ation of air pressure as sound. We are able to hear frequencies in the range of approximately 20 Hz to 15 kHz, where Hz (hertz) represents the number of cycles in a second. An example of the different frequencies is heard in the keys of a piano. The right-hand keys generate basic frequencies of the order of 1,000 Hz and the left-hand keys of the order of 100 Hz. In electrical terms, an alternating current (ac) changes its direction of flow several times per second. This variation in direction is known as a cycle, and the term frequency refers to the number of cycles in a second that is meas- ured in hertz. If a signal has 1,000 complete cycles in a second, then its frequency is 1,000 Hz or 1 kHz. A pure sine wave, like that shown in Figure 3.2, is generated with a loop of wire rotated in a magnetic field at a constant rate. This fundamental waveform can be seen as a cosine of the Voltage or Constant rotation current 1 Cycle rate, f complete Phase = 0 cycles in a second angle =2ft+ Acos(2rtt+) Example: v(t)= 1 COS (2t-90°)V 1 second, 5 cycles per second = 5 Hz Wavelength: How long distance signal propagates during one cycle or periodic time. A=c/f C = velocity, speed of the wave Cycle or periodic time T= 1/5 Hz = 200 ms Figure 3.2 Cosine wave and frequency. Signals Carried over the Network angle of the phasor rotating at a constant rate. The strength of the voltage or current alters according to the cosine curve when time increases. The length of the phasor corresponds to the maximum value of the signal and it is called amplitude, shown as A in Figure 3.2. We can see any telecommunications signal as a sum of these fundamen- tal waveform cosine waves that are expressed as v(t) = Acos(wt+)= Acos(2rf+) = (3.1) where f is frequency, the number of complete cycles in a second expressed in hertz, 1 Hz = 1/sec; t is time in seconds, and is the phase shift (phase of the cosine wave at time instant t = 0). The angular frequency W in radians per second is W = 2rf, which comes from the fact that one complete cycle of a phasor