When Adding Noise Helps

It’s a counterintuitive result that you might need to add noise to an input signal to get the full benefits from oversampling in analog to digital conversion. [Paul Allen] steps us through a simple demonstration of why this works on his blog. If you’re curious about oversampling, it’s a good read.

Oversampling helps to reduce quantization noise, which is the sampling equivalent of rounding error. In [Paul’s] one-bit ADC example, the two available output values are zero volts and one volt. Any analog signal between these two values is rounded off to either zero or one, and the resulting difference is the quantization error.

In oversampling, instead of taking the bare minimum number of samples you need you take extra samples and average them together. But as [Paul] demonstrates, this only works if you’ve got enough noise in the system already. If you don’t, you can actually make your output more accurate by adding noise on the input. That’s the counterintuitive bit.

We like the way he’s reduced the example to the absolute minimum. Instead of demonstrating how 16x oversampling can add two bits of resolution to your 10-bit ADC, it’s a lot clearer with the one-bit example.

[Paul’s] demo is great because it makes a strange idea obvious. But it got us just far enough to ask ourselves how much noise is required in the system for oversampling to help in reducing quantization noise. And just how much oversampling is necessary to improve the result by a given number of bits? (The answers are: at least one bit’s worth of noise and 22B, respectively, but we’d love to see this covered intuitively.) We’re waiting for the next installment, or maybe you can try your luck in the comment section.

Vintage DACs And A Raspberry Pi


Before the days of iPod docks in every conceivable piece of audio equipment, most devices were actually built very well. Most shelf top equipment usually came with well designed circuits using quality components, and late 90s CD players were no exception. [Mariosis] heard of some very nice DACs found in some of these units and decided to take one out for a spin. He’s using a Raspberry Pi to play audio with the DAC found in a late 90s Kenwood CD player.

After fortune favored a CD player with a dead drive on [Mariosis]’ workbench, he dug up the service manual and found some interesting chips – a PCM56 DAC, a little bit of logic, and an SM5807 oversampling chip that does all the conversion for the DAC.

This oversampling chip uses an I2S – not I2C – bus to carry the data from the CD to the DAC. There is, of course, an I2S driver for the Raspi, but the first attempts at playing audio didn’t result in anything. It turned out there was a problem with what the oversampler expected – the ‘standard’ I2S signal delays the data one tick behind the LRCLK signal.

There are two ways to fix this problem: programming a kernel driver, or building some custom logic to fix the problem. Obviously breaking out some flip-flops and NOR gates was the cooler option, giving [Mariosis] a great sounding stereo with a vintage DAC.