![]() ![]() It also provides some conveniences like being able to add when we would normally multiply (as we will see in the Link Budgets chapter). ![]() The logarithmic scale of dB lets us have more dynamic range when we express numbers or plot them. In DSP we deal with really big numbers and really small numbers together (e.g., the strength of a signal compared to the strength of the noise). You can barely see the signal on the left in the linear scale.įor a given value x, we can represent x in dB using the following formula:ĭon’t get caught up in the formula, as there is a key concept to take away here. Both representations use the exact same colormap, where blue is lowest value and yellow is highest. The left-hand side is the original signal in linear scale, and the right-hand side shows the signals converted to a logarithmic scale (dB). To further illustrate the problems of scale we encounter in signal processing, consider the below waterfalls of three of the same signals. To represent these scales simultaneously, we work in a log-scale. If the scale of the y-axis went from 0 to 3 watts, for example, the noise would be too small to show up in the plot. Frankly, if we were to plot something like Signal 1 over time, we wouldn’t even see the noise floor. Without dB, meaning working in normal “linear” terms, we need to use a lot of 0’s to represent the values in Examples 1 and 2. Consider how cumbersome it would be to work with numbers of the scale in Example 1 and Example 2.Įxample 1: Signal 1 is received at 2 watts and the noise floor is at 0.0000002 watts.Įxample 2: A garbage disposal is 100,000 times louder than a quiet rural area, and a chain saw is 10,000 times louder than a garbage disposal (in terms of power of sound waves). Working in dB is extremely useful when we need to deal with small numbers and big numbers at the same time, or just a bunch of really big numbers. You may have heard of dB, and if you are already familiar with it feel free to skip this section. We are going to take a quick tangent to formally introduce dB. Variance equals standard deviation squared ( ). It is for this reason that variance defines the noise power. A higher variance will result in larger numbers. The variance changes how “strong” the noise is. We already discussed how the mean can be considered zero because you can always remove the mean, or bias, if it’s not zero. The Gaussian distribution has two parameters: mean and variance. The Gaussian distribution is also called the “Normal” distribution (recall a bell curve). In other words, when a lot of random things happen and accumulate, the result appears approximately Gaussian, even when the individual things are not Gaussian distributed. The central limit theorem tells us that the summation of many random processes will tend to have a Gaussian distribution, even if the individual processes have other distributions. ![]() It’s a good model for the type of noise that comes from many natural sources, such as thermal vibrations of atoms in the silicon of our receiver’s RF components. We call this type of noise “Gaussian noise”. Also note that the individual points in the graph are not “uniformly random”, i.e., larger values are rarer, most of the points are closer to zero. If the average value wasn’t zero, then we could subtract the average value, call it a bias, and we would be left with an average of zero. Note how the average value is zero in the time domain graph. Most people are aware of the concept of noise: unwanted fluctuations that can obscure our desired signal(s). We will also introduce decibels (dB) along the way, as it is widely within wireless comms and SDR. Concepts include AWGN, complex noise, and SNR/SINR. In this chapter we will discuss noise, including how it is modeled and handled in a wireless communications system. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |