Apparatus and method for trigonometric interpolation

In a communications device, a method of determining an interpolation value between two data samples at an offset μ that is referenced from one of the two data samples, the method comprising the steps of:

• (1) receiving a set of N data samples having the two data samples that are to be interpolated;
• (2) determining coefficients for a trigonometric polynomial based on said set of N data samples, comprising the step of multiplying one or more of said data samples by a complex scaling factor WNkn, wherein WN=e31 j2π/N, wherein n represents an nth data sample of N total data samples;
• and
• (3) evaluating said trigonometric polynomial at the offset μ, wherein a real part of said trigonometric polynomial represents the desired interpolation value including the steps of
• (a) determining a WN−kμ value for a kth coefficient of said trigonometric polynomial, wherein WN=e−2π/N;
• and
• (b) multiplying said kth coefficient by said corresponding WN−kμ value to evaluate said trigonometric polynomial.

In a communications device, a method of determining an interpolation value between two data samples at an offset μ that is referenced from one of the two data samples, the method comprising the steps of:

• (1) receiving a set of N data samples comprising the first data sample and the second data sample;
• (2) generating a first complex coefficient and a second coefficient based on said set of N data samples;
• (3) rotating said first complex coefficient and said second complex coefficient in a complex plane based on the offset μ to produce a first rotated complex number and a second rotated complex number;
• and
• (4) determining the interpolation value based on a real part of said first rotated complex number and a real part of said second rotated complex number, whereby the interpolation value is data processed by said communications device.

In a communications device, a method of determining an interpolation value between two data samples at an offset μ that is referenced from one of the two data samples, the method comprising the steps of:

• (1) receiving a set of N data samples that includes the two data samples that are to be interpolated;
• (2) generating a complex coefficient and a non-complex coefficient based on said set of N data samples;
• (3) rotating said complex coefficient in a complex plane based on the offset μ to produce a rotated complex number;
• and
• (4) determining the interpolation value based on a real part of said rotated complex number and said non-complex coefficient, whereby the interpolation value is data processed by said communications device.

An apparatus for interpolating between two data samples at an offset μ that is referenced from one of the two data samples, wherein the two data samples are part of a set of N data samples, the apparatus comprising:

• a delay module that receives the set of N data samples;
• an adder/subtractor module, coupled to an output of said delay module, wherein said adder module generates one or more coefficients based on delayed data samples from said delay module, wherein at least one of said coefficients is a complex coefficient;
• and
• an angle rotator, coupled to an output of said adder module, said angle rotator rotating said complex coefficient in a complex plane based on the offset μ to generate a rotated complex coefficient, whereby said interpolation value is determined based on said rotated complex coefficient.

An apparatus for interpolating between two data samples at an offset μ that is referenced from one of the two data samples, wherein the two data samples are part of a set of N data samples, the apparatus comprising:

• a delay module that receives the set of N data samples;
• an adder/subtractor module, coupled to an output of said delay module, wherein said adder module generates one or more coefficients based on delayed data samples from said delay module, wherein at least one of said coefficients is a complex coefficient, and wherein said adder/subtractor module generates a K value that is determined so that cN/2=0;
• an angle rotator, coupled to an output of said adder module, said angle rotator rotating said complex coefficient in a complex plane based on the offset μ, said angle rotator including,
• a lookup table that is indexed by μ, wherein said lookup table stores a first value that is based on {circumflex over (F)}μ·cosine (x·π·μ) and stores a second value based on {circumflex over (F)}μ·sine (x·π·μ), wherein x is a fraction between 0 and 1;
• wherein {circumflex over (F)}μ is chosen to adjust a frequency response of said apparatus so that it is consistent with a frequency response of the N data samples and the offset μ, and
• a first multiplier for multiplying said complex coefficient by said first value and said second value, to produce a real part of said rotated complex coefficient;
• a second multiplier that multiples said K value from the adder/subtractor module with the offset μ, to produce a Kμ value;
• and
• an output adder, coupled to an output of said first multiplier and an output said second multiplier and an output of said adder/subtractor module, wherein said output adder adds together said real part of said rotated complex number and said Kμ value and at least one non-complex coefficient from said adder/subtractor module.

An apparatus for increasing a sampling rate of a set of data samples by a factor L, the apparatus comprising:

• a delay module that receives the set of N data samples;
• an adder/subtractor module, coupled to an output of said delay module, wherein said adder module generates one or more coefficients based on delayed data samples from said delay module, wherein one or more of said coefficients is a complex coefficient;
• a plurality of N angle rotator modules, coupled to an output of said adder module, each angle rotator rotating one or more of said coefficients in a complex plane based on a corresponding offset μ to generate a rotated complex coefficient, wherein μ varies for each angle rotator module according to μ=n(L−1)/L, where n increases from n=1 to N and represents one of the N angle rotator modules;
• and
• a multiplexer, coupled to outputs of said plurality of angle rotator modules, said multiplexer operating at a rate of Lr.