Claims Analysis
Total Claims: 43
Claim 1
Independent Claim
226 words
An apparatus for generating modulated signals within discrete increment channels in a frequency band by modulating carrier signals in accordance with information signals, each of the information signals including in-phase (I) and quadrature (Q) signal components, comprising: a filter for filtering the I and Q signal components to generate filtered I and Q signal components; an interpolation module for generating processed I signal components and processed Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to a pair of the processed I signal components and processed Q signal components for modulating a selected one of the carrier signals with a selected one of the information signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the discrete increment channels of the frequency band.
Claim 2
Independent Claim
226 words
An apparatus for generating modulated signals within discrete increment channels in a frequency band by modulating carrier signals in accordance with information signals, each of the information signals including in-phase (I) and quadrature (Q) signal components, comprising: a filter for filtering the I and Q signal components to generate filtered I and Q signal components; an interpolation module for generating processed I signal components and processed Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to a pair of the processed I signal components and processed Q signal components for modulating a selected one of the carrier signals with a selected one of the information signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the discrete increment channels of the frequency band.
Claim 3
Dependent Claim
36 words
The apparatus of claim 1 further comprising a control module for controlling access by the I and Q signal components to the filter by queuing and serially inputting each of the I and Q signal components.
Claim 4
Dependent Claim
76 words
The apparatus of claim 2, wherein the control module comprises: a plurality of shift registers, one for each of the I and Q signal components, for storing the I and Q signal components; and a multiplexor, connected to the plurality of shift registers, for supplying a selected one of the I and Q signal components to the filter in response to an address signal corresponding to the selected one of the I and Q signal components.
Claim 5
Dependent Claim
30 words
The apparatus of claim 3 further comprising a demultiplexor, connected between the filter and the channel modulators, for supplying the filtered I and Q signal components to the channel modulators.
Claim 6
Dependent Claim
241 words
In a bidirectional communications system comprising a plurality of customer interface unite (CIU), each defining a destination for incoming data and an origin for outgoing data and including a multi-channel modulator for generating modulated signals within discrete increment channels of a frequency band of the bidirectional communications system by modulating assigned carriers for a plurality of upstream channels with a outgoing data, the multi-channel modulator comprising; filter, responsive to in-phase (I) signal components and quadrature (Q) signal components of the outgoing data, for filtering the I signal components and the Q signal components to generate filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to the filtered I and Q signal components for modulating a selected one of the assigned carriers for the plurality of upstream channels with the outgoing data to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the discrete increment channels.
Claim 7
Dependent Claim
241 words
In a bidirectional communications system comprising a plurality of customer interface unite (CIU), each defining a destination for incoming data and an origin for outgoing data and including a multi-channel modulator for generating modulated signals within discrete increment channels of a frequency band of the bidirectional communications system by modulating assigned carriers for a plurality of upstream channels with a outgoing data, the multi-channel modulator comprising; filter, responsive to in-phase (I) signal components and quadrature (Q) signal components of the outgoing data, for filtering the I signal components and the Q signal components to generate filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to the filtered I and Q signal components for modulating a selected one of the assigned carriers for the plurality of upstream channels with the outgoing data to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the discrete increment channels.
Claim 8
Dependent Claim
40 words
The multi-channel modulator of claim 5 further comprising an interpolation module, connected between the filter and the channel modulators, for increasing the data rate of the filtered I and Q signals by upsampling the filtered I and Q signal components.
Claim 9
Dependent Claim
42 words
The apparatus of claim 5 further comprising a control module for controlling access by the I signal components and the Q signal components to the filter by queuing and serially inputting each of the I signal components and the Q signal components.
Claim 10
Dependent Claim
88 words
The apparatus of claim 7, wherein the control module comprises: a plurality of shift registers, one for each of the I signal components and the Q signal components, for storing the I signal components and the Q signal components; and a multiplexor, connected to the plurality of shift registers, for supplying a selected one of the I signal components and the Q signal components to the filter in response to an address signal corresponding to the selected one of the I signal components and the Q signal components.
