Yes, I've had problems with aliasing too, and would be grateful for any ways to get around it.

Just to check my understanding of it: If I try to synthesize a 66150Hz sine wave at 44100Hz sampling-rate (after doodline on a bit of paper) the samples end up looking like a 22050Hz sine wave.

As Matt points out, the obvious way to get around this is not to try and create such high frequencies.

But unfortunately, square-waves and saw-tooth waves (for example) have ridiculously high harmonics, whether you want them or not. When you represent them at a certain bit-rate, all the harmonics above half the sampling rate gets aliased somewhere where you don't want them.

So how does this link up with Matt's suggestion that aliasing doesn't happen in the purely digital domain? Well I guess in a sense the square and saw-tooth waves in my head/formulae are analogue (i.e. infinite bandwidth.) and realising them in the digital domain involves quantising and sampling from that. So it is certainly aliasing.

The only way I can think to get around it is to build all complex tones from sine-waves, which is a little calculation intensive, and doesn't solve the quantisation problem.

Trevor

PS I tried to pose that as a question, but now suspect I've just joined an argument... Rather than delete it, I've marked it 'off-topic' as an acknowledgement of that. Please don't flame...

Message: 5 From: "matthew jones" m.jones@signal.qinetiq.com To: "Larry Troxler" lt@westnet.com, "PD-List" pd-list@iem.kug.ac.at, "Johannes Taelman" j0@advalvas.be Subject: Re: [PD] band-limited square wave Date: Mon, 8 Mar 2004 13:40:55 -0000

interesting arguments larry. But you're definitely wrong....! ;) how amusing.

For the next experiment, imagine that you are sampling a non-filtered square wave through an ADC. In other words, there is no anti-aliasing filter in place. What do you expect the digitized samples to look like

in

this case? Would they not be exactly the same as a square wave

constructed

entirely in the digital domain?

well, this is where aliasing will occur. aliasing MEANING more than one analogue signal will give rise to the observed digital signal. aliasing is MEANINGLESS if you're already in the digital domain. it refers to going from a high bandwidth to a lower bandwidth.

The reconstruction filters in an DAC are there to remove all analogue frequency content above nyquist, without affecting the frequency

content

below nyquist. So, yes it would ripple, but not in the right way.

no, this would be in the right way! the ripples are due to filtering out all above Nyquist as you say, which is what we want...!!! that IS naturally bandlimited.

A bandwith-limited square digital osc sould give the same output as ADC'ing a squarly analog square wave. So antialiasing filters are

required. ?? what ?? sorry, don't get u

And it's not the only way to get aliasing: nonlinearities

(waveshaping),

all kinds of modulation (fm, am,...), and much more. Digital sine oscillators and digital filters are bandwith-limited by

nature.(<-AGREED)

First, set your sampling rate to 44100Hz. Now take a digital sine oscillator, say [osc~] in PD and set its frequency to 30000Hz. What do you expect to hear from the DAC? A sine wave at 30000Hz, even though that frequency is higher than fs/2? No, you will in fact here an aliased sine at 14100Hz - do you agree. But wait, we constructed

this

signal entirely in the digital domain, and yet we have aliasing!

well, in DSP terminology, this isn't aliasing. of course in the digital domain you can't synthesise ANYTHING higher than nyquist, it's impossible. if your own code runs functions that attempt to do that, but end up doing something else (ie return numbers that represent tones that have the same reflected frequency as the equivalent aliased signals) then that function is not producing aliased outputs, but correctly generating frequencies that are lower than YOU intended. again, aliasing only applies to going from high bandwidth to low bandwidth, so if you're sample rate hasn't changed, you're not getting aliasing. this is getting pedantic, I can see what you're getting at but at the end of the day:-

constructing a bunch of numbers in the digital domain cannot produce 'aliased' outputs because the bandwidth has not changed. reconstruction will 'perfectly' bandlimit the output (although perfect sinc functions are impossible) everytime.

Matt

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