Apparatus and method for direct digital frequency synthesis

A digital frequency synthesizer for simultaneously producing a sine wave and a cosine wave, the sine wave and the cosine wave being at a prescribed frequency, the digital frequency synthesizer comprising:

• an amplitude sample generator, configured to compute Haar coefficients corresponding to a desired phase angle, and configured to transform said Haar coefficients into a particular in-phase amplitude sample and a particular quadrature amplitude sample, and configured to generate amplitude samples that lie within a first phase octant ranging from 0 degrees to 45 degrees, said amplitude sample generator comprising:
• in-phase amplitude samples, for indicating sine wave amplitudes within said first phase octant;
• quadrature amplitude samples, for indicating cosine wave amplitudes within said first phase octant;
• and
• a symmetry controller, coupled to said amplitude sample generator, for receiving a phase signal from a phase accumulator, said phase signal indicating said desired phase angle, and for selecting said particular in-phase amplitude sample and said particular quadrature amplitude sample to provide a desired sine wave amplitude and a desired cosine wave amplitude at said desired phase angle;
• and
• interpolation logic, coupled to said symmetry controller, configured to add a first first-order Taylor series term to said particular in-phase amplitude sample, thereby increasing precision of the sine wave, said interpolation logic comprising:
• a multiplier, configured to multiply fine phase bits of said phase signal by a 90 degree term to account for digital scaling difference between amplitude magnitude representations and phase magnitude representations within the frequency synthesizer.

A computer program product for use in designing, simulating, fabricating, or testing a direct digital frequency synthesizer circuit, the computer program product comprising:

• a storage medium, having computer readable instructions embodied thereon, for causing a computer upon which said computer readable instructions are executed to describe the digital frequency synthesizer circuit such that it can be modified, simulated, fabricated, or tested, said computer readable instructions comprising:
• first instructions, for causing said computer to describe a phase signal, for indicating a desired phase angle of a sinusoidal waveform;
• and
• second instructions, for causing said computer to describe a phase-to-amplitude converter, coupled to said phase signal, for providing a desired amplitude sample corresponding to said desired phase angle, wherein said desired amplitude sample is derived from amplitude samples corresponding to an octant of said sinusoidal waveform, wherein said phase-to-amplitude converter comprises:
• a Haar Transform-based coarse octant amplitude sample generator, configured to compute Haar coefficients corresponding to said phase signal, and configured to transform said Haar coefficients into said desired amplitude sample.

A method for generating a sine wave and a cosine wave at a prescribed frequency by direct digital frequency synthesis, the method comprising:

• providing a phase angle signal, wherein the rate of change of the phase angle signal corresponds to the prescribed frequency;
• generating Haar coefficients that correspond to a first octant of the sine wave and the cosine wave;
• selecting specific Haar coefficients that correspond to a specific phase offset within the first octant, wherein a desired phase angle for the sine wave and the cosine wave is determined by summing a true octant base angle with the specific phase offset;
• and
• translating the specific Haar coefficients into a cosine amplitude sample and a sine amplitude sample that correspond to the desired phase angle.