Claim 11
Dependent Claim
30 words
The apparatus of claim 8 further comprising a demultiplexor, connected between the filter and the channel modulators, for supplying the filtered I and Q signal components to the channel modulators.
Claim 12
Dependent Claim
43 words
The apparatus of claim 9, wherein the multi-channel modulator further comprises an interpolation module, connected between the demultiplexor and the channel modulators, for increasing the data rate of the filtered I and Q signals by upsampling the filtered I and Q signal components.
Claim 13
Dependent Claim
81 words
The apparatus of claim 5, wherein the adder module comprises a first adder and a second adder, the first adder responsive to the complex modulated signal generated by each of the channel modulators for summing the real signal component of each channel modulator to produce a real resultant signal, and the second adder responsive to the complex modulated signal generated by each of the channel modulators, for summing the imaginary component of each channel modulator to produce an imaginary resultant signal.
Claim 14
Dependent Claim
47 words
The apparatus of claim 5, wherein the digital-to-analog converter (DAC) module comprises a first DAC for converting the real resultant signal to a first one of the analog signals and a second DAC for converting the imaginary resultant signal to a second one of the analog signals.
Claim 15
Dependent Claim
84 words
The apparatus of claim 5, wherein the transmitter comprises: a frequency shifter, responsive to the analog signals and to a frequency shift signal having a selected frequency for one of the discrete increment channels of the frequency band, for shifting the first analog signal by the selected frequency and for shifting the second analog signal by the selected frequency; and an adder for summing the first and second analog signals to generate the modulated signals within the discrete increment channels of the frequency band.
Claim 16
Dependent Claim
70 words
The apparatus of claim 5, wherein each of the channel modulators is a quadrature phase shift keying (QPSK) modulator operative at one of the assigned carriers varying in the discrete increment channels of 49.5 kHz, each of the assigned carriers positioned within one of 101 channels of a 5.0 MHz subband of the frequency band of the bidirectional communications system, with a nominal data rate of 144 kbps per channel.
Claim 17
Dependent Claim
314 words
A customer interface unit (CIU) for connection to a broadband communication network, the CIU operative for receiving first signals in a first frequency band from a headend associated with the broadband communication network and for communicating telephony signals between a subscriber and the headend in a second frequency band of the broadband communication network, the customer interface unit comprising: a first demodulator for demodulating the first signals in the first frequency band to produce demodulated first signals and for coupling the demodulated first signals to an output port of the customer interface unit; and a multi-channel modulator for generating modulated signals in the second frequency band by modulating carrier signals in accordance with the telephony signals, each of the telephony signals including in-phase (I) and quadrature (Q) signal components, the multi-channel modulator comprising: a filter for filtering the I and Q signal components to produce filtered I and Q signal components; an interpolation module for generating processed I and Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to the processed I and Q signal components for modulating a selected one of the carrier signals with a selected one of the telephony signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the second frequency band of the broadband communications network.
Claim 18
Dependent Claim
314 words
A customer interface unit (CIU) for connection to a broadband communication network, the CIU operative for receiving first signals in a first frequency band from a headend associated with the broadband communication network and for communicating telephony signals between a subscriber and the headend in a second frequency band of the broadband communication network, the customer interface unit comprising: a first demodulator for demodulating the first signals in the first frequency band to produce demodulated first signals and for coupling the demodulated first signals to an output port of the customer interface unit; and a multi-channel modulator for generating modulated signals in the second frequency band by modulating carrier signals in accordance with the telephony signals, each of the telephony signals including in-phase (I) and quadrature (Q) signal components, the multi-channel modulator comprising: a filter for filtering the I and Q signal components to produce filtered I and Q signal components; an interpolation module for generating processed I and Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to the processed I and Q signal components for modulating a selected one of the carrier signals with a selected one of the telephony signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals; and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the second frequency band of the broadband communications network.
Claim 19
Dependent Claim
36 words
The apparatus of claim 15 further comprising a control module for controlling access by the I and Q signal components to the filter by queuing and serially inputting each of the I and Q signal components.
