Noise Spectrum Level

An important property of gaussian noise is that it is comprised of a large number of sinusoidal components of equal average power. If we plot the average power of each sinusoidal component as a function of the frequency of each component, we have what is called the power spectrum of the noise. We will talk more about the power spectrum of sounds later. The power spectrum of a band of gaussian noise is shown below.

The noise spectrum level of the noise is a measure of noise intensity and is denoted as No. It is the average power in a 1-Hz band of the noise (watts/Hz). The bandwidth of the noise is the number of 1-Hz bands comprising the noise and is denoted with the letter W. In this example the bandwith is 1000-Hz. Since there are W, 1-Hz bands each with an average power of No, the total average power (P) of the noise is

P = NoW = 5 watts/Hz X 1000 Hz = 5000 watts/Hz

Note: that the computation of P amounts to little more than taking the area of a rectangle. In this case the rectangle described by the power spectrum of the band of noise.