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Introduction to Noise

What is noise? And how did it suddenly start coming in colors? For a long time, when I'd see the terms "white noise" and "pink noise", I had to wonder what was going on.

The word noise is derived from the same Latin word as "nausea," meaning seasickness. Noise is unwanted sounds--or in electronics, unwanted signals. From an electronics perspective, all devices produce noise at a power level that is proportional to the temperature of the device. This noise is generated by the random vibrations of conducting electrons and holes in the material used within the device. This noise is referred to as thermal noise.

Before we get into details on the "colors" of noise, we need to discuss the concept of power spectral density. If we have 10 watts of power and use, for example, amplitude modulation to send our voice (say 300-3,000 Hz) we end up spreading that 10 watts across approximately 6 kHz. If we divide the 10 watts by the 6 kHz, you find that we have an average power spectral density of around 1.7 watts/kHz. Some modulation techniques (like spread-spectrum) spread their signal over much wider portions of spectrum. Say a spread spectrum transmitter uses the same 10 watts, but spreads it over 20 MHz. Our average power spectral density now drops to around 0.0005 watts/kHz.

The "colors" of noise refer to different power-spectral densities.

White noise is noise whose energy is uniform over wide range of frequencies. It is similar in spectrum characteristics to white light. For example, assume we have a noise source that we are using to generate noise between 1 MHz and 8 MHz. In a white noise source, the power contained in the spectrum between 1 MHz and 2 MHz would be the same as the power contained in the spectrum between 7 MHz and 8 MHz (and, in fact, in each of the 1 MHz bands in between).

One important concept here is that measuring noise can be tricky business. How much power you measure depends on the bandwidth of the system used to measure it. If the measurement bandwidth is doubled, the measured noise power will double (an increase of 3 dB).

We talked earlier about thermal noise. Thermal white noise power can be calculated from the equation:


where N is the noise power at the output of the thermal noise source, k is Boltzmann's constant (1.38 x 10-23 J/K), T is the temperature, and B is the noise bandwidth.

One more quick explanation before we move on. An octave is a range of frequencies where the ratio between the highest frequency and the lowest frequency if two. For example, the frequencies between 1 MHz and 2 MHz are an octave as are the frequencies between 2 MHz and 4 MHz.

Pink noise is noise with a constant energy per octave. This is typically used (in my experience) at audio frequencies. For example, an audio noise source might have as much energy between 1 kHz and 2 kHz as it does between 2 kHz and 4 kHz or between 4 kHz and 8 kHz.


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