Walsh synthesis

Whereas AM, FM and waveshaping are synthesis techniques inherited from the world of analog synthesis, Walsh synthesis is an inherently digital technique. Walsh synthesis works based upon square waves instead of sinewaves it creates other waveforms by combining square waves. Inasmuch digital systems work with only two numbers at their most fundamental level (i.e. 0 and 1), square waves are very straightforward to manipulate digitally. 

It is curious to note that although Walsh synthesis may resemble the additive synthesis method of sinewave summations, this technique is based upon a very different paradigm. 

Walsh synthesis produces waveforms from the summation of Walsh functions rather than from the summation of partials. Walsh functions are measured in zero crossings per second (zps) instead of cycles per second (cps or Hz) and they are not explicitly related to specific 

Although is it possible to predict the spectrum of Walsh synthesis by means of complex mathematical calculations, this technique is not efficient for methods rooted in Fourier s theory. Actually, the most difficult waveform to produce with Walsh synthesis is the sinewave, which is the fundamental unit of Fourier s theory. Conversely, the most difficult waveform to produce by summing sinewaves is the square wave, which is the fundamental unit of Walsh s)mthesis. 

Despite its affinity with the digital domain, Walsh synthesis has not been sufficiently studied and composers have rarely used it. There is great potential, however, for an entirely new theory for sound synthesis based on Walsh functions for example, sounds could be analysed using a Walsh-based technique and resynthesised using fast Walsh transform (FWT). Also, modulation involving Walsh functions may be able to produce certain types of waveforms much more efficiently than modulation using sinusoids. A few technical articles about Walsh synthesis can be found in various issues of Journal of the Audio Engineering Society e.g. Hutchins (1973,1975). 

---

On the whole, loose modelling techniques tend to be very easy to implement, but their synthesis parameters are not straightforward to control because they bear little relation to the acoustic world. Computer technology also inspired a few loose modelling techniques, such as Walsh synthesis and synthesis by binary instruction. 

Figure 2.26 Walsh functions are the backbone of Walsh synthesis... 

Synthesis by binary instruction is a curious technique developed in the 1970s at the Institute of Sonology in the Netherlands. This technique is commonly known as non-standard synthesis, but in this book we prefer to use the more specific term - binary synthesis - in order to distinguish it from other methods that could also be classified as non-standard for example, Walsh synthesis and sequential waveform composition (discussed in Chapter 5). 

Electrochemical techniques, proposed for the synthesis of naphthaquinone, anisaldehyde, and benzaldehyde (Walsh and Mills, 1993). 

Chand P, Kotian PL, Morris PE, Bantia S, Walsh DA, Babu YS (2005b) Synthesis and inhibitory activity of benzoic add and pyridine derivatives on influenza neuraminidase. Bioorg Med Chem 13 2665-2678... 

The mechanism of fluoroacetate toxicity in mammals has been extensively examined and was originally thought to involve simply initial synthesis of fluorocitrate that inhibits aconitase and thereby the functioning of the TCA cycle (Peters 1952). Walsh (1982) has... 

There are several examples in which metabolites that toxify the organism responsible for their synthesis are produced. The classic example is fluoroacetate (Peters 1952), which enters the TCA cycle and is thereby converted into fluorocitrate. This effectively inhibits aconitase—the enzyme involved in the next metabolic step—so that cell metabolism itself is inhibited with the resulting death of the cell. Walsh (1982) has extensively reinvestigated the problan and revealed both the complexity of the mechanism of inhibition and the stereospecihcity of the formation of fluorocitrate from fluoroacetate (p. 239). It should be noted, however, that bacteria able to degrade fluoroacetate to fluoride exist so that some organisms have developed the capability for overcoming this toxicity (Meyer et al. 1990). 

Tao, J., Hu, S., Pacholec, M. and Walsh, C.T. (2003) Synthesis of proposed oxidation-cyclization-methylation intermediates of the coumarin antibiotic biosynthetic pathway. Organic Letters, 5, 3233-3236. 

Steve Walsh and John Perkins, Operability and Control inn Process Synthesis and Design... 

Walsh FC (1992) The design and performance of electrochemical reactors for environmental treatment and efficient synthesis, 43rd ISE Meeting, Cordoba, Argentina, Sept 20-25, IL-3-09... 

Gertrude Walsh Robinson developed a new method for the synthesis of high-molecular-weight fatty acids, and she was active in penicillin research during the Second World War. Baker writes (1954) "It is perhaps not generally known that she was the first chemist to prepare synthetical material with genuine antibiotic character of the penicillin type" (567). 

Southwick Walsh J. Am. Chem. Soc. 1955, 77, 405. See also Suzuki Okano Nakai Tcrao Sekiya Synthesis 1983, 723. 

Didier C, Critcher DJ, Walshe ND, Kojima Y, Yamauchi Y, Barrett AGM (2004) Full Stereochemical Assignment and Synthesis of the Potent Anthelmintic Pyrrolobenzoxazine Natural Product CJ-12662. J Org Chem 69 7875... 

---