Claim 20
Dependent Claim
88 words
The apparatus of claim 16, wherein the control module comprises: a plurality of shift registers, one for each of the I signal components and the Q signal components, for storing the I signal components and the Q signal components; and a multiplexor, connected to the plurality of shift registers, for supplying a selected one of the I signal components and the Q signal components to the filter in response to an address signal corresponding to the selected one of the I signal components and the Q signal components.
Claim 21
Dependent Claim
34 words
The apparatus of claim 17, wherein the multi-channel modulator further comprises a demultiplexor, connected between the filter and the channel modulators, for supplying the filtered I and Q signal components to the channel modulators.
Claim 22
Dependent Claim
44 words
The apparatus of claim 18, wherein the multi-channel modulator further comprises an interpolation module, connected between the demultiplexor and the channel modulators, for increasing the data rate of the filtered I and Q signal components by upsampling the filtered I and Q signal components.
Claim 23
Dependent Claim
73 words
The apparatus of claim 15, wherein the adder module comprises a first adder and a second adder, the first adder responsive to the complex modulated signal generated by each of the channel modulators for summing each real signal component to produce a real resultant signal, and the second adder responsive to the complex modulated signal generated by each of the channel modulators, for summing each imaginary component to produce an imaginary resultant signal.
Claim 24
Dependent Claim
47 words
The apparatus of claim 15, wherein the digital-to-analog converter (DAC) module comprises a first DAC for converting the real resultant signal to a first one of the analog signals and a second DAC for converting the imaginary resultant signal to a second one of the analog signals.
Claim 25
Dependent Claim
74 words
The apparatus of claim 21, wherein the transmitter comprises: a frequency shifter, responsive to the analog signals and to a frequency shift signal having a selected frequency of the second frequency band, for shifting the first analog signal by the selected frequency and for shifting the second analog signal by the selected frequency; and an adder for summing the first and second analog signals to generate the modulated signals of the second frequency band.
Claim 26
Dependent Claim
389 words
A customer interface unit (CIU) for connection to a broadband communication network, the CIU operative for receiving first signals in a first frequency band from a headend associated with the broadband communication network, for receiving second signals from the headend, and for communicating telephony signals between a subscriber and the headend, said customer interface unit comprising: a first demodulator for demodulating the first signals in the first frequency band and for coupling them to an output port of the customer interface unit; a second demodulator for receiving the second signals and for identifying, from the second signals, one of a plurality of frequency sub bands in a second frequency band in the broadband communication network for communicating the telephony signals to the headend; and a frequency agile modulator, responsive to the identified one of said plurality of frequency sub bands in the second frequency band, for generating modulated signals by modulating the telephony signals from the customer interface unit in the identified frequency subband, each of the telephony signals including in-phase (I) and quadrature (Q) signal components, the frequency agile modulator comprising: a filter for filtering the I and Q signal components to produce filtered I and Q signal components; an interpolation module for generating processed I and Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to a pair of the processed I and Q signal components for modulating one of a plurality of carrier signals selected in response to the identified one of the plurality of frequency subbands in the second frequency band with a selected one of the telephony signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals, and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the identified frequency subband of the second frequency band of the broadband communications network.
Claim 27
Dependent Claim
389 words
A customer interface unit (CIU) for connection to a broadband communication network, the CIU operative for receiving first signals in a first frequency band from a headend associated with the broadband communication network, for receiving second signals from the headend, and for communicating telephony signals between a subscriber and the headend, said customer interface unit comprising: a first demodulator for demodulating the first signals in the first frequency band and for coupling them to an output port of the customer interface unit; a second demodulator for receiving the second signals and for identifying, from the second signals, one of a plurality of frequency sub bands in a second frequency band in the broadband communication network for communicating the telephony signals to the headend; and a frequency agile modulator, responsive to the identified one of said plurality of frequency sub bands in the second frequency band, for generating modulated signals by modulating the telephony signals from the customer interface unit in the identified frequency subband, each of the telephony signals including in-phase (I) and quadrature (Q) signal components, the frequency agile modulator comprising: a filter for filtering the I and Q signal components to produce filtered I and Q signal components; an interpolation module for generating processed I and Q signal components by upsampling the filtered I and Q signal components; a plurality of channel modulators, each of the channel modulators responsive to a pair of the processed I and Q signal components for modulating one of a plurality of carrier signals selected in response to the identified one of the plurality of frequency subbands in the second frequency band with a selected one of the telephony signals to produce a complex modulated signal having a real signal component and an imaginary signal component; an adder module, responsive to the complex modulated signal generated by each of the channel modulators, for summing the real signal component of each channel modulator to produce a real resultant signal and for summing the imaginary signal component of each channel modulator to produce an imaginary resultant signal; a digital-to-analog converter (DAC) module for converting the real resultant signal and the imaginary resultant signal to analog signals, and a transmitter, responsive to the analog signals, for transmitting the modulated signals within the identified frequency subband of the second frequency band of the broadband communications network.
