What Is The Fourier Transform?

September 12, 2025 by John Elliot V 20 Comments

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform?

[Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation who founded the field of harmonic analysis in the early 1800s.

Fourier’s basic insight was that you can represent everything as a sum of very basic oscillations, where the basic oscillations are sine or cosine functions with certain parameters. [Shalma] explains that the biology of our ear can do a similar thing by picking the various notes out from a tune which is heard, but mathematicians and programmers work without the benefit of evolved resonant hairs and bone, they work with math and code.

[Shalma] explains how frequency components can be discovered by trial and error, multiplying candidate frequencies with the original function to see if there are large peaks, indicating the frequency is a component, or if the variations average to zero, indicating the frequency is not a component. [Shalma] tells how even square waves can be modeled with an infinite set of frequencies known as the Fourier series.

Taking a look at higher-dimensional problems [Shalma] mentions how Fourier transforms can be used for graphical compression by dropping the high frequency detail which our eyes can barely perceive anyway. [Shalma] gives us a fascinating look at the 64 graphical building blocks which can be combined to create any possible 8×8 image.

[Shalma] then mentions James Cooley and John Tukey and the development of the Fast Fourier Transform in the 1960s. This mathematical tool has been employed to study the tides, to detect gravitational waves, to develop radar and magnetic resonance imaging, and to support signal processing and data compression. Even quantum mechanics finds use for harmonic analysis, and [Shalma] explains how it relates to the uncertainty principle. The Fourier transform has spread through pure mathematics and into number theory, too.

[Shalma] closes with a quote from Charles Fefferman: “If people didn’t know about the Fourier transform, I don’t know what percent of math would then disappear, but it would be a big percent.”

If you’re interested in the Fourier transform and want to dive deeper we would encourage you to read The Fastest Fourier Transform In The West and Even Faster Fourier Transforms On The Raspbery Pi Zero.

Header image: Joseph Fourier, Attributed to Pierre-Claude Gautherot, Public domain.

Restoring A Vintage Intel Prompt 80 8080 Microcomputer Trainer

September 3, 2025 by John Elliot V 3 Comments

Over on his blog our hacker [Scott Baker] restores a Prompt 80, which was a development system for the 8-bit Intel 8080 CPU.

[Scott] acquired this broken trainer on eBay and then set about restoring it. The trainer provides I/O for programming, probing, and debugging an attached CPU. The first problem discovered when opening the case is that the CPU board is missing. The original board was an 80/10 but [Scott] ended up installing a newer 80/10A board he scored for fifty bucks. Later he upgraded to an 80/10B which increased the RAM and added a multimodule slot.

[Scott] has some luck fixing the failed power supply by recapping some of the smaller electrolytic capacitors which were showing high ESR. Once he had the board installed and the power supply functional he was able to input his first assembly program: a Cylon LED program! Making artistic use of the LEDs attached to the parallel port. You can see the results in the video embedded below.

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Front and back of the replacement OLED module by Sir68k

Reviving A Piece Of Yesterday’s Tomorrow

August 20, 2025 by Tyler August 12 Comments

To anyone who remembers Y2K, Sony’s MiniDisc format will probably always feel futuristic. That goes double for Sony’s MZ-RH1, the last MiniDisk recorder ever released, back in 2006. It’s barely larger than the diminutive disks, and its styling is impeccable. There’s a reason they’ve become highly collectible and sell for insane sums on e-Bay.

Unfortunately, they come with a ticking time-bomb of an Achilles heel: the first-generation OLED screens. Failure is not a question of if, but when, and many units have already succumbed. Fortunately enterprising hacker [Sir68k] has come up with replacement screen to keep these two-decade old bits of the future alive.

Replacement screens glowing brightly, and the custom firmware showing track info, something you’d never see on a stock RH1.

Previous revisions required some light surgery to get the twin OLED replacement screens to fit, but as of the latest incarnation (revision F+), it’s now a 100% drop-in replacement for the original Sony part. While it is a drop-in, don’t expect it to be easy. The internals are very densely packed, and fairly delicate — both in the name of miniaturization. You’ll need to break out the micro-screwdrivers for this one, and maybe some magnifiers if your eyes are as old as ours. At least Sony wasn’t gluing cases together back in 2006, and [Sir68k] does provide a very comprehensive repair guide.

He’s even working on new firmware, to make what many considered best MD recorder better than ever. It’s not ready yet, but when it is [Sir68k] promises to open-source the upgrade. The replacement screens are sadly not open source hardware, but they’re a fine hack nonetheless.

We may see more MiniDisc hacks as the format’s apparent revival continues. Things like adding Bluetooth to the famously-cramped internals, or allowing full data transfer — something Sony was unwilling to allow until the RH1, which is one of the reasons these units are so desirable.

2003 Samsung CD player playing a clear vs normal audio CD. (Credit: Adrian's Digital Basement)

Why Lorde’s Clear CD Has So Many Playback Issues

August 15, 2025 by Maya Posch 72 Comments

Despite the regularly proclaimed death of physical media, new audio albums are still being published on CD and vinyl. There’s something particularly interesting about Lorde’s new album Virgin however — the CD is a completely clear disc. Unfortunately there have been many reports of folks struggling to get the unique disc to actually play, and some sharp-eyed commentators have noted that the CD doesn’t claim to be Red Book compliant by the absence of the Compact CD logo.

