Dissertation: Digital Sound Synthesis and Usability

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[. . .] It offers two oscillators, a resonant low-pass filter, and two envelope generators (ADSR). There are always a handful of alternative waveforms available as well as a noise source (as cited in Huovilainen and Valimaki, 2006).

Figure 1: taken from Huovilainen and Valimaki, 2006

Digital Oscillators

The jagged boundaries of geometric waveforms used nowadays in digital oscillators, like the saw-tooth or the square wave, result in the creation of assumptions, as these kinds of signals aren't band-limited. Three various classes of techniques are recognized to avoid this issue:

1. Band-limited techniques that produce harmonics only beneath the Nyquist boundary, for example additive synthesis and its own variants, e. g., wavetable synthesis and the discrete summation formulae (as cited in Huovilainen and Valimaki, 2006);

2. Quasi-band-limited techniques by which aliasing is small and its own level could be regulated or altered by design to truly save computational expenses, for example in the BLIT [9] and the minBLEP [1] methods (as cited in Huovilainen and Valimaki, 2006);

3. Alias-suppressing techniques by which it is established that various assumptions will surface and be created but an effort is built to attenuate it adequately (as cited in Huovilainen and Valimaki, 2006).

In a recent study conducted by Huovilainen and Valimaki (2006) the researchers concentrate on the 3rd group of techniques. They highlighted two particular approaches here which were: the distortion and filtering of sine waves, which the termed in their paper is Lane's method (Lane et al., 1997) as well as the differentiated parabolic waveform (DPW) (as cited in Valimaki, 2005). They discussed the latter in the following way:

"DPW algorithm: The simplest version of the DPW algorithm [11] generates the saw-tooth waveform in four stages, as illustrated in Fig. 2: First generate the trivial saw-tooth waveform using a modulo counter, then raise the waveform to the second power, differentiate the signal with a first difference filter with transfer function H (z) = 1 -- z -- 1, and, finally, scale the obtained waveform by factor c = f/(4f), where f is the fundamental frequency of the saw-tooth signal and fs is the sampling rate. The waveform produced by the modulo counter resembles the saw-tooth waveform, as seen in Fig. 3(a), but it sounds badly distorted. The reason is that its spectrum decays slowly, about 6 dB per octave. When it is sampled, the spectral components above the Nyquist limit are mirrored down to the audible frequencies. This is clearly seen in Fig. 4(a), where the desired harmonics are indicated by circles and the rest of the peaks are aliased images" (as cited in Huovilainen and Valimaki, 2006).

Figure 2: obtained from Huovilainen and Valimaki, 2006

Figure 3: obtained from Huovilainen and Valimaki, 2006

Figure 4: obtained from Huovilainen and Valimaki, 2006

Figure 5: obtained from Huovilainen and Valimaki, 2006

The researchers further asserted that raising the signal to the 2nd power modifies the waveform such that it now includes bits of parabola, see Fig. 3(b). The spectral range of this waveform decays about 12 dB per octave, and for this reason aliasing is suppressed in Fig. 4(b) [11]. Finally, when the piecewise parabolic signal is differentiated and scaled, the signal again appears like the saw-tooth waveform, see Fig. 3(b), however the aliased components are suppressed, as observed in Fig. 4(c) (as cited in Huovilainen and Valimaki, 2006).

They also write that another problem is that at high frequencies the amount of aliased components is near to that of the harmonics. This might lead in some instances to beating. An answer of avoid this would be to replace the differentiator using its averaged version HD (z) = 1 - z-2 = (1 + z-1) (1 - z-1). The resulting waveform and spectrum are shown in Fig. 5. It sometimes appears that in the discrete-time waveform in Fig. 5(a) the transitions from the most value (near +1) to the minimum value (near -1) are smoother than in Fig. 3(c). The corresponding spectrum, see Fig. 5(b), decays faster at high frequencies than that in Fig. 4(c) (as cited in Huovilainen and Valimaki, 2006).

Improved Moog Model: Non-Linear Method

Huovilainen is promoting a better model that designs the ladder trip by placing the nonlinearities within the one-pole segments (2004). He asserts that this enhanced design far more intimately imitates or reflects the typical resonance and it is effective at self-oscillation. A disadvantage may be the importance of five hyperbolic tangent (tanh) function assessments done as per sample and oversampling by factor two at the very least (Huovilainen, 2004).

