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<div><br class=""><blockquote type="cite" class=""><div class="">On 14 Dec 2023, at 21:27, Gordonjcp <<a href="mailto:gordonjcp@gjcp.net" class="">gordonjcp@gjcp.net</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="">On Thu, Dec 14, 2023 at 03:53:39PM +0000, Mike Bryant wrote:<br class=""><blockquote type="cite" class="">If by 'continuous' you mean DC, then there is an image before filtering - at the sampling rate :-)<br class=""><br class=""></blockquote><br class="">No. If you've got a DC output from a DAC, it's just that - DC. There's no change in level. You're writing the same value to it over and over, and it does not change.<br class=""><br class="">The output from a DAC is continuous. It does not have steps. It has steep slopes, but not steps. Even then, that's not going to allow the sample rate to leak out particularly. If you pick a pathological case where your DAC is swinging fully positive for one sample time and fully negative the next, you'll get a signal at half the sample rate. Even though that's a squarewave right at Nyquist, it still won't alias, because the harmonics are being generated *after* the discrete-time part.<br class=""><br class="">So I'm having a hard time seeing where these images could come from, or how you'd ever detect them. You definitely couldn't hear them.<br class=""></div></div></blockquote></div><div class=""><br class=""></div><div class="">The basic principle is that a given set of DAC output samples don't have a single interpretation, but many. Yes, the samples *could* represent a waveform below Nyquist, and they'd all be exactly where we expect them to be. But they *could equally well* represent a waveform *above* Nyquist and they'd *still* all be exactly where we expect them to be. Here's a little diagram demonstrating the idea - which of these two sinewaves was the intended output?</div><div class="">This can be extended indefinitely to higher and higher frequencies. If we want to limit the DAC's output to signals within a certain band, we *actually have to do that*, we can't assume it is already done for us. Maybe we can't *hear* them, but that doesn't mean we didn't just create a ton of ultrasonic noises, because we most likely did.</div><div class=""><br class=""></div><div class="">At least, that's how I understand it. If that's not right, perhaps someone else can correct me.</div><div class=""><img class="lazyautosizes ls-is-cached wp-post-image size-goodlife-post-style1 thb-lazyload lazyloaded attachment-goodlife-post-style1" alt="" decoding="async" fetchpriority="high" sizes="770px" data-src="https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained.jpg" data-sizes="auto" data-srcset="https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained.jpg 445w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-80x55.jpg 80w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-320x219.jpg 320w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-249x170.jpg 249w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-220x150.jpg 220w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-40x27.jpg 40w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-160x109.jpg 160w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-20x14.jpg 20w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-15x10.jpg 15w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-439x300.jpg 439w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-13x9.jpg 13w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-385x263.jpg 385w" srcset="https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained.jpg 445w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-80x55.jpg 80w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-320x219.jpg 320w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-249x170.jpg 249w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-220x150.jpg 220w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-40x27.jpg 40w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-160x109.jpg 160w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-20x14.jpg 20w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-15x10.jpg 15w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-439x300.jpg 439w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-13x9.jpg 13w, https://producelikeapro.com/blog/wp-content/uploads/2020/05/Digital-Audio-Basics-Aliasing-Explained-385x263.jpg 385w" apple-inline="yes" id="4E47CD08-C95F-4D79-84F9-27886556809C" src="cid:B64F23E4-BC13-45C2-87E4-0684F225B4E4"></div></body></html>