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Actually, that formula is specifically for an unmodulated sine wave at full scale just prior to clipping. This SNR result provides a reference point as to what the total quantization noise power will relative to that full scale sine wave at the input to the ADC, and that noise power will be at that similar total power level relative to that full scale ...


SNR should only be concerned within the spectrum of interest (Signal in Band to Noise in Band) as it is assumed that the rest can be filtered out(and that we would ultimately or could ultimately decimate down to Nyquist filtering out all upper frequency components in the process and provide reasonably sharp frequency selectivity at the lower sampling rate). ...


% create complex white normal noise noise = randn(size(Signal)) + 1i*randn(size(Signal)); % calculate the gain for the noise noiseGain = rms(Signal)./rms(noise)*exp(-SNR(i)*log(10)/20); % add it SignalN = Signal + noiseGain*noise;


Upsampling is useful for noise shaping because it gives you some space in the spectrum for you to shape or steer the noise into. Suppose your application space is audio. You need to sample at least 40 kHz (or 44.1 or 48 kHz). So suppose it was upsampled to 96 kHz, instead. In the bit-reduction operation (quantization) much or most of that quantization ...


If you are taking about SNR 3 and 6 in dB scale then yes SNR of 6dB is double the power. In dB scale increment of 3dB implies doubling of power.

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