An alternative solution and extended model is shown in figure 7 (taken from Huovilainen and Valimaki, 2006). The embedded nonlinearities inside each and every segment is replaced with a single nonlinearity in the reaction sphere, hence greatly reducing the computational expenditures of the filter. We now have used the tanh utility for the nonlinearity, but any efficiently saturating function can be utilized. There's a big difference in the resonance set alongside the full nonlinear Moog filter model, but this particular design chosen can emulate all the activities and mannerism, for example self-oscillation. Its output can, in addition, be constantly restricted.

The brand new and innovative design also includes two additional improvements. The standard Moog filter and comparable cascaded one-pole filters suffer with declining the pass-band gain while the quality and tone/sound is elevated, since the resonance is fashioned with a worldwide negative feedback. If a few of the contribution is subtracted from the reactive or response signal before the sound degree are multiplied, the pass-band gain change could be controlled (Curtis Electromusic Specialties, 1984). A value of just 1.0 for the comp parameter keeps the pass-band gain constant. This, on the other hand, creates a sizable increase and elevation of the output amplitude while the resonance is also simultaneously risen. To help keep the entire intensity roughly steady, comp must be rested at 0.5 producing a 6 dB pass-band gain reduction at the most resonance (when compared with a 12 dB reduction in the initial Moog model).

Figure 7: taken from Huovilainen and Valimaki, 2006

Yet another improvement may be the accumulation of numerous frequency response modes form original 24 dB/oct lowpass mode. This is often easily attained by mixing the patient section outputs with differing weights. The idea was initially established in the Oberheim Xpander and Matrix-12 synthesizers (Oberheim, 1984 as cited in Huovilainen and Valimaki, 2006), however the researchers asserts that "it was not widely used due to a large number of required components and the need for precision resistors. Accurate mixing is trivial in the digital domain, and a large number of different low-pass, band-pass, high-pass, and notch filter responses and their combinations can be realized. The response can be morphed between these modes by changing the coefficients at runtime, thus allowing interesting modulation possibilities" (Huovilainen and Valimaki, 2006).

Digital subtractive synthesis is really a modern approach by which aspects of analogue music synthesizers are designed with the utilization of the signal processing techniques. So far, in this paper, we have highlighted the use of the digital oscillators and resonant filtering algorithms as discussed in numerous relevant research studies. It is important to note here that the DPW oscillator algorithm creates a saw-tooth waveform estimate that has paid down aliasing and assumptions with regards to the trivial saw-tooth waveform (i.e., the modulo counter output). This new method has become the simplest of use technique for this function, because only the trivial saw-tooth is very simple, however it is practically useless because of its heavy aliasing (Huovilainen and Valimaki, 2006).

"The new nonlinear model of the Moog ladder filter is based on a cascade of four one-pole filters and a feedback loop that contains a memory-less nonlinearity. The proposed new Moog filter structure has nice advantages, such as a smaller computational cost than that of a recently proposed nonlinear filter structure, the decoupling of the cutoff frequency and the resonance parameters, and the possibility to obtain various types of filter responses by selecting a weighted sum of different output points. The proposed methods allow the synthesis of retro sounds with modern signal processing techniques" (Huovilainen and Valimaki, 2006).

Usability testing

In addition to meeting the rising opportunities, there are lots of concrete remunerations for procuring companies from superior usability of interactive structures. Work efficiency and organization are elevated when utilizing IT systems with high-quality usability, and you will find a smaller number of 'user errors'; less preparation of staff is needed to facilitate valuable and efficient make utilization of the structure, users tend to be more satisfied, and there might be decrease in the overall percentage of staff turnover. You will find profits and advantages both for users and producers for the reason that less sustenance and certification is needed. Such benefits could be enumerated, measured, and integrated right into a production case for requesting usability production in system expansion (Macleod, 1994). Karat (1993) gives abundant examples.

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Digital Sound Synthesis and Usability.  (2011, October 24).  Retrieved July 17, 2019, from https://www.essaytown.com/subjects/paper/digital-sound-synthesis-usability/6582126

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"Digital Sound Synthesis and Usability."  Essaytown.com.  October 24, 2011.  Accessed July 17, 2019.