Design Article
Which filters are noisier – analog or digital? (Part 2)
Kendall Castor-Perry, Principal Architect, Cypress Semiconductor Corp.
8/19/2011 3:56 PM EDT
In Part 1 of this pair of articles, we ran SPICE noise simulations on a simple second order lowpass filter. We saw that there is something fundamental about the 'hold' that the filter's capacitor network has over the total output noise level. Scaling all the filter's resistors by a constant factor, to change the cutoff frequency of the filter without changing any of the capacitor values, leaves the total noise voltage unchanged. With practical amplifiers, the noise level is degraded from the ideal case, but it's still pretty straightforward to predict what they will be.
Can we make useful noise level predictions if our filters are implemented digitally? In modern electronic product design, one can often make a choice between analog and digital signal processing. With analog processing, the filtering and other signal manipulation is done before converting the signal to digital (if it's indeed ever converted). The digital model involves converting as early as possible in the signal chain, doing the processing in the digital domain, and then perhaps converting back to analog.
The device I spend most time solving people's problems with, Cypress's PSoC3, has op amps for constructing analog active filters, and also a fast digital filter engine that can implement a wide range of filters in the digital domain. To help make the choice, systems engineers need a reliable method for directly comparing the noise performance of analog and digital filtering approaches.
We're taught that “going digital” creates quantization noise, which is the per-sample error involved in fitting a value of arbitrarily high precision into a lower-resolution number system, usually an N-bit binary system with 2N available states. For any real-world signal, this error is completely uncorrelated with the actual signal and therefore can be treated as random noise, whose value is uniformly distributed between -0.5 LSB and +0.5 LSB. Textbooks demonstrate both that this noise is 'white’ (has a frequency-independent spectral density), and also that the rms value is {LSB}/√(12), when integrated from DC to Nyquist.
Quantization noise is different from analog noise in one particular way: it’s deterministic. Process an identical signal a second time in your system and you’ll get the same error again. In an analog system, the noise is different every time.
This article explores the critical filter issues in detail; to read the complete article, click here.
About the author
Kendall Castor-Perry is a Principal Architect at Cypress Semiconductor Corp., doing mixed-signal system analysis and design for the PSoC platform. Kendall uses decades of experience in analog engineering, filtering and signal processing to capture signals across many domains, extract the information from them and do something useful with it.
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Frank Eory
8/19/2011 8:31 PM EDT
Good article, and thanks for detailing your simulation methodology that compares analog & digital filter noise performance.
The conclusion is a good one to point out, for the benefit of digital filtering "newbies," but I hope most engineers who have been doing DSP for awhile are well aware of the pitfalls of the Direct Form implementation for cases where the poles and zeros tend toward extreme values.
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kendallcp
8/20/2011 5:26 PM EDT
I agree - "once bitten, twice shy". The feedback I'm getting, from the many engineers that don't regularly practice the filtering arts, is that this doesn't get covered in 'basic training' at University. Students are presented with various topologies, both digital and analogue, but aren't given an understanding of how signal-handling performance is affected.
And there's a lot of engineers who wouldn't consider a filter operating at 30Hz to be an extreme case in a digital audio system - it might set off alarm bells for you and I, but it seems perfectly reasonable to some people.
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Dr DSP
8/24/2011 2:58 PM EDT
The book recommended in part 1 is an excellent addition to a DSP library- Doug Self’s new book “The Design of Active Crossovers”. Check it out.
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The Escapist
8/25/2011 1:16 PM EDT
Good article and thanks for it.
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the lavender fan
8/29/2011 7:23 PM EDT
I was wondering if the author has done any experiments to verify the results. After all, it's a simulation, and some assumptions are made along the way.
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kendallcp
8/30/2011 5:37 PM EDT
It's a good point, and the answer is, not personally, but the results were compared against someone else's direct measurements, and FFT-based dynamic simulations, both of the Direct Form and on a less noise-challenged topology, as part of our audio filter research program. It's notoriously difficult to get meaningful, stable measurements of quantization noise, since the noise needs to be carefully separated out from the signal that triggered it. The resistor-equivalence method idealizes away a lot of those details, and its function is to evade these difficulties and give a good base case for comparison of different approaches, not prediction to the last milli-dB.
In terms of it being a simulation, a difference between the predicted results and measurement would reflect inadequacies in the assumptions (as you say), not in the concept of simulation itself. You sometimes see simulation getting beaten up as if there was something inherently flawed with it. We do intrinsic simulation in our everyday lives when we use a simple model of some real-world process to estimate some outcome. It's just maths; sensible-in, sensible-out. Garbage-in, garbage-out.
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