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# What is Power Spectral Density & it’s benefits?

A composite signal is composed of several frequency components. Each frequency component corresponds to a signal. Such signals of different frequencies put togetherforms a composite signal. Different signal frequencies present in the signal respond differently to the channel noise conditions. Power spectral density specifies the power levels of the frequency components present in a signal. It is denoted as PSD inshort. The PSD specifies the power of various frequencies present in the signal and we can determine the range of power over which the signal frequencies are operating at. Essentially, the PSD profile is a plot of the power over frequency.

The figure shows the normalized distribution of power per unit of frequency (Power per Hertz) for different frequencies on the X-axis

## Unit Of Power Spectral Density

The PSD gives the power level of all the frequency components present in the signal. So, the power profile is obtained for the entire range of frequencies of interest (termed bandwidth).

PSD is specified as W/Hz

Where, W = Power in Watt

Hz = Hertz, unit of frequency

## Interpreting Power Spectral Densities

Let us arbitrarily assume a signal having bandwidth of 4 MHz and it is composed of four frequency components- 10 MHz, 11 MHz, 12 MHz and 13 MHz. Let us assume the power levels measured for these frequencies are 4W, 5W, 6W and 7W respectively.

For 11 MHz frequency component, the power level is 5W. So, the power per Mega Hertz is 5/11 W and the power per unit Hz is 5/11 μW/ Hz. Therefore, PSD is usually represented as the power level per Hz of frequency.

Signal frequency component: 11 MHz, Power level is 5 MHz Power per Mega Hertz: 5/11 W Power per unit Hertz: 5/11 µW = 0.454 μW

## Benefits Of Power Spectral Density Profile

Using the PSD profile, we can identify the frequency components having relatively weaker power levels in the given frequency range of interest.

The received test signal (control signal) is studied using a spectrum analyzer. The PSD profile is studied and this is compared to the PSD of the test signal before it was transmitted through the channel.

By studying the PSD profile, we can determine the frequency components with reduced power levels as a result of channel noise. These frequency components have relatively been more vulnerable to the noise when compared to the other frequency components present in the signal.

We can therefore adjust the power levels of the signal to be transmitted to combat the effects of channel noise.

## How Power Spectral Density is used to Classify Noise?

**White Noise – Commonly found in Wireless Communication**

The most commonly used noise model in wireless communication systems is the ‘white’ noise model. The PSD profile of white noise is flat over frequency ranges. Thus, the PSD of white noise is uniform and is independent of the signal frequency components. White noise PSD is represented as a straight line parallel to the frequency axis in the PSD plot.

**Pink Noise or Flicker Noise**

Pink noise is also termed ‘flicker’ noise. In this noise model, the noise power is inversely proportional to the frequency. Thus, the noise power level is low for higher signal frequency components. The flicker noise is therefore termed ‘1/f’ noise because of this inverse relation between power and frequency.

**Brown Noise also known as Popcorn Noise.**

Brown noise is termed ‘1/f^{2}’ noise. The rate of fall of the noise power with increasing signal frequency is higher than that in pink noise model. Brown noise is also called popcorn noise or avalanche noise.

**Purple Noise**

Purple noise is termed ‘f^{2}’ noise. The noise power follows a quadratic relation with the signal frequency components.

**Blue Noise**

The noise power has a linear relation with the signal frequency component and this is termed ‘f’ noise.

Y-axis: Power/Hz, X-axis: Frequency

PSD of white noise

PSD of pink noise

PSD of brown noise.

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