By Don Estes & Randy Stack, InnerSense, Inc.
Analog signals are continuous and therefore exists in the continuum, whereas Digital signals are samples taken at specific intervals of a sampling rate. The greater the sampling rate and the more bits used to represent a single sample, the more accurate the digital signal represents the true nature and full signal of its analog counterpart. This is why the latest audio enhancement technologies revolve around the concept of improved analog to digital conversion through sophisticated and expensive A/D converters.
Figure One (A) Digital Square Wave
Figure One (B): Analog Sine Wave
The diagram above reveals the difference between the shape of analog and digital signals. It’s evident that the digital signal does not follow the smooth flow of its analog compliment. This factor is the main argument used to support the idea that analog is superior.
However, closer analysis reveals that each has advantages and disadvantages…abilities versus limitations… and both have a place in signal analysis and feedback, especially is the field of human biometrics.
Both analog and digital signals consist of three main components…frequency, phase and amplitude. When it comes to analyzing and reproducing signals for brain, heart or voice analysis and feedback systems…accuracy and precision of all three of those three microstructure elements become extremely important.
Since the introduction of digital audio processing, especially the availability of compact discs, digital audio tape and flash drives, arguments have arisen over the difference between the two, particularly regarding the supposed superiority of analog over digital. These complaints have mostly originated within the music industry where purists claim to hear a huge difference between them. However, research with the general public has shown that the average person doesn’t hear such differences because they’re beyond the Nyquist limit that defines the maximum frequency representable by digitization before a psychoacoustic difference can be noticed.
This disagreement has now found its way into the sound and vibrational healing community, so it’s become important for them to truly understand the difference between analog and digital and the applications of both. To begin with, it’s important to note that there’s a difference between single frequency sine waves and multi-frequency complex waveforms that, as proven by Fourier theory, consist of many sine and cosine waves.
The analog/digital argument does not apply to simple sine waves because single frequencies don’t have any harmonic overtones and therefore don’t exceed the limit of the sampling rate. Therefore, there is no difference whatsoever between an analog sine wave and a digital one. They both exhibit the characteristic bell-shaped curve of a sine wave on an oscilloscope.
Complex waves are a totally different story. A digital square wave takes on the shape of its namesake by producing the following waveshape.
Figure Two: Digital Square Wave
The signal must travel from left to right making all of the right angle turns, reaching its peak instantaneously (ie. within one sample) and staying at its maximum value before transitioning instantaneously to its most negative point and holding that value, between each wave. Each wave suddenly turns up, travels to the top, drastically turns right, travels a bit more and then abruptly drops back to its starting point making a sharp left turn to the next wave. This creates a harsh, scratchy sound because of all those sharp turns. This type of wave is called a synthetic or digital square wave.
Musical instruments like clarinets, on the other hand, produce what is called a natural analog square wave that looks like…
Figure Three: Natural Square Wave
Compared to a digital square wave of the same frequency, it’s clear that the natural square wave rounds or smooths out those drastic turns producing a warmer and more organic sound. At a sufficiently high sample rate and bit resolution, the difference between analog and digital signals is immeasurable and insignificant when dealing with simple sine waves. Differences begin to appear only when a full complement of harmonic frequencies are present as in the case of a complex acoustic wave. However, with proper and uncompressed digital processing a near perfect reproduction can be made of a complex waveform. But…why even use digital if analog is even slightly better?
To create complex frequencies with multiple sine waves it is necessary to have full control over the phase of each frequency to accurately replicate the precise waveshape. However, it’s impossible to control the phase of an analog signal without very expensive oscillators. The phase and amplitude of digital processors can be controlled with a high degree of accuracy and precision to many decimal points.
Analog processors are extremely sensitive to temperature, so unless a sophisticated cooling system is utilized frequency can be off up to as much as 2-3% across the range from 20 Hz. to 20 kHz. This dramatically affects both the accuracy and precision of analog equipment. Digital is much more stable, accurate and precise… in InnerSense’s case, up to 16 decimal points.
Turntables and tape recorders, both analog, may have a “warmer” feeling than digital sources (CDs, digital files, etc.) but can’t even come close to their low level of noise and high level of dynamic range. Scratches on the vinyl, dust and inexpensive needles make pops and noise intolerable for many listeners. Warble on tape recorders sounds distorted and unnatural to others. The dynamic range of a live recording has to be compressed on vinyl whereas on digital masters the full band can be accurately reproduced so the recording sounds more alive. Therefore, for the most accurate, precise and full range of recorded music, digital is preferred by some.
Digital compression is a different from digitalization. Compression takes a digital signal of a specific sample rate and compresses it into a smaller amount of samples, thereby making the file smaller and easier to stream download and store. Compression dramatically reduces the quality of music and is not the preferred way of listening to it. The labels on MP3 discs and other devices reveal that the sound has been compressed and only consists of the cosine waves because the sine waves have been removed by the DCT transform.
We paid for ALL of the sound…shouldn’t we have a right to it? The streaming companies have done an excellent job of convincing the younger generation that there’s no difference. Luckily, technology that resolves that problem, by creating infinite phase, is currently available with the IRIS Flow technology.
The Sensorium™ LSV III Function Generators and Altitudinal Oscillators utilize a polynomial transition region algorithm to create wave shapes that smooth out and faithfully reproduce the natural wave shapes of instruments such as the human body.
Figure Four: Polynomial Transition Region Algorithm
The frequencies, amplitudes and phases entered into the Tone Bank determines the waves shape generated. For example, the diagram below shows a square wave based on the Fourier transform of the first 12 harmonics of the square wave.
Figure Five: Fourier transform with 12 Harmonics from Sensorium™ LSV III Tone Bank.
Below is a tracing that shows the same Fourier transform utilizing the first 24 harmonics of the wave. Notice how it is the same as the example of the natural analog square wave that was shown above.
Figure Six: Fourier transform with 24 Harmonics from Sensorium™ LSV III Tone Bank
In addition, InnerSense technologies utilize a floating point architecture that more faithfully “connects the dots” between samples. For example, a 24 bit, 192 kHz. master recording each amplitude sample must be one of the 16,777,216 possible values that 24 bits provides. If the actual amplitude is 8000.0005 the 24 bit sample would only be able to approximate that to 8000 or 8001, whereas the 64 bit floating point used by the Sensorium™ LSV III can hit the 8000.0005 amplitude precisely. The Sensorium™ LSV III is accurate to 16 decimal digits.
These two secrets, the floating point architecture and the algorithmic techniques used in the generation and processing of digital signals, makes the Sensorium™ the cutting edge and state of the art leader in the field of digital signal processing, analysis and biofeedback.
With regard to simple, single sine wave frequencies, there is virtually no difference between an analog or digital signal. However, with complex frequencies, digital sources don’t capture the full essence of analog sources unless special care is taken with their reproduction as with the Sensorium™ LSV III.
Note – All scope images and waveform examples in this paper were produced by the Sensorium™ LSV III Sensory Interface. The Nyquist limit has been shown to be exactly 1/2 of the sampling rate.
www.lrislistenwell.com and the Iris Audio Dimensionalizer based on U.S. Patent 8788557 by Don Estes and Randy Stack, 2014.
http://home.mit.bme.hu/~bank/publist/smc13.pdf and https://www.researchgate.net/publication/221780582