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Integrate countersign resolution

hello guys today I am going to discuss the increasing of the solution of an ADC with over sampling and how much power simply needs to be done to increase the resolution by one bit and why so let's look at this two bit ADC and over here I want to explain one three requisite that a signal noise should be bigger than a smallest quantization step that is how much voltage increment or decrement does it take to change the lowest pit and for this two bit ADC that I have over here here is the AVC output value here is the voltage it's 0.25 fourth so in order for this method to work for this two bit ADC we need a signal noise of at least 0.25 volts if it's more than this it's okay but if it's less than this this method will not work and so let's go further with it here we have nice here we have an error of 0.125 fault and the error power is 0.125 scared that's on zero point zero one five six to five now let's take another ABC that's a three bit ADC and see what happens here here we have increased fun bit so our error is reduced by half it's not 0.125 now but 0.0625 and that error power is zero point two two six two five scared that zero point zero zero three nine zero six two five that's around four times less than the power noise power that we had because of this quantization when we had a two bit so the quantization noise is YouTube by a factor of four just for general information the signal-to-noise ratio is 6 point zero two n plus one point seven six TV the zero points this six point zero two also represents the lowering of noise by a factor of four so let's move on to our over sampling over here we have a graph of frequency against the power of the signal at this frequency and the quantization noise is uniformly distributed over the whole range and it remains constant it does not matter what frequency of sampling you have the quantization noise is always the same so here we have our signal and here we have a low-pass filter so that we can get rid of the noise so what happens when you sample it at a higher frequency let's say we sample it at frequency four times higher than the frequency in the first case so now what happens is as the base has increased by a factor of four here it was two FS here it said it FS as height or the magnitude of a noise power goes down by four and when we use this filter here which is the same filter as here the frequency is the same let's say that this is f of X here it's also f of X the better the closer it is to our...