Graphs 2 and 3 are in decibels so a ratio is transformed in a diferencia due to logarithmic properties. In the first graph we see some distance between the signal and the noise although this is quite misleading because SNR is a ratio not a distance. For example, every single graph at the beginning of this document present our signal and noise as separate elements given that through this abstraction we are able to visualize what SNR is. Very clearly they are related but its easy to fall in misleading assumptions. Very often we study bit depth in relation to dynamic range and SNR (signal to noise ratio). Now that we have a clear preamble, here’s what I’d really like to present. However, others exist such as Power-Law Companding, Logarithmic commanding and floating point quantization which we use regularly. The most common way to achieve this in audio is through a uniform mid tread quantization scheme. No matter what, we need a finite number of quantization steps to represent our signal but we can make many decisions on how to assign these quantization steps to amplitudes to achieve specific behaviors. However, it is important to understand that there are many many ways to build quantization and codification schemes (it is even possible that many ADCs take different approaches to some details we’ll check later). So for 16 bits we have 65536 quantization steps and for 24 bits we have 16777216. With 1 bit we have two possible options (1, 0) with 2 bits we have 4 (00, 01, 10, 11), etc… then we conclude that for n bits we have 2^n different options. You’ve probably studied how this happens analyzing the number of possible amplitudes expressed by different number of bits. This is an important distinction because it implies that quantization error doesn’t have a constant behavior but a signal dependent behavior as we’ll see later.Īs expected this quantization error is directly affected by the number of available steps in our system and because the number of steps available is defined by the bit-depth so is the quantization error. This error is commonly known as quantization noise, although I prefer the term quantization distortion because although noise and distortion are both aberrations in our signals, distortion is characterized by being signal dependent while noise isn’t. Accordingly, we are introducing an error (0.0023) into our signal a deviation from its real value that represents some loss of information. At each sample our ADC (analog to digital converter) determines that an analog value (1.0123) is close enough to a digital quantization step (1.01) to be represented by it. Because of this, when digitizing a signal we encounter discrepancies between the analog true values and their digital representations. At this point you should know that digital signals have a finite set of possible steps to represent signal amplitudes known as quantization steps.
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