM signal Predictor Decoder Output Signal DPCM Encoder DPCM Decoder Input Signal Quantizer Smoothing Filter + _ +   + + DM signal Sampler Delay TS DM signal Input Signal + Delay TS Output Signal Smoothing Filter DM Encoder DM Decoder Lecture Notes in “Digital Communications” Sampling & Pulse Modulation Electrical Engineering | University of Anbar by: Dr. Mohammed AlMahamdy -24- And by filtering this noise to a bandwidth 𝐵, we get: 𝑁𝑞 = 𝑛𝑞2̅̅ ̅ = ∆2𝐵 3𝑓𝑠 The mean-square value of the information signal is: 𝑆 = 𝑔2(𝑡)̅̅ ̅̅ ̅̅ ̅ = ( 𝑉𝑝 √2 ) 2 = 𝑏2 2 = 1 8 ( ∆𝑓𝑠 𝜋𝑓𝑚 ) 2 ∴ SNqR = 3𝑓𝑠 3 8𝜋2𝑓𝑚2𝐵 Adaptive Delta Modulation We have seen that: a large step size causes unacceptable quantization noise, and a small step size results in sample-overload distortion. This means that a good choice for ∆ is a “medium” value, but in some cases, the performance of the best “medium” values is not satisfactory. An approach that works well in these cases is to change the step size according to changes in the input: if the input tends to change rapidly, the step size is chosen to be large (and vice versa). So, the output can follow the input quickly without distortion. Errors in DM If the SNR is not sufficiently high, then the DM receiver will occasionally interpret a received symbol in error (i.e. +∆ instead of −∆ or the converse), and this is equivalent to the addition of an error of 2∆ to the accumulated signal at the DM receiver, as shown below. This situation continues until another error occurs which either cancels the first error or double it! DM is primarily used for telemetry systems and speech transmission in telephone. It has been found that: PCM is preferable for high quality speech transmission, whereas DM is easier to implement and yields transmission of acceptable quality. Adaptive DM Sampling & Pulse Modulation Lecture Notes in “Digital Communications” by: Dr. Mohammed AlMahamdy Electrical Engineering | University of Anbar -25-