Properties of sinusoid signals

Simple signals are modelled with sine and cosine functions and are termed sinusoid.

1. Period.
   The period of a simple periodic signal is the value of T, the interval over which the signal is repeated. For example: a sinusoid signal with a period of 5 msec will repeat itself 500 times per second. The number of repetitions of a sinusoid signal per second is its frequency, counted in Hertz (Hz). The period and the frequency of a signal are related as follows:

   

   A sinusoid signal with a period of 2 sec has a frequency of 0.5 Hz, and one with a frequency of 2 Hz has a period of 0.5 sec. Likewise, a sinusoid signal with a period of 2 msec has a frequency of 0.5 kHz, and one with a frequency of 2 kHz has a period of 0.5 msec.

2. Phase.
   The phase of a simple periodic signal is the argument of the sine function in degrees or radians. For example:

   

   e.g. , or
   

   

   e.g. 1.57 rad
   In more practical terms, a sinusoid signal starts at value zero, after a quarter of the period it has reached its positive peak (maximum) value, after half the period it has reached zero again, after three-quarters of the time it has reached its negative peak (minimum) value, and after the full period it has again reached zero. A point at which a signal has the value zero is called a zero crossing; if the signal moves from a positive to a negative value, it is a negative-going zero crossing, and if the signal moves from a negative to a positive value, it is a positive going zero crossing.
   Imagine walking across sand with a stick, and tracing a line very slowly moving the stick evenly back and forth from left to right. The resulting trace is approximately sinusoidal, the zero-crossing is when the stick is immediately in front of you, the positive peak being the furthest distance on the left (say), and the negative peak being the furthest distance on the right.

3. Amplitude.
   The amplitude of the signal is the value of the quantity being measured at a given value of the independent variable, and varies between the positive and negative peak values.