The Fastest Fourier Transform In The West

An interesting aspect of time-varying waveforms is that by using a trick called a Fourier Transform (FT), they can be represented as the sum of their underlying frequencies. This mathematical insight is extremely helpful when processing signals digitally, and allows a simpler way to implement frequency-dependent filtration in a digital system. [klafyvel] needed this capability for a project, so started researching the best method that would fit into an Arduino Uno. In an effort to understand exactly what was going on they have significantly improved on the code size, execution time and accuracy of the previous crown-wearer.

A complete real-time Fourier Transform is a resource-heavy operation that needs more than an Arduino Uno can offer, so faster approximations have been developed over the years that exchange absolute precision for speed and size. These are known as Fast Fourier Transforms (FFTs). [klafyvel] set upon diving deep into the mathematics involved, as well as some low-level programming techniques to figure out if the trade-offs offered in the existing solutions had been optimized. The results are impressive.

Fastest FFT code benchmarking results in ms
Benchmarking results showing speed of implementation versus the competition (ApproxFFT)

Not content with producing one new award-winning algorithm, what is documented on the blog is a masterclass in really understanding a problem and there are no less than four algorithms to choose from depending on how you rank the importance of execution speed, accuracy, code size or array size.

Along the way, we are treated to some great diversions into how to approximate floats by their exponents (French text), how to control, program and gather data from an Arduino using Julia, how to massively improve the speed of the code by using trigonometric identities and how to deal with overflows when the variables get too large. There is a lot to digest in here, but the explanations are very clear and peppered with code snippets to make it easier and if you have the time to read through, you’re sure to learn a lot!¬† The code is on GitHub here.

If you’re interested in FFTs, we’ve seen them before around these parts. Fill your boots with this link of tagged projects.

three sensory bridge audio spectrum analyzers, one in use with a lit LED array plugged in, the other facing the camera and leaning against the third, all on a table

The Sensory Bridge Is Your Path To A Desktop Rave

[Lixie Labs] are no strangers to creating many projects with LEDs or other displays. Now they’ve created a low latency music visualizer, called the Sensory Bridge, that creates gorgeous light shows from music.

The Sensory Bridge has the ability to update up to 128 RGB LEDs at 60 fps. The unit has an on-board MEMS microphone that picks up ambient music to produce the light show. The chip is an ESP32-S2 that does Fast Fourier Transform trickery to allow for real-time updates to the RGB array. The LED terminal supports the common WS2812B LED pinouts (5 V, GND, DATA). The Sensory Bridge also has an “accessory port” that can be used for hardware extensions, such as a base for their LED “Mini Mast”, a long RGB array PCB strip.

The unit is powered by a 5 V 2 A USB-C connector. Different knobs on the device adjust the brightness, microphone sensitivity and reactivity of the LED strip. One of the nicer features is its “noise calibration” that can record ambient sound and subtract off the background noise frequency components to give a cleaner music signal. The Sensory Bridge is still new and it looks like some of the features are yet to come, like WiFi communication, accessory port upgrades and 3.5 mm audio input to bypass the on-board microphone.

The stated goals of the Sensory Bridge are to provide an open, powerful and flexible platform. This can be seen with their commitment to releasing the project as open source hardware, providing firmware, PCB design files and even the case STLs under a libre/free license. Audio spectrum analyzers are a favorite of ours and we’ve seen many different iterations ranging from ones using Raspberry Pis to others use ESP32s.

Video after the break!

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Teensy Spectrum Analyzer Has 170 Channels

While high-fidelity audio has come a long way in the past several decades, a lot of modern stereo equipment is still missing out on some of the old analog meters that were common on amplifiers and receivers of the 60s through the 80s. Things like VU meters don’t tend to be common anymore, but it is possible to build them back in to your sound system with the help of some microcontrollers. [Mark] shows us exactly how to reclaim some of the old-school functionality with this twin audio visualizer display.

Not only does this build include two displays, but the microcontroller is keeping up with 170 channels in real-time in order to drive the display. What’s more impressive is that it’s being done all on a Teensy 4.1. To help manage all of the data and keep the speed as fast as possible it uses external RAM soldered to the board, and a second Teensy audio board is used to do the real time FFT analysis. Most of the channels are sent to the display hosting the spectrum analyzer but two are reserved for left and right stereo VU meters on the second display.

The project from [Mark] is originally based on this software from [DIYLAB] so everything is open-source. While it was originally built for a specific piece of hardware, [Mark] has it set up with a line in and line out plus a microphone input so it can be used for virtually any audio hardware now. For another take on the classic VU meter, take a look at this design based on an Arudino instead.

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Balancing A Motor With An Oscilloscope

With all things in life, one must seek to achieve balance. That may sound a little like New Age woo-woo, but if you think it’s not literally true, just try tolerating a washing machine with a single comforter on spin cycle, or driving a few miles on unbalanced tires.

Anything that rotates can quickly spin itself into shrapnel if it’s not properly balanced, and the DIY power tools in [Matthias Wandel]’s shop are no exception. Recent upgrades to his jointer have left the tool a bit noisy, so he’s exploring machine vibrations with this simple but clever setup. Using nothing but a cheap loudspeaker and an oscilloscope, [Matthias] was able to characterize vibrations in a small squirrel-cage blower — he wisely chose to start small to validate his method before diving into the potentially dangerous jointer. There was quite a lot to be learned from the complex waveforms coming back from the transducer, analysis of which was greatly helped by the scope’s spectrum analyzer function. The video below shows the process of probing various parts of the blower, differentiating spectral peaks due to electrical noise rather than vibration, and actually using the setup to dynamically balance the fan.