Claim 28
Dependent Claim
33 words
The customer interface unit of claim 23, wherein said first signals comprise television program signals, and wherein said output port comprises a video signal port for connection to a CATV set top converter.
Claim 29
Dependent Claim
25 words
The customer interface unit of claim 23, wherein said output port comprises a telephony port for receiving the telephony signals into the customer interface unit.
Claim 30
Dependent Claim
53 words
The customer interface unit of claim 23, wherein the second signals are communicated in the first frequency band and comprise a message including address information corresponding to a selected subscriber and frequency subband information corresponding to a one of the frequency sub bands in the second frequency band in the broadband communications network.
Claim 31
Dependent Claim
71 words
The customer interface unit of claim 23, wherein said frequency agile modulator is operative to change the frequency at which the telephony signals are being communicated to the headend from a first frequency subband of the second frequency band in the broadband communications network to a second frequency subband of the second frequency band in the broadband communications network in response to a command received as one of the second signals.
Claim 32
Dependent Claim
115 words
The apparatus of claim 1, wherein each of the channel modulators comprises: first and second look-up tables, the first look-up table storing cosine function values and the second-look-up table storing sine function values the cosine function values and the sine function values being accessed in response to a phase value corresponding to the selected carrier signal; a plurality of multipliers, responsive to the cosine function value and the sine function values and to the processed I and Q signal components, to produce cross products; and a plurality of adders, responsive to the cross products, to produce the real signal component of the complex modulated signal and the imaginary signal component of the complex modulated signal.
Claim 33
Dependent Claim
145 words
The apparatus of claim 28, wherein each channel modulator further comprises: a first invert/pass block, connected between the first look-up table and the multipliers for passing the cosine function values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine function values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second lock-up table stores the positive half cycle of the sine function.
Claim 34
Dependent Claim
189 words
The apparatus of claim 1, wherein each of the channel modulators comprises: first and second look-up tables, the first look-up table storing a plurality of cosine function values and the second-look-up table storing a plurality of sine function values, the cosine function values and the sine function values being accessed in response to a phase value corresponding to the selected carrier signal; a first multiplier responsive to the cosine function values and the processed Q signal components to produce a first product; a second multiplier responsive to the sine function values and the processed Q signal components to produce a second product; a third multiplier responsive to the cosine function values and the processed I signal components to produce a third product; a fourth multiplier responsive to the sine function values and the processed I signal components to produce a fourth product; a first adder, responsive to the second product and the third product to produce the real signal component of the complex modulated signal; and a second adder responsive to the first product and the fourth products to produce the imaginary signal component of the complex modulated signal.
Claim 35
Dependent Claim
151 words
The apparatus of claim 30, wherein each channel modulator further comprises: a first invert/pass block, connected between the first look-up table and the first and third multipliers, for passing the cosine function values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine function values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the second and fourth multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second look-up table stores the positive half cycle of the sine function.
