Chapter 10 Applications in Communications

Transcription

1 Chapter 10 Applications in Communications School of Information Science and Engineering, SDU. 1/ 47

2 Introduction Some methods for digitizing analog waveforms: Pulse-code modulation (PCM) Differential PCM (DPCM) Adaptive differential PCM (ADPCM) Delta modulation (DM) Adaptive delta modulation (ADM) Linear predictive coding (LDC) 2/ 47

3 Pulse-Code Modulation (PCM) PCM is used for quantizing an analog signal to transmit storing the signal in digital form Speech transmission Telemetry systems 3/ 47

4 - law compressor A logarithmic compressor employed in U.S. and Canadian telecommunications systems ( +µ s ) ln 1 y= sgn( s ); s 1, y 1 ln 1 ( +µ ) s : the mormalized input; y : the normalized output; sgn( ) : the sign funciton; : a parameter that is selected to give the desired compression characteristic. 4/ 47

5 A law compressor The logarithmic compressor standard used in European telecommunication systems: ( ) 1+ ln A s 1 sgn ( s ), s 1 y = 1+ lna A As 1 sgn ( s ), 0 s 1+ lna A where A is chosen as / 47

6 Figure 10.1 Comparison of -law and A-law nonlinearities 6/ 47

7 Project 10.1: PCM Purpose of this project: To gain an understanding of PCM comprssion (linear-to-logarithmic) PCM expansion (logaithmic-to-linear). 7/ 47

8 Three Matlab functions are needed: A -law compressor function A quantizer function A -law expander funciton 8/ 47

9 Figure 10.2 PCM project 9/ 47

10 The signal-to-quantization noise ratio (SQNR) in db is: SQNR = 10log 10 N N n= 1 ( n) ( ) ( ) ( s n s ) q n n= 1 s / 47

11 Differential PCM (DPCM) p s n = a i s n i ( ) ( ) ( ) i= 1 s(n): the current sample of speech s( n) : the predicted value of s(n) a(i): the predictor coefficients 11/ 47

12 The error function is the sum of squared errors, so we select the a(i) to minimize: N ε p = = n= 1 n= 1 n= 1 N p 2 e n s n a i s n i ( ) ( ) ( ) ( ) p p p ( ) () () () () ( ) = r 0 2 a i r i + a i a j r i j ss ss ss n= 1 i= 1 j= 1 where r ss (m) is the autocorrlation function of s(n) N rss m = s i s i+ m ( ) ( ) ( ) i= / 47

13 Figure 10.3 Block diagram of a DPCM transcoder 13/ 47

14 The output of the predictor is p s = a() i s ( n i) i= 1 The difference ( ) ( ) e n = s n s ( n) is the input to the quantizer. 14/ 47

15 The estimate value s ( n) of s(n) is obtained by taking a linear combination of past values, k=1,2,,p. s n ( ) The estimate of s(n) is p p ( ) () ( ) () ( ) = + s n a i s n i b i e n i k i= 1 i= 1 15/ 47

16 Project 10.2: DPCM Generate correlated random sequences using a pole-zero signal model of the form: ( ) = ( ) ( ) + ( ) + ( ) s n a 1 s n 1 b x n b x n where x(n) is a zero-mean unit variance Gaussian sequence. filter function 16/ 47

17 Some modules for this project: A model predictor function A DPCM encoder function A DPCM decoder function 17/ 47

18 Figure 10.4 DPCM modified by the linearly filtered error sequence 18/ 47

19 Adaptive PCM (ADPCM) and DPCM Adaptive quantizer: feedforward adaptive quantizer Adjust its step size for each signal sample feedback adaptive quantizer Employ the output of the quantizer in the adjustment of the step size. 19/ 47

20 Figure 10.5 Example of a quantizer with an adaptive step size 20/ 47

21 Table 10.1 Multiplication factors for adaptive step size adjustment 21/ 47

22 Figure 10.6 ADPCM block diagram (Encoder part) 22/ 47

23 Figure 10.6 ADPCM block diagram (Decoder part) 23/ 47

24 Project 10.3: ADPCM Figure 10.7 ADPCM interface to PCM system 24/ 47

25 Delta Modulation (DM) DM may be viewed as asimplified form of DPCM in which a two-level (1-bit) quantizer is used in conjunction with a fixed first-order predictor. 25/ 47

26 We note that s n = s n 1 = s n 1 + e n 1 Since ( ) ( ) ( ) ( ) q n = e n e n = e n s n s n ( ) ( ) ( ) ( ) ( ) ( ) It follows that s n = s n 1 + q n 1 ( ) ( ) ( ) 26/ 47

27 Figure 10.8 Block diagram of a delta modulation system 27/ 47

28 Figure 10.9 An equivalent realization of a delta modulation system 28/ 47

29 Adaptive Delta Modulation (ADM) Figure Two types of distortion in the DM encoder 29/ 47

30 Figure An example of a delta modulation system with adaptive step size Encoder part 30/ 47

31 Decoder part 31/ 47

32 Project 10.4: DM and ADM A Hanning filter that has the impulse response 1 2πn h( n) = 1 cos,0 n N 1 2 N 1 may be used, where the length N may be selected in the range 5 N / 47

33 Linear Predictive Coding (LPC) of Speech The LPC method is based on modeling the vocal tract as a linear all-pole filter. The system function: H z ( ) = p + k= 1 ( ) p : the number of poles; G : the filter gain; {a p (k)}: parameters that determine the poles. G 1 a k z p k 33/ 47

34 Figure Block diagram model for the generation of a speech signal 34/ 47

35 Figure Encoder and decoder for LPC 35/ 47

36 Project 10.5: LPC The encoder divides speech signals into short-time segments, and process each segment, separately. The decoder that performs the synthesis is an all-pole lattice filter. The output is a synthetic speech signal. 36/ 47

37 Dual-Tone Multi-frequency (DTMF) Signals DTMF is the generic name for push-button telephone signaling. DTMF also finds widespread use in electronic mail systems and telephone banking systems. A combination of a high-frequency tone and low-frequency tone represent a specific digit or the characters * and #. 37/ 47

38 Figure DTMF digits 38/ 47

39 The Goertzel Algorithm The Goertzel algorithm exploits the k periodicity of the phase factors W N and allows us to express the computation of the DFT as a linear filtering operation. kn Since W, we can multiply the DFT by N = 1 this factor. Thus N 1 = = N m= 0 kn ( ) ( ) ( ) X k W X k x m W ( ) k N m N 39/ 47

40 Figure Realization of two-pole resonator for computing the DFT 40/ 47

41 Project 10.6: DTMF Signaling Design the following Matlab modules: A tone generation function A dial-tone generator A decoding funciton 41/ 47

42 Binary Digital Communications A binary digital communications system employs two signal waveforms: s 1 (t)=s(t) s 2 (t)=-s(t) To measure the performance, we normally use the average probability of error, which is often called the bit error rate (BER). 42/ 47

43 Project 10.7: Binary Data Communications System Five Matlab functions are required: A binary data generator module A modulator module A noise generator A demodulator module A detector and error-counting module 43/ 47

44 Figure Model of binary data communications system 44/ 47

45 Spread-Spectrum Communications Figure Basic spread spectrum digital communications system 45/ 47

46 Project 10.8: Binary Spread-Spectrum Communications Figure Block diagram of binary PN spread-spectrum system for simulation experiment 46/ 47

47 That s all! 47/ 47