Great article explaining how DSPs work
DSP Decrypted Part I – The Sky is the Limit
Posted by Michael
Nice to meet you. I’m Michael—the new guy here at Strymon. In the last six months, I have shipped, repaired, filmed, and (my personal favorite) continuously played the wonderful bits of technology that are Strymon pedals. As much as I enjoy contributing to this amazing, innovative company, I will concede that, at times, I feel as if I’m in over my head. At a lunch table full of accomplished engineers, I’m the one who dropped out of high school calculus. I’m Muhammed Ali in the ring of movie quotes, which has gained me considerable respect here at Strymon HQ. However, when conversation shifts from Lebowski to Thermodynamics, I’m a first round knockout.
Coming to work often feels like hanging out at a think tank. This is why I’ve come to the Strymon blogosphere—to share the information that I learn everyday from the minds at Strymon HQ and assist folks (like myself) who are genuinely interested in the complexities of sound technology but lack the time and the chutzpah to brave industry textbooks like Embedded Media Processing. Believe me, I’ve tried.
Without further adieu, let us begin the first installment of “DSP Decrypted”! In this article, we’re going to focus on a few broad strokes of DSP (Digital Signal Processing) that will help illuminate what makes DSP such a powerful tool for musical innovation.
What is DSP?
The short answer is, DSP is a process of converting analog, real-world signals into a digital format in which they can be mathematically manipulated before being converted back to analog. The basic idea is simple. The practice is wildly complex. And the specifics are fascinating.
To begin, I’d like you to play, on your guitar or in your mind, a low E. The sound wave of that low E has a fundamental frequency of 80 Hz. In DSP, that 80 Hz signal is digitally converted and sampled at a rate of 96 kHz. Think of the sampling process as taking 96,000 high definition snapshots of the signal that become represented by 96,000 different numbers—each of which can be mathematically manipulated. Now, the plot thickens.
Strymon digital pedals run on an Analog Devices SHARC DSP chip. The SHARC is designed to carry out operations based on mathematical equations programmed by a DSP engineer. Here at Strymon, that DSP engineer is Pete Celi, who offered me some insight into how powerful a creative tool the SHARC really is: “In analog, achieving a certain ‘equation’ for a specific sound might require very complicated and time-consuming circuitry. Whereas, in DSP, it’s as easy as typing ab + cy and boom. Basically DSP is this free-running process where we can take a signal and, within a set period of time, we can do whatever we want to it mathematically before converting it back to analog. The sky is the limit.”
Pete’s job is a lot more complicated than he makes it seem. Although, I definitely don’t understand the equation Pete mentioned. But let’s not get hung up on minor details. Back to the big picture.
So, we have a low E played on a guitar—that is digitally sampled at a rate of 96 kHz (96,000 snapshotsper second). The SHARC is designed to perform its instructions (based on programmed equations) within a single clock cycle. One math operation = one clock cycle. If you take the equation that Pete mentioned, for instance:
ab + cya x b = one clock cyclec x y = one clock cycle(ab) + (cy) = one clock cycle
This particular math operation is executed in three clock cycles. For most Strymon digital pedals, the SHARC DSP’s clock frequency is 266 MHz (BigSky’s is 366 MHz)—which means it completes 266,000,000 clock cycles per second, or, if you prefer, it completes a single clock cycle in just under four nanoseconds. (As a frame of reference, light travels about four feet in four nanoseconds!). If you divide the clock frequency by the sample rate (266,000,000 / 96,000), you arrive at the number of instructions the SHARC can execute per sample. So, we can apply 2,770 instructions to each sample before the samples are converted back to analog. That, my friends, is processing power.
Here’s an analogy that might help visualize the SHARC DSP’s power. We’re in the back room of a massive bakery—I’m talking Willy Wonka sized, here—where all the confectionary magic happens. There’s a gigantic conveyor belt running from one end of the room to the other. At the start of this conveyor belt is a single, plain cake—our sample. Standing alongside this conveyor belt are 2,770 cake artists, each of which can add one specific ingredient as the cake goes down the line. By the time the cake reaches the finish line – it is decorated to perfection. And these cake artists are so good, they can crank out 96,000 of these bad boys every second!
Here’s another visual. Knowing that I’m a cinephile, Gregg Stock (analog engineer/wizard) provided me with a model of how DSP works that I’ll share with you. Imagine a film projector with a built-in SHARC processor. A reel of celluloid film runs through a projector at 24 frames per second. If each frame is a sample, our sample rate is 24 Hz. The DSP projector’s clock frequency is 266 MHz—meaning we can apply 11,080,000 edits to each frame. As long as we don’t exceed the 11 million or so operations, by the time one frame is finished and projected upon the screen (converted back to analog), the following frame has just been finished and is ready for projection. And so on.
While the SHARC DSP cannot accomplish 11 million plus clock cycles per sample when sampling audio at 96 kHz, its processing power is still immense. Especially compared to its predecessors. Unlike earlier versions of DSP chips, the SHARC processor is not limited to a small amount of tasks it can execute. Strymon pedals devote all of the SHARC’s clock cycles to creating the richest, most nuanced effects possible. Couple that insane processing power with the kind of creativity, dedication, and vision that the good folks at Strymon possess, and what do you get? Well, “the sky is the limit.”
Link to Blog post: http://www.strymon.net/2014/05/29/dsp-anyway/
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