Abstract: An apparatus and method are provided for performing both forward and inverse Haar transforms of a sequence of n-bit data samples. The forward Haar transform apparatus has sum-and-truncate logic and a plurality of coefficient generators. The sum-and-truncate logic generates a plurality of n-bit intermediate terms. The plurality of coefficient generators is coupled to the sum-and-truncate logic. The plurality of coefficient generators generate a plurality of spectral coefficients, where at most n+1 bits are required to represent each of the plurality of spectral coefficients. The inverse Haar transform apparatus has index signal and inverse transform logic. The index signal indicates a specific n-bit sample, the specific n-bit sample being one of a sequence of n-bit samples corresponding to the Haar transform. The inverse transform logic is coupled to the index signal.

Abstract: An apparatus and method are provided for synthesizing a variable frequency sinusoidal waveform. The apparatus and method exploit octant symmetry properties of sine and cosine waveforms, when taken together. The digital frequency synthesis apparatus includes a phase signal and a phase-to-amplitude converter. The phase signal indicates a desired phase angle of the sinusoidal waveform. The phase-to-amplitude converter is coupled to the phase signal. The phase-to-amplitude converter provides a desired amplitude sample corresponding to the desired phase angle, where the desired amplitude sample is derived from amplitude samples corresponding to an octant of the sinusoidal waveform. The phase-to-amplitude converter includes a Haar Transform-based coarse octant amplitude sample generator that computes Haar coefficients corresponding to the phase signal and transforms the Haar coefficients into the desired amplitude sample.

Abstract: An apparatus and method are provided for performing both forward and inverse Haar transforms of a sequence of n-bit data samples. The forward Haar transform apparatus has sum-and-truncate logic and a plurality of coefficient generators. The sum-and-truncate logic generates a plurality of n-bit intermediate terms. The plurality of coefficient generators is coupled to the sum-and-truncate logic. The plurality of coefficient generators generate a plurality of n+1-bit spectral coefficients. The inverse Haar transform apparatus has index signal and inverse transform logic. The index signal indicates a specific n-bit sample, the specific n-bit sample being one of a sequence of n-bit samples corresponding to the Haar transform. The inverse transform logic is coupled to the index signal. The inverse transform logic computes the specific n-bit sample, where the specific n-bit sample is derived from selected n+1-bit spectral coefficients.