Center for New Music and Audio Technologies

Amplitude

Each sinusoid needs to be weighted appropriately to its magnitude within the spectrum. The normal way to do this is to use a multiplier controlled by the parameter amplitude. At the beginning of this chapter we mentioned the expense of multiplication in digital hardware and found a way around by using CORDIC for computing the sine function. At this point a simple replacement of multiplication by the CORDIC algorithm would be possible but is not necessarily a gain of resources. However, as described by equation 1.2.1 the CORDIC algorithm contains a gain due to the K-factor. We compensated this gain by initializing the rotation with a vector of length $\vert K\vert$, ($\vert K\vert,0$) respectively, so that the final vector was the unary vector. Hence, initializing with different $\vert K\vert$'s would result in a vector with length which is not one. This leads to the idea of initializing the rotation with the control parameter for amplitude and performing multiplication and computation of sine using the same resources. Thus, it is to be proved that the gain inherent in the CORDIC algorithm is linear and indepent of varying conditions, e.g., input angle, sequence of directions, initial values.

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