Claim 36
Dependent Claim
121 words
The apparatus of claim 5, wherein each of the channel modulators comprises; first and second look-up tables, the first look-up table storing a plurality of cosine function values and the second-look-up table storing a plurality of sine function values, the cosine function value and the sine function values being accessed in response to a phase value corresponding to the selected assigned carrier; a plurality of multipliers, responsive to the cosine function values and the sine function values and to the filtered I and Q signal components, to produce cross products; and a plurality of adders, responsive to the cross products, to produce the real signal component of the complex modulated signal and the imaginary signal component of the complex modulated signal.
Claim 37
Dependent Claim
145 words
The apparatus of claim 32, wherein each channel modulator further comprises: a first invert/pass block, connected between the first look-up table and the multipliers, for passing the cosine function values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine function values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second look-up table stores the positive half cycle of the sine function.
Claim 38
Dependent Claim
188 words
The apparatus of claim 5, wherein each of the channel modulators comprises: first and second look-up tables, the first look-up table storing a plurality of cosine function values and the second-look-up table storing a plurality of sine function values, the cosine function values and the sine function values being accessed in response to a phase value corresponding to the selected carrier; a first multiplier responsive to the cosine function values and the filtered Q signal components to produce a first product; a second multiplier responsive to the sine function values and the filtered Q signal components to produce a second product; a third multiplier responsive to the cosine function values and the filtered I signal components to produce a third product; a fourth multiplier responsive to the sine function values and the filtered I signal components to produce a fourth product; a first adder, responsive to the second product and the third product to produce the real signal component of the complex modulated signal; and a second adder responsive to the first product and the fourth product to produce the imaginary signal component of the complex modulated signal.
Claim 39
Dependent Claim
151 words
The apparatus of claim 34, wherein each channel modulator further comprises: a first invert/pass block, connected between the first look-up table and the first and third multipliers, for passing the cosine function values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine function values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the second and fourth multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second look-up table stores the positive half cycle of the sine function.
Claim 40
Dependent Claim
121 words
The apparatus of claim 15, wherein each of the channel modulators comprises: first and second look-up tables, the first look-up table storing a plurality of cosine function values and the second-look-up table storing a plurality of sine function values, the cosine function values and the sine function values being accessed in response to a phase value corresponding to the selected carrier signal; a plurality of multipliers, responsive to the cosine function values and the sine function values and to the processed I and Q signal components, to produce cross products; and a plurality of adders, responsive to the cross products, to produce the real signal component of the complex modulated signal and the imaginary signal component of the complex modulated signal.
Claim 41
Dependent Claim
145 words
The apparatus of claim 36, wherein each channel modulator further comprises: a first invert/pass block, connected between the first look-up table and the multipliers, for passing the cosine function values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine function values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second look-up table stores the positive half cycle of the sine function.
Claim 42
Dependent Claim
189 words
The apparatus of claim 15, wherein each of the channel modulators comprises; first and second look-up tables, the first look-up table a plurality of storing cosine function values and the second-look-up table storing a plurality of sine function values, the cosine function values and the sine function values being accessed in response to a phase value corresponding to the selected carrier signal; a first multiplier responsive to the cosine function values and the processed Q signal components to produce a first product; a second multiplier responsive to the sine function values and the processed Q signal components to produce a second product; a third multiplier responsive to the cosine function values and the processed I signal components to produce a third product; a fourth multiplier responsive to the sine function values and the processed I signal components to produce a fourth product; a first adder, responsive to the second product and the third product to produce the real signal component of the complex modulated signal; and a second adder responsive to the first product and the fourth product to produce the imaginary signal component of the complex modulated signal.
Claim 43
Dependent Claim
149 words
The apparatus of claim 38, wherein each channel modulator further comprises: a first invert/pass module, connected between the first look-up table and the first and third multipliers, for passing the cosine values from the first look-up table for the positive half cycle of the cosine function, and inverting the cosine values from the first look-up table for the negative half cycle of the cosine function; a second invert/pass module, connected between the second look-up table and the second and fourth multipliers, for passing the sine function values from the second look-up table for the positive half cycle of the sine function, and inverting the sine function values from the second look-up table for the negative half cycle of the sine function; wherein the first look-up table stores the positive half cycle of the cosine function and the second look-up table stores the positive half cycle of the sine function.