The clear Lorde audio CD in all its clear glory. (Credit: Adrian's Digital Basement, YouTube) — The clear Lorde audio CD in all its clear glory. (Credit: Adrian’s Digital Basement, YouTube)

To see what CD players see, [Adrian] of Adrian’s Digital Basement got out some tools and multiple CD players to dig into the issue. These players range from a 2003 Samsung, a 1987 NEC, and a cheap portable Coby player. But as all audio CDs are supposed to adhere to the Red Book standard, a 2025 CD should play just as happily on a 1980s CD player as vice versa.

The first step in testing was to identify the laser pickup (RF) signal test point on the PCB of each respective player. With this hooked up to a capable oscilloscope, you can begin to see the eye pattern forming. In addition to being useful with tuning the CD player, it’s also an indication of the signal quality that the rest of the CD player has to work with. Incidentally, this is also a factor when it comes to CD-R compatibility.

While the NEC player was happy with regular and CD-R discs, its laser pickup failed to get any solid signal off the clear Lorde disc. With the much newer Samsung player (see top image), the clear CD does play, but as the oscilloscope shot shows, it only barely gets a usable signal from the pickup. Likewise, the very generic Coby player also plays the audio CD, which indicates that any somewhat modern CD player with its generally much stronger laser and automatic gain control ought to be able to play it.

That said, it seems that very little of the laser’s light actually makes it back to the pickup’s sensor, which means that along with the gain the laser output gets probably cranked up to 11, and with that its remaining lifespan will be significantly shortened. Ergo it’s probably best to just burn that CD-R copy of the album and listen to that instead.

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A red Sony PSP gaming console is shown, displaying the lines “Audio Mechanica,” “Brek Martin 2006-2025,” and “Waiting for Headphones.”

Running Guitar Effects On A PlayStation Portable

August 13, 2025 by Aaron Beckendorf 8 Comments

If your guitar needs more distortion, lower audio fidelity, or another musical effect, you can always shell out some money to get a dedicated piece of hardware. For a less conventional route, though, you could follow [Brek Martin]’s example and reprogram a handheld game console as a digital effects processor.

[Brek] started with a Sony PSP 3000 handheld, with which he had some prior programming experience, having previously written a GPS maps program and an audio recorder for it. The PSP has a microphone input as part of the connector for a headset and remote, though [Brek] found that a Sony remote’s PCB had to be plugged in before the PSP would recognize the microphone. To make things a bit easier to work with, he made a circuit board that connected the remote’s hardware to a microphone jack and an output plug.

[Brek] implemented three effects: a flanger, bitcrusher, and crossover distortion. Crossover distortion distorts the signal as it crosses zero, the bitcrusher reduces sample rate to make the signal choppier, and the flanger mixes the current signal with its variably-delayed copy. [Brek] would have liked to implement more effects, but the program’s lag would have made it impractical. He notes that the program could run more quickly if there were a way to reduce the sample chunk size from 1024 samples, but if there is a way to do so, he has yet to find it.

If you’d like a more dedicated digital audio processor, you can also build one, perhaps using some techniques to reduce lag.

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Whispers From The Void, Transcribed With AI

August 8, 2025 by Heidi Ulrich 14 Comments

‘Hearing voices’ doesn’t have to be worrisome, for instance when software-defined radio (SDR) happens to be your hobby. It can take quite some of your time and attention to pull voices from the ether and decode them. Therefore, [theckid] came up with a nifty solution: RadioTranscriptor. It’s a homebrew Python script that captures SDR audio and transcribes it using OpenAI’s Whisper model, running on your GPU if available. It’s lean and geeky, and helps you hear ‘the voice in the noise’ without actively listening to it yourself.

This tool goes beyond the basic listening and recording. RadioTranscriptor combines SDR, voice activity detection (VAD), and deep learning. It resamples 48kHz audio to 16kHz in real time. It keeps a rolling buffer, and only transcribes actual voice detected from the air. It continuously writes to a daily log, so you can comb through yesterday’s signal hauntings while new findings are being logged. It offers GPU support with CUDA, with fallback to CPU.

It sure has its quirks, too: ghost logs, duplicate words – but it’s dead useful and hackable to your liking. Want to change the model, tweak the threshold, add speaker detection: the code is here to fork and extend. And why not go the extra mile, and turn it into art?

Spatial Audio In A Hat

August 5, 2025 by Lewin Day 5 Comments

Students from the ECE4760 program at Cornell have been working on a spatial audio system built into a hat. The project from [Anishka Raina], [Arnav Shah], and [Yoon Kang], enables the wearer to get a sense of the direction and proximity of objects in the immediate vicinity with the aid of audio feedback.

The heart of the build is a Raspberry Pi Pico. It’s paired with a TF-Luna LiDAR sensor which is used to identify the range to objects around the wearer. The sensor is mounted on a hat, so the wearer can pan the sensor from side to side to scan the immediate area for obstacles. Head tracking wasn’t implemented in the project, so instead, the wearer uses a potentiometer to indicate to the microcontroller the direction they are facing as they scan. The Pi Pico then takes the LIDAR scan data, determines the range and location of any objects nearby, and creates a stereo audio signal which indicates to the wearer how close those objects are and their relative direction using a spatial audio technique called interaural time difference (ITD).

It’s a neat build that provides some physical sensory augmentation via the human auditory system. We’ve featured similar projects before, too.

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