Figure 4.13 Symbol rate (baud rate) and bandwidth. Introduction to Telecommunications Network Engineering lowpass channel with a bandwidth higher than W, it is suitable for transmit- ting sinc pulses that have their first zero crossing at t = 1/2 W without distor- tion. The shape of the pulse remains the same because all frequency components are the same at the output as at the input of the channel. The sinc pulses have zero crossings at regular periods in time. These periods are 1/(2W) seconds for a sinc pulse with a spectrum up to frequency W as shown in Figure 4.13. We can transmit the next pulse at the time instant 1/(2W) SO that the previous pulse has no influence on the reception because it crosses zero at that time instant. The decision for the value of the pulse is made in the receiver exactly at time instants N 1/(2W), where n The time between pulses T=1/(2W), which makes data rate r=1/T=2W. If we now increase the data rate SO that W B, the time between pulses becomes 1/T = 2B, which gives the theoreti- cal maximum rate for transmission of symbols and we can say that the sym- bol rate and bandwidth are related according to r 2B or B r/2. This kind of pulse does not exist in reality, but the result gives the theo- retical maximum symbol rate, which we can never exceed, through a lowpass channel. In real-life systems quite similar pulse shapes are in use and typically a 1.5 to 2 times wider bandwidth is needed. 4.3.2 Symbol Rate and Bit Rate In digital communications a set of discrete symbols is employed. Binary sys- items have only two values represented by binary digits 1 and 0. In the previ- ous section we found that the fundamental limit of the symbol rate is twice the bandwidth of the channel. With the help of the symbols with multiple values the data rate, in bits per second, can be increased. As an example, with four pulse values we could transmit the equivalent of 2-bit binary words 00, 01, 10, and 11. Thus each pulse would carry the information of 2 bits and one symbol per second (1 baud) would co