preliminary analysis of achievable SNR
Problem:
Initial work indicates that using 10X magnification, we are able to achieve sampling frequencies of several hundred kHz and upwards. However, lateral resolution appears to be quite low and the question has been raised if whether the high sampling rate overcomes this quantization error in a manner similar to delta-sigma modulation.
Analysis:
Differential pulse code modulation and delta-sigma modulation operate using the following principles:
1) transmitter/ADC: Using a prediction method, the quantized value of the current input is estimated based on past values. The difference ("delta") between the predicted quantized value and the actual analog value is quantized and stored/transferred digitally.
2) receiver/DAC: Using an identical prediction method to the transmitter/ADC, the quantized value of the current output is estimated based on past output values. By adding these values ("sigma") to the difference values determined in (1), a quantized version of the original output signal is obtained.
3) Quantization noise is further reduced by noise shaping.
It is clear that DPCM or delta-sigma modulation work by attempting to transmit/store the derivative of the analog signal. Since OAR cannot make comparisons with the actual analog position of the groove with the quantized groove, (1) does not occur and the principles do not apply.
However, oversampling alone provides the benefit of lowering the average noise floor in the spectrum. The SNR is identical to a non-oversampled signal, but since the bandwidth is wider, the noise energy is spread out over a larger range. Therefore, LPFing the recovered signal to remove quantization noise outside of the bandwidth of interest increases SNR. With appropriate filtering, each time the sampling rate is doubled we will reduce the noise in the band of interest by 3dB, i.e. gain 0.5 bit of resolution in the band of interest.
There is a good online reference here:
http://www.maxim-ic.com/appnotes.cfm?appnote_number=1870&CMP=WP-10
Initial work indicates that using 10X magnification, we are able to achieve sampling frequencies of several hundred kHz and upwards. However, lateral resolution appears to be quite low and the question has been raised if whether the high sampling rate overcomes this quantization error in a manner similar to delta-sigma modulation.
Analysis:
Differential pulse code modulation and delta-sigma modulation operate using the following principles:
1) transmitter/ADC: Using a prediction method, the quantized value of the current input is estimated based on past values. The difference ("delta") between the predicted quantized value and the actual analog value is quantized and stored/transferred digitally.
2) receiver/DAC: Using an identical prediction method to the transmitter/ADC, the quantized value of the current output is estimated based on past output values. By adding these values ("sigma") to the difference values determined in (1), a quantized version of the original output signal is obtained.
3) Quantization noise is further reduced by noise shaping.
It is clear that DPCM or delta-sigma modulation work by attempting to transmit/store the derivative of the analog signal. Since OAR cannot make comparisons with the actual analog position of the groove with the quantized groove, (1) does not occur and the principles do not apply.
However, oversampling alone provides the benefit of lowering the average noise floor in the spectrum. The SNR is identical to a non-oversampled signal, but since the bandwidth is wider, the noise energy is spread out over a larger range. Therefore, LPFing the recovered signal to remove quantization noise outside of the bandwidth of interest increases SNR. With appropriate filtering, each time the sampling rate is doubled we will reduce the noise in the band of interest by 3dB, i.e. gain 0.5 bit of resolution in the band of interest.
There is a good online reference here:
http://www.maxim-ic.com/appnotes.cfm?appnote_number=1870&CMP=WP-10
posted by Simon at 2:26 PM
0 comments
