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How to decide threshold for quantizing of signal detection?

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Advanced Member level 3
Jun 21, 2002
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adc quantization levels

How do I decide the threshold for quantizing for signal detection.
The MSB (sign bit) is easy, i.e., zero cross over but how about the magnitude bit?

The link is a good one.

The SNR of a "single bit quantized" signal is supposed to decrease by 2dB (theoretically) but what I observe is far greater than 2dB on spectrum analyzer. Is the theory wrong or my observation.

If by "single bit quantized" you mean a sigma-delta type A2D (or D2A for that matter), then the SNR you get depends on the over-sampling ratio (i.e. the ratio between your sampling frequency and Nyquist frequency). I'm not aware of any 2dB mandatory penalty.

2 dB

The 2 dB comes from hard limiting the signal. This reduces the SNR by 2 dB over keeping the system linear. This is from purely analog signal processing of radar and sonar type signals where you are looking for the presence or absence of a signal. It may be misapplied to the area of selecting the number of bits of an ADC.

Hi flautulent,
Is there any general reference for quantizing for signal detection, effect of sampling for detection and tracking.

My application is in the area of GPS. If I were to quantize to 1 bit the received signal, I thought the response would be 2dB worse. I find it to be much more. A reference on this will definitely help.


no general ones

I do not have any specific references in mind. The 2 dB for hard limiting means that the received signal has to be 2 dB higher to get the same probability of detecting a radar or sonar return.

As far as ADC noise, the first bit gives you something like 7.8 dB or so and the rest give you 6 dB each. Since even bpsk requires about 10-15 dB snr you will have to use several bits in your ADC.

Maxim has an ap note on this **broken link removed**

In general some should look at the dynamic range of the signal to be quantized. For instance if some assume a sensor with signal of 1 mVrms and noise of 10 nVrms over the sensor signal bandwidth, the dynamic range is 10^5. For an ADC to accuratelly quntize such signal, the ADC quantization noise (Q/SqRt(12)) RTI should be at least three times smaller than the sensor noise, and the maximuum input (Q*2^N) should be larger than the sensor signal:

3*Q/SqRt(12) = SNoise (or SNoise = Q) and Q*2^N = SSignal


SSignal/SNoise = SNR = 2^N

hence the ADC resolution should be at least

N = ceil( log2(SNR) ) or N = ceil(20*log10(SNR)/20*log10(2))

assuming Nyquist sampling @ twice the sensor signal bandwidth.

In our example N should be at least 17 bit.

Hope this is helpfull.

The explanations are good, but what I am looking is for signal below noise power. The voltage leves in the above explanations should be swapped. In such case how do we handle quantization?

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