{"id":8373,"date":"2025-02-18T14:37:37","date_gmt":"2025-02-18T12:37:37","guid":{"rendered":"https:\/\/www.tonmeister.ca\/wordpress\/?p=8373"},"modified":"2025-02-25T15:13:22","modified_gmt":"2025-02-25T13:13:22","slug":"bit-depth-conversion-part-3","status":"publish","type":"post","link":"https:\/\/www.tonmeister.ca\/wordpress\/2025\/02\/18\/bit-depth-conversion-part-3\/","title":{"rendered":"Bit depth conversion: Part 3"},"content":{"rendered":"\n

Converting fixed point to floating point<\/h2>\n\n\n\n

In Part 1 <\/a>of this series, I talked about three different options for converting from a fixed-point representation to another fixed-point representation with a bigger bit depth.<\/p>\n\n\n\n

This happens occasionally. The simplest case is when you send a 16-bit signal to a 24-bit DAC. Another good example is when you send a 16-bit LPCM signal to a 24- or 32-bit fixed point digital signal processor. <\/p>\n\n\n\n

However, these days it’s more likely that the incoming fixed-point signal (incoming signals are almost always<\/strong> in a fixed-point representation) is converted to floating point for signal processing. (I covered the differences between fixed- and floating-point representations in another posting<\/a>.)<\/p>\n\n\n\n

If you’re converting from fixed point to floating point, you divide the sample’s value by 2^(nBits-1). In other words, if you’re converting a 5-bit signal to floating point, you divide each sample’s value by 2^4, as shown below.<\/p>\n\n\n

\n
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Figure 1. Converting a 5-bit fixed point signal to floating point<\/figcaption><\/figure>\n<\/div>\n\n\n

The reason for this is that there are 2^(nBits-1) quantisation levels for the negative portions of the signal. The positive-going portions have one fewer levels due to the two’s complement representation (the 00000 had to come from somewhere…).<\/p>\n\n\n\n

So, you want the most-negative value to correspond to -1.0000 in the floating point world, and then everything else looks after itself.<\/p>\n\n\n\n

Of course, this means that you will never hit +1.0. You’ll have a maximum signal level of 1 – 1\/2^(nBits-1), which is very close. Close enough.<\/p>\n\n\n\n

The nice thing about doing this conversation is that by entering into a floating point world, you immediately gain resolution to attenuate and headroom to increase the gain of the signal – which is exactly what we do when we start processing things.<\/p>\n\n\n\n

Of course, this also means that, when you’re done processing, you’ll need to feed the signal out to a fixed-point world again (for example, to a DAC or to an S\/PDIF output). That conversion is the topic of Part 4.<\/p>\n","protected":false},"excerpt":{"rendered":"

Converting fixed point to floating point In Part 1 of this series, I talked about three different options for converting from a fixed-point representation to another fixed-point representation with a bigger bit depth. This happens occasionally. The simplest case is when you send a 16-bit signal to a 24-bit DAC. Another good example is when […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[63,4,59],"tags":[],"class_list":["post-8373","post","type-post","status-publish","format-standard","hentry","category-analysis","category-audio","category-digital-audio"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p48hIM-2b3","_links":{"self":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/comments?post=8373"}],"version-history":[{"count":2,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8373\/revisions"}],"predecessor-version":[{"id":8387,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8373\/revisions\/8387"}],"wp:attachment":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/media?parent=8373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/categories?post=8373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/tags?post=8373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}