Transmitting Information Using Rectangular Pulses

Consider transmitting a series of rectangular pulses (pulse width  ) to represent a sequence of “1”s and “0”s: T = bit period = 1 r b 

What is the optimum relationship between  and T? Observations: 1) We are transmitting 1/T pulses/sec and each pulse represents one bit. We are therefore transmitting r b = 1/T bits/sec T = bit period = 1 r b 

What is the optimum relationship between  and T? (cont.) Observations (continued): 2) We want to transmit as many bits (pulses) per second as possible without having the pulses overlap, so choose T = .

Normalized Energy Spectral Density of a Single Rectangular Pulse Hz  = A 2  2 sinc 2 (  f  ) A 2  2 volts 2 - sec/Hz 0  3   2   1  1  2  3 

Average Normalized Energy Spectral Density of a Series of n Rectangular Pulses nA 2  2 Hz  AVE, n = nA 2  2 sinc 2 (  f  ) volts 2 - sec/Hz 0  3   2   1  1  2  3 

Define: Using this definition: Avg. Normalized Power Spectral Density of a Series of Rectangular Pulses

A 2  Hz G(f ) = A 2  sinc 2 (  f  ) volts 2 /Hz 0  3   2   1  1  2  3  Avg. Normalized Power Spectral Density of a Series of Rectangular Pulses

Importance of Average Normalized Power Spectral Density

Relating Pulse Width to Channel Bandwidth

Optimum width is  = T. Since T = 1/r b, 1/  = r b 90% in-band power if channel bandwidth = r b 93% in-band power if channel bandwidth = 1.5r b 95% in-band power if channel bandwidth = 2r b Relating Bandwidth, Transmission Speed, and Accuracy