Numerically controlled oscillator and oscillation method for generating function values using recurrence equation

A numerically controlled oscillator for generating function values in respective clock cycles by using a recurrence equation, comprising:

• an oscillation circuit including
• a multiplier having a latency of k clock cycles and an adder, wherein the oscillation circuit generates, in each of the clock cycles, a current one of the function values by multiplying, using the multiplier, a first one of the function values by a coefficient, the first one of the function values being generated in a first one of the clock cycles that is one of the clock cycles j cycle(s) ago from a current one of the clock cycles and adding, using the adder, an output of the multiplier and at least one of the function values generated in previous ones of the clock cycles that are 1 to i−1 cycles before the current one of the clock cycles excluding the first one of the clock cycles,
• where i is an integer greater than 2, j is an integer greater than 1 and less than i, and k is an integer greater than 0 and less than j;
• and
• a coefficient generation circuit that generates and supplies the coefficient to the oscillation circuit, wherein
• the oscillation circuit generates sinusoidal function values at phases with an interval of Δω as the function values;
• i=5 and j=2;
• and
• the coefficient is M−=2 {cos(2Δω)−cos(Δω)} and the adder adds two of the function values generated in two of the previous ones of the clock cycles that are one cycle before the current one of the clock cycles and three cycles before the current one of the clock cycles as they are and further adds one of the function values generated in one of the previous ones of the clock cycles that is four cycles before the current one of the clock cycles after a sign thereof is inverted;
• or
• the coefficient is M+=2 {cos(2Δω))+cos(Δω)} and the adder adds three of the function values generated in three of the previous ones of the clock cycles that are one cycle before the current one of the clock cycles, three cycles before the current one of the clock cycles, and four cycles before the current one of the clock cycles after signs thereof are inverted.

A numerically controlled oscillator for generating function values in respective clock cycles by using a recurrence equation, comprising:

• an oscillation circuit including
• a multiplier having a latency of k clock cycles and an adder, wherein the oscillation circuit generates, in each of the clock cycles, a current one of the function values by multiplying, using the multiplier, a first one of the function values by a coefficient, the first one of the function values being generated in a first one of the clock cycles that is one of the clock cycles j cycle(s) ago from a current one of the clock cycles and adding, using the adder, an output of the multiplier and at least one of the function values generated in previous ones of the clock cycles that are 1 to i−1 cycles before the current one of the clock cycles excluding the first one of the clock cycles,
• where i is an integer greater than 2, j is an integer greater than 1 and less than i, and k is an integer greater than 0 and less than j;
• and
• a coefficient generation circuit that generates and supplies the coefficient to the oscillation circuit, wherein:
• the oscillation circuit generates sinusoidal function values at phases with an interval of Δω as the function values;
• i=5 and j=2;
• and
• the coefficient is M−=2 {cos(2Δω*L)cos(Δω*L)} and the adder adds two of the function values generated in two of the previous ones of the clock cycles that are one cycle before the current one of the clock cycles and three cycles before the current one of the clock cycles as they are and further adds one of the function values generated in one of the previous ones of the clock cycles that is four cycles before the current one of the clock cycles after a sign thereof is inverted;
• or
• the coefficient is M+=2{cos(2Δω*L)+cos(Δω*L)} and the adder adds three of the function values generated in three of the previous ones of the clock cycles that are one cycle before the current one of the clock cycles, three cycles before the current one of the clock cycles, and four cycles before the current one of the clock cycles after signs thereof are inverted.

An oscillation method for generating function values in respective clock cycles by using a recurrence equation, comprising:

• generating, via a processor, a current one of the function values in each of the clock cycles, including:
• multiplying, via the processor, a first one of the function values by a coefficient with a latency of k clock cycles, the first one of the function values being generated in a first one of the clock cycles that is one of the clock cycles j cycle(s) ago from a current one of the clock cycles;
• and
• adding, via the processor an result of the multiplying and at least one of the function values generated in previous ones of the clock cycles that are 1 to i−1 cycles before the current one of the clock cycles excluding the first one of the clock cycles, where i is an integer greater than 2, j is an integer greater than 1 and less than i, and k is an integer greater than 0 and less than j, wherein
• the multiplying includes receiving the current one of the function values after delaying for j−k clock cycles as the first one of the function values.