We’d rate this as yet another handy shop tip from [Matthias], and we’ll be looking out for the analysis of his jointer. Want to do the same but you don’t have an oscilloscope? No problem — an earbud and Audacity might be all you need.

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Stanislaw playing notes on his MIDI keyboard, with the LEDs on the LED strip lighting up right above the note he's playing, driven by the Raspberry Pi that runs a script based on the Pianolizer toolkit

Pianolizer Helps Your Musical Projects Distinguish Notes

[Stanislaw Pusep] has gifted us with the Pianolizer project – an easy-to-use toolkit for music exploration and visualization, an audio spectrum analyzer helping you turn sounds into piano notes. You can run his toolkit on a variety of different devices, from Raspberry Pi and PCs, to any browser-equipped device including smartphones, and use its note output however your heart desires. To show off his toolkit in action, he set it up on a Raspberry Pi, with Python code taking the note data and sending color information to the LED strip, displaying the notes in real time as he plays them on a MIDI keyboard! He also created a browser version that you can use with a microphone input or an audio file of your choosing, so you only need to open a webpage to play with this toolkit’s capabilities.

He took time to make sure you can build your projects with this toolkit’s help, providing usage instructions with command-line and Python examples, and even shared all the code used in the making of the demonstration video. Thanks to everything that he’s shared, now you can add piano note recognition to any project of yours! Pianolizer is a self-contained library implemented in JavaScript and C++ (which in turn compiles into WebAssembly), and the examples show how it can be used from Python or some other language.

[Stanislaw] also documented the principles behind the code, explaining how the note recognition does its magic in simple terms, yet giving many insights. We are used to Fast Fourier Transform (FFT) being our go-to approach for spectral analysis, aka, recognizing different frequencies in a stream of data. However, a general-purpose FFT algorithm is not as good for musical notes, since intervals between note frequencies become wider as frequency increases, and you need to do more work to distinguish the notes. In this toolkit, he used a Sliding Discrete Fourier Transform (SDFT) algorithm, and explains to us how he derived the parameters for it from musical note frequencies. In the end of the documentation, he also gives you a lot of useful references if you would like to explore this topic further!

What are you going to build with this? Maybe, a box that records you playing the flute and instantly turns it into sheet music? Or, perhaps, an AI that continues the song for you when you stop?

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Woodworking, Blinkenlites, And FFT’s Dance To The Music

We all have that one project on our minds that we’d love to build if we could just find the right combination of time, energy, and knowledge to dive right in. For [Jonathan], that project was a sound sculpture that’s finally made it from concept to complete. [Jonathan] describes the sound sculpture as the culmination of a decade of learning, and in a moment you’ll understand why.

The sculpture itself is a beautiful display of woodwork mixed with what appear to be individually addressable LED’s. The varying length of the individual enclosures evokes the idea that the sculpture is somehow involved in the sound production, which is a nice touch.

An Adafruit microphone module feeds detected audio into a PSoC 5 microcontroller. You’d expect that [Jonathan] just used one of the FFT libraries that are available. But you’ll recall that this was the culmination of a decade of learning- why so? Because [Jonathan] went through the process of procuring his own grey hairs by writing his own FFT function. A homebrew FFT function¬†and blinkenlites? What’s not to love!

You may also enjoy this discussion of Sine Waves, Square Waves, and FFT’s with our own Bil Herd.

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FFT display on 16x16 RGB LED grid

Art Project Fast And Fouriously Transforms Audio Into Eye Candy

Fast Fourier Transforms. Spectrum Analyzers. Waterfall displays. Not long ago, such terms were reserved for high end test gear. But oh, how things have changed! It’s no surprise to many Hackaday readers that modern microcontrollers have transformed the scene as they become more powerful and as a result are endowed with more and more powerful software libraries. [mircemk] has used such a library along with other open source software combined with mostly off the shelf hardware to create what he calls the DIY FFT Spectrum Analyzer. Rather than being a piece of test gear, this artful project aims to please the eye.

The overall build is relatively simple. Audio is acquired via a line-in jack or a microphone, and then piped into an ESP32. The ESP32 runs the audio through the FFT routine, sampling, slicing, and dicing the audio into 16 individual bands. The visual output is displayed on a 16 x 16 WS2812 Led Matrix. [mircemk] wrote several routines for displaying the incoming audio, with a waterfall, a graph, and other visualizations that are quit aesthetically pleasing. Some of them are downright mesmerizing! You can see the results in the video below the break.

Of course the build doesn’t stop with slapping some hardware and a few passive components together. To really be finished, it needs to be encased in something worth displaying. [mircemk] does not disappoint, as a beautiful 3D-printed enclosure wraps it all up nicely.

We think that the final product is great, and it reminds us of some of the very things that inspired us early on in our hacking careers. We would love to see this project integrated with an Interactive Musical Art Installation of any kind, the more esoteric the better. Perhaps a 555 timer synth could fit the bill? Be sure to share your own hacks with us via the Tip Line!

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