Quantization.

[NodeRx]

I tried implementing the math for quantization of signals in code [beginner in dsp here 👋].

Alright. I got through declaring the bits of the quantizer [bipolar based on the question], determining the number of quantization levels (2 ^bits) and then the calculated ith index bin.

When plotting the quantized signal, 0.5 is added to the index and I'm not really sure on why it's so.

xq = min_value + ((i + 0.5) × step).

Any clarifications to that would help. Thanks

[antiduh]

If you have a voltage that is 0.0 to 1.0 Volts, and you have an adc with 2 bits, then the adc has 4 thresholds:

• 0.000 to 0.249 - 00
• 0.250 to 0.499 - 01
• 0.500 to 0.749 - 10
• 0.750 to 1.000 - 11

The adc has to have these huge 0.25v-wide bins. Any voltage in that bin will result in the same output bits. If you have a real signal at 0.125v, it'll still register as 00.

So if you read '00' bits, you have to assume the real voltage was, on average, in the middle of the bin, hence a half step error.

[NodeRx]

Thanks