Communication Systems - Essay Example

[Place here and delete brackets] [place and delete brackets] [Place the lecture here and delete brackets] 23 March 2010 Pulse Code Modulation Pulse modulation converts the sample analog information signals into a discrete pulses which will then be transported from its source to certain destination via a physical transmission media. With the pulse code modulation (PCM), in order to transmit the sample information analog signal as an output, the signals are converted to a series of n-bit binary codes. Note that each code is the same in number of bits and each code requires the same amount of time in transmitting pulses from the source to its destination (Tomasi 275). Filtering. Filtering is the initial step in converting the analog signal to a digital form. In this step, the higher frequency of the signal is filtered out to make the conversion of the analog signal easier. When people speak, the energy in their voices is normally between the range of 200 to 300 hertz for the lower limits and 2,700 to 2,800 hertz for upper limits (Tomasi 275). In the case of standard voice or speech communication, this reaches up to 3000 hertz bandwidth. The purpose of this bandwidth limiting is to eliminate aliasing or anti aliasing. Aliasing refers to the frequency of fold over distortion and in order to avoid aliasing, the following equation should be satisfied: fs 2fa , where fs=minimum Nyquist sample rate (hertz) and fa = maximum analog input frequency (hertz). Note that aliasing and antialiasing occurs due to under sampling of the input analog signals (voice). The Nyquist criterion fs 2fa happens because frequency of sample signals is less than the maximum frequency of the analog input signal (Cisco). Thus, an overlapping of the sampling frequency spectrum and the maximum frequency of the analog input signal. Overlapping happens due to inaccuracy of the output low-pass filter to detect the occurrence of overlapping between the frequency spectrum of samples and the analog input signals. The output low-pass filter is used in the reconstruction of the original input signal. As a result, a new signal (false signal) is created from the original source which is then termed as aliasing (Ciscosystems). Sampling. After the process of filtering in which the higher components of signal frequency are filtered out, the next step is the sampling. In this second stage of converting the analog input signal to digital output voice signal, a sample is taken from the filtered input signal at a condition of constant sampling frequency. The sampling of filtered input is done by using the pulse amplitude modulation (PAM) process. In sampling, the original analog signal is used in modulating the train of pulse amplitude having a constant frequency and amplitude (see figure 1.). Figure 1. Sampling of Analog Input The train of pulses moves at the same frequency which is termed as the frequency of sampling. The sampling of voice analog signal can be done at several million times per second. The sampling of the frequency was first determined by a scientist named as Harry Nyquist. He discovered that reconstruction of signal is possible by using the output low-pass filter. Additionally, the signal reconstruction can be done if the frequency of the sample is twice the highest or the maximum frequency of initial input voice signal. The following is the Nyquist criterion (Rumsy 210): Fs > 2(BW) Fs = Sampling frequency BW = Bandwidth of original analog voice signal Voice digitizing. The next step after the filtering and sampling (using the pulse amplitude modulation, PAM) of the analog input voice signal, is the digitization of samples to be transmitted over a telephone network. This process of digitization of analog input voice signals is termed as the pulse code modulation or PCM. Note that the single difference between the pulse amplitude modulation, PAM and the pulse code modulation, PCM is the fact that the PCM takes one step further in the process (Cisco systems). The PCM decodes every analog input sample by using the words of binary codes. The pulse code modulation initially converts the analog input signals into digital signals from the source and does the same at the destination. This is due to the fact that the PCM has analog-to-digital converters both in the source and on the destination section. Another technique used in the conversion of analog input to digital output by the PCM is the quantization. This technique is used to encode the samples (Digital Systems 201). Quantization and coding. The process of quantization involves the conversion of every sample value of analog input into a particular discrete value which the unique word of digital code can be assigned. Figure 2. The Nyquist Theorem of Pulse Code Modulation The moment the samples of input signals enter the phase of quantization, they are automatically assigned to a certain quantization interval. Note that quantization intervals are uniform or have equal spaces between them throughout the range of analog input signal. a discrete value of binary code word is assigned to every interval of quantization. The standard size of binary code word is eight bits. This means that if the analog input signal is sampled at 8000 times per second and if every sample is assigned a binary code word of length 8 bits, then the highest transmission bit rate is 64,000 bits / second, this is for the Telephony systems that uses pulse code modulation (PCM). Figure 2 shows the derivation of the bit rate for pulse code modulation (PCM) system. Figure 3 shows the diagram of a standard pulse code modulation. A certain quantization interval closest to the amplitude height is assigned to each sample of input signal. In the event that a there is a failure in the assignment of quantization interval corresponding to the height of a certain input signal sample, then the pulse code modulation process shall consider this as an error in the system. This error is then termed as a noise. This noise otherwise known as the quantization noise is normally equal to a random noise impacting the ratio of the signal-to-noise (SNR) of a particular voice signal. The signal- Figure 3. Standard Pulse Code Modulation to-noise (SNR) is simply the measure of the strength of signal relative to the background noise and the unit for this measure is expressed in decibels (dB). For example, if the incoming strength of signal is in Vs and the corresponding level of noise is in Vn, then the ratio of signal-to-noise (S/N) is in terms of decibels. Note that both the Vn and Vs units refer to microvolts and the unit of the ratio S/N is in decibels. In order to solve the problem involving the signal-to-noise ratio, the following formula is used: S/N = 20 