# Asymptotic behavior of least energy solutions of a by Ben Ayed M., El Mehdi K., Grossi M.

By Ben Ayed M., El Mehdi K., Grossi M.

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Most fixed-point DSPs use a 16-bit format, providing 16 bits of precision. So, while in theory the choice between fixed- and floating-point arithmetic could be independent of the choice of precision, in practice floating-point processors usually provide higher precision. As mentioned above, dynamic range is defined as the ratio between the largest and smallest number representable in a given data format. It is in this regard that floating-point formats provide their key advantage. For example, consider a 32-bit fixed-point fractional representation.

Software-only DSP-based products are appropriate where the signal processing requirements are not demanding and where a PC or workstation is already available to the end user. Many scientific and engineering applications that involve non-real-time synthesis or analysis of signals take this approach and run on conventional PCs and workstations. Perhaps the most visible example of this approach to signal processing is Intel's native signal processing (NSP) initiative. NSP seeks to use the host ("native") processor in PC-compatible computers for low-end multimedia applications, such as audio compression and decompression, music and sound synthesis, and more.

A shifter in the data path eases this selection by scaling (multiplying) its input by a power of two (Z"), Scaling is an important operation in many fixed-point DSP applications. This is because many basic DSP functions have the effect of expanding or contracting the range of values of the signals they process. Consider the simple example of a filter, as illustrated in Figure 4-4. The example filter has a gain of 100. This means that the range of values at the output of the filter can be as much as 100 times larger than the range of values at the input to the filter.

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