Signals and Systems/Noise
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Noise is a unfortunate phenomenon that is the greatest single enemy of an electrical engineer. Without noise, digital communication rates would increase almost to infinity.
White Noise
White Noise, or Gaussian Noise is called white because it affects all the frequency components of a signal equally. We don't talk about Frequency Domain analysis till a later chapter, but it is important to know this terminology now.
Colored Noise
Colored noise is different from white noise in that it affects different frequency components differently. For instance in the United States, high-voltage power lines have a frequency of 60Hz. Noise generated by these power lines will affect only the 60Hz component of passing electromagnetic waves.
White Noise and Autocorrelation
White Noise is completely random, so it would make intuitive sense to think that White Noise has zero autocorrelation. As the noise signal is time shifted, there is no correlation between the values. In fact, there is no correlation at all until the point where t = 0, and the noise signal perfectly overlaps itself. At this point, the correlation spikes upward. In other words, the autocorrelation of noise is an Impulse Function centered at the point t = 0.
Where n(t) is the noise signal.
Noise Power
Noise signals have a certain amount of energy associated with them. The more energy and transmitted power that a noise signal has, the more interference the noise can cause in a transmitted data signal. We will talk more about the power associated with noise in later chapters.
Thermal Noise
Thermal noise is a fact of life for electronics. As components heat up, the resistance of resistors change, and even the capacitance and inductance of energy storage elements can be affected. This change amounts to noise in the circuit output. In this chapter, we will study the effects of thermal noise.