log10(Vs/Vn). Generally, getting higher values for signal-to-voice (S/N) ratio, the better as this means a more enhanced voice quality. The role of quantization noise if to diminish or reduce the SNR of a particular signal. Therefore, increasing the quantization noise will degrade the voice quality of the signal. Below is figure 4 which quantization noise is produced (Cisco systems). Figure 4. The Conversion of Analog to Digital Figure 5. Diagram of Quantisizer and PCM Coder In order to reduce the noise, the values for quantization intervals should be increased. The only way to increase the quantization intervals is to decrease the difference between the quantization interval and amplitude height of the input signal, thus decreasing quantization noise. Remember that there is a need to increase the amount binary code words proportionate to the quantization intervals (Cisco systems). In the case of SNR that includes the quantization noise, SNR is the most essential factor affecting the voice quality in constant quantization. The uniform quantization utilizes the equality of quantization levels in the entire range of analog input signal. Simply put, low signals have smaller SNR (low-level of signal voice quality) and high signals have larger SNR (high -level of signal voice quality). Due to the fact that generated voice signals are normally low, digitizing the quality voice at higher levels of signals can be very inefficient and therefore to improve the quality of voice at low-level signals, the uniform quantization must be replaced by the process of non-uniform quantization, this process is termed as companding (Pulse Code Modulation). Companding. This process involves compressing at its source the analog signal and consequently expanding the particular signal back to its initial size upon reaching its destination. The word companding is simply the combination of two words, the compressing and expanding. During the process of companding, the samples of analog signals are automatically compressed into their logarithmic segments. Every segment is quantized and eventually coded by using constant quantization. The increase in compression process (logarithmic process) also increases the sample signals. To summarize, more bigger sample signals are compressed than smaller signals. As a result, quantization noise increases together with the increase in sample signals (PCM). Alaw companding. A-law is a compression type where A is a parameter whose value is 87.7 applicable only in Europe and values of linear samples are limited to 12 bits while x is the integer for compression. U-law companding. This type of compression limits linear samples to 13 bits where m is a compression parameter equal to 255, this value is only applicable to United States as well as in Japan. The variable x assumes any normalized integer for compression. Below is the u-law compander: Note the A-law is typically used in Europe and the rest of the contries while the u-law is used in North America as well as in Japan. U-law and A-law similarities. Both audio laws are linear approximations of the logarithmic relationships of output and input. Also, both audio laws are implemented by using the 8-bit binary code words which allow 64, 000 bits per second bit rate. A-law and u-law divide the dynamic range into 16 equal segments (8 positive and 8 negative segments). The individual segment is twice the total length of the previous segment. Another similarity that exists between audio laws is the fact that both use the same approach in coding the 8 bit binary code word (PCM). U-law and A-law differences. First these audio laws differ from each other with respect to the differences in linear approximations consequently causing variations in lengths and slopes as well. A-law gives larger dynamic range as opposed to u-law. Additionally, u-law gives better performance in terms of signal and distortion as compared to the A-law (u-LAW and A-LAW definitions). Limitations of PCM. Just like any other programming language or technology, the pulse code modulation has limitations such as the error in quantization due to the definite conversion difference from an analog to a digital signal. In other words, there is inaccuracy in the conversion of the signal from analog to digital. In addition, aliasing is another problem which is evident in the conversion of two different analog sounds. When these two varied sounds generate signals and then sampled, the digital versions of these supposed different signals sound similar. This is termed as the aliasing (Conversion Process). Recommendations. Enhancement is recommended in terms of digital mode and the pulse code modulation upstream. It is highly difficult to avoid the production of quantization noise and therefore, in order to minimize this, it is important to lock accurately timing of a network clock and the upstream transmitter, which then necessitates that loopback timing is run in the pulse code modulation analog modem. Analog channel must then be modeled in such manner that signal arrives at the converter given a sampling instances of voltage levels equivalent to the right PCM levels of encoding. Moreover, another recommendation is to develop a particular technique enabling the digital modem to deal with nonlinear echo which results from the PCM process of encoding in echo path (Waveform Coding Techniques). Works Cited Barry, John R., Lee, Edward A., Messerschmitt, David G. Digital Communication .3rd ed. New York: Leww,E.A.;Messerschmitt,D.G.2003. Print. "Conversion Process." frank.mtsu.edu. frank.mtsu, 26 April 2004. web. 23 March 2010. "G.711 Pulse Code Modulation (PCM)." vocal.com. vocal, n.d. web. 22 March 2010. "Method for encoding analog signals using PCM difference code word for forming a code word of specified length." freepatentsonline.com. freepatents, n.d. web. 23 March 2010. "PCM." Homedamping.com. Homedamping, n.d.web. 23 March 2010. Proakis, John. Digital Communications. 4th ed.Ney York: Thomas Casson. 2001.Print. "Pulse Code Modulation." topbits.com.topbits, n.d.web. 23 March 2010. Roden, Martin. S. Analog and Digital Communiation Systems. 5th ed. Califonia: Discovery Press, 2003. Print. Sklar, Bernard. Digital Communications: Fundamentals and Applications.2nd ed. Prentice Hall. 2001. Print. Silage, Dennis. Digital Communication Systems Using SystemVue.Da Vinci Engineering Press. 2006. Print. Tocci, Ronald. Digital Systems, Principles and Applications. Singapore: Prentice Hall,1991. Print. Tomasi, Wayne.Advanced Electronic Communications Systems. New Jersey: Pearson Prentice Hall, 2004. Print. "u-LAW and A-LAW definitions." epanorama.net. epanorama, n.d. web. 23 March 2010. "Waveform Coding Techniques." Ciscosystems.com. Ciscosystems, n.d. web. 20 March 2010. Read More