Introduction
by W. J. Miller, PhD

INTRA Wavelet Technology And Intellectual Property Platforms:
Very Broad, Universal, Generalized, and Powerful

The modem modulation method called INTRA (INformation TRAnsformations) is based on Wavelet Theory. The transmitter is a Wavelet Synthesizer and the receiver is a Wavelet Analyzer. In a wholly equivalent description, the transmitter performs a baseband rotation of data vectors and the receiver performs the counter-rotation. That is, modulation and demodulation behave as rotations in a vector space, so they are commuting operators --- this commuting feature makes INTRA modems suitable for a new form of digitally encrypted communication described in PART 2 on Secure Communications.

The meanings of these terms (i.e. Synthesizer, Analyzer, and Rotation) are very extensive within the realm of generalized Wavelet Theory. For example, generalized Wavelet Theory is not restricted to Finite Impulse Response (FIR) filtering, or to binary dilations and dyadic translations to form the Scaling and Residual basis functions. Thus the more familiar FIR Quadrature Mirror Filter Bank (QMF) description of Wavelet Transforms is in fact a subset of the generalized Theory of Wavelets. In a very general description, a Wavelet Synthesizer suitable for INTRA modems performs a baseband invertible transform having the mathematical properties of a Rotation in a vector space.

Therefore, a generalized description of a modem based on Wavelets is necessarily couched in terms of "Rotations" and "Synthesizers" rather than in the less general terms of QMFs or specific wavelet functions (i.e. Haar Wavelets, Cosine-Modulated Wavelets etc.). Of course, the design techniques of FIR QMFs are much more fully developed than, say, IIR solutions in today's literature, so FIR QMFs are recommended for easy mathematical implementation of INTRA modems.

It is only necessary that the FIR or IIR polyphase filter matrices for the Synthesizer and Analyzer behave as perfect or near-perfect Rotations. The well known concept of polyphase matrices is explained below. With many possible ways to make a "generalized INTRA modem", it becomes more instructive to describe simple examples that both illustrate the concept, have utility in some practical cases, and illustrate distinctions from prior modulation methods. Thus, Analyzers with only a few FIR coefficients, or Rotations through only a few angles are presented below.

A Low-Cost INTRA RF-Modem

Figure 1 illustrates a novel FIR version of the INTRA concept for Cable Modems having zero computational complexity (no multiplications). The INTRA transmitter is a look-up table driving a low cost CMOS D/A converter directly at RF frequency in a 1 or more MHz channel in the 5 to 40 MHz Upstream CATV band. The head-end receiver for one channel is shown as a Surface Acoustic Wave Filter (SAW) followed by one comparator. There is no A/D converter or DSP in this low-cost INTRA receiver. Many other configurations with and without SAWs, IF mixers, and multiple bits-per-symbol are possible for coax, twisted pair and wireless applications.

The operation of the modem in Figure 1 can be explained in several mathematically equivalent ways. From a Wavelet perspective, the transmitter sends a short burst of narrow-band RF energy --- called a wavelet --- for each data symbol.

In the illustration, the receiver uses an analog SAW filter and comparator to correlate the received waveform with the known wavelet shape. Here the sign of the correlation determines if a 1 or a 0 was received. By design, the correlation properties of the wavelets assure there is no Inter-Symbol Interference (ISI) or Adjacent Channel Interference (ACI). For adaptive pre-equalization a RAM replaces the ROM.

Another way to understand Figure 1 is to view the transmitter and receiver in terms of baseband rotation operators. This viewpoint is explained in PART 1. A related use for INTRA modems for Secure Communications, digital encryption of analog signals without bandwidth expansion and without digital compression, is explained in PART 2.