Fractional fourier transform convolver arrangement
An M-point Fractional Fourier is described using several 2M-points traditional Fourier transforms. The signal path is fed through a series of blocks including a first multiplier, a zero pad, an FFT, a second multiplier, an IFFT, a first half element, and a third multiplier. The first and third multipliers have as their other inputs a value exp(−jΠn 2 α) for n=0:M−1, derived from the clock offset signal represented by α.
1. An electronic device for performing an M-point Fractional Fourier Transform on an input signal, where M is a nonzero integer, the electronic device comprising:
a first 2M-points fast Fourier transformer having an input for receiving the input signal;
a second 2M-points fast Fourier transformer having an input for receiving an independent signal;
a first multiplier having respective inputs coupled to an output of said first 2M-points fast Fourier transformer, and to an output of said second 2M-points fast Fourier transformer;
a 2M-points inverse fast Fourier transformer having an input coupled to an output of said first multiplier;
a first half element coupled to an output of said 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points;
a second multiplier coupled to an output of said first half element and providing an output signal representing an M-point Fractional Fourier Transform of the input signal;
a third multiplier coupled to the input of said first 2M-points fast Fourier transformer; and
a first exponential circuit coupled to inputs of said second and third multipliers for calculating exp(−jΠn 2 α) for n=0:M−1, derived from the independent signal having a value α.
2. An electronic device according to claim 1 , further comprising:
a second exponential circuit for calculating a value exp(jΠn 2 α) for n=0:M, where α is a value of the independent signal; and
a phase copy circuit having an input coupled to an output of said second exponential circuit for copying an output signal thereform, and having an output coupled to said second 2M-points fast Fourier transformer.
3. An electronic device according to claim 1 , wherein the electronic device is configured as a transmitter.
4. An electronic device according to claim 1 , wherein the electronic device is configured as a receiver.
5. An electronic device according to claim 1 , wherein the electronic device is configured as a modem.
6. An electronic device according to claim 1 , further comprising a substrate; and
wherein said first and second 2M-points fast Fourier transformers, said first multiplier and said 2M-points inverse fast Fourier transformer are on said substrate so that the electronic device is an integrated circuit.
7. A computer-readable medium having computer-executable instructions for causing a receiver to perform steps comprising:
calculating a first 2M-points fast Fourier transform using a first 2M-points fast Fourier transformer having an input for receiving an input signal, where M is a non-zero integer;
calculating a second 2M-points fast Fourier transform using a second 2M-points fast Fourier transformer having an input for receiving an independent signal;
performing a first multiplication of the first and second 2M-points fast Fourier transforms using a second multiplier having respective inputs coupled to an output of the first 2M-points fast Fourier transformer, and to an output of the second 2M-points fast Fourier transformer;
calculating a 2M-points inverse fast Fourier transform using a 2M-points inverse fast Fourier transformer having an input coupled to an output of the first multiplier;
calculating a first halving of a signal output by the 2M-points inverse fast Fourier transformer using a first half element coupled to an output of the 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points;
performing a second multiplication based on the first halving signal using a second multiplier coupled to an output of the first half element for providing an output signal representing an M-point Fractional Fourier Transform of the input signal;
performing a third multiplication using a third multiplier coupled to the input of the first 2M-points fast Fourier transformer; and
calculating a first exponential equation of exp(−jΠn 2 α) for n=0:M−1 using a first exponential block coupled to inputs of the second and third multipliers, the calculating being derived from the independent signal having a value α.
8. A computer-readable medium according to claim 7 , further comprising:
calculating a second exponential calculation of exp(jΠn 2 α) for n=0:M using a second exponential block, where α is a value of the independent signal; and
copying an output signal from the second exponential block using a phase copy block having an input coupled to an output of the second exponential block for copying an output signal therefrom, and having an output coupled to the second 2M-points fast Fourier transformer for performing a Fractional Fourier Transform in the additional 2N-points fast Fourier transform block.
9. A receiver comprising:
a splitter for splitting a received multicarrier signal into first and second data paths, with the first data path providing a first data stream corresponding to data symbols and with the second data path providing a second data stream;
each respective data path comprising the following for processing the first and second data streams with different delays to independently extract cyclic prefixes and the data symbols therefrom
a first 2M-points fast Fourier transformer having an input for receiving the input signal,
a second 2M-points fast Fourier transformer having an input for receiving an independent signal,
a second multiplier having respective inputs coupled to an output of said first 2M-points fast Fourier transformer, and to an output of said second 2M-points fast Fourier transformer,
a 2M-points inverse fast Fourier transformer having an input coupled to an output of said first multiplier,
a first half element coupled to an output of said 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points,
a second multiplier coupled to an output of said first half element,
a third multiplier coupled to the input of said first 2M-points fast Fourier transformer,
a first exponential circuit coupled to inputs of said second and third multipliers for calculating exp(−jΠn 2 α) for n=0:M−1, derived from the independent signal having a value α, and
with said second 2M-points fast Fourier transformer and said first exponential circuit being shared by the respective data paths; and
a combiner for combining the independently extracted cyclic prefixes and the data symbols.
10. A receiver according to claim 9 , further comprising:
a second exponential circuit for calculating a value exp(jΠn 2 α) for n=0:M, derived from a signal having a value α;
a phase copy circuit having an input coupled to an output of said second exponential circuit for copying an output signal therefrom, and having an output coupled to an input of said second 2M-points fast Fourier transformer;
with said second exponential circuit and said phase copy circuit being shared by the respective data paths.
11. A method for processing a multicarrier signal comprising data symbols and cyclic prefixes, the method comprising:
splitting the multicarrier signal into a first data stream corresponding to the data symbols and into a second data stream corresponding to the cyclic prefixes;
processing each respective data stream with different delays to independently extract the cyclic prefixes and the data symbols therefrom, the processing comprising
calculating a first 2M-points fast Fourier transform using a first 2M-points fast Fourier transformer having an input for receiving an input signal, where N is a nonzero integer,
calculating a second 2M-points fast Fourier transform using a second 21M-points fast Fourier transformer having an input for receiving an independent signal,
performing a second multiplication of the first and second 2M-points fast Fourier transforms using a first multiplier having respective inputs coupled to an output of the first 2M-points fast Fourier transformer, and to an output of the second 2M-points fast Fourier transformer,
calculating a 2M-points inverse fast Fourier transform using a 2M-points inverse fast Fourier transformer having an input coupled to an output of the first multiplier,
calculating a first halving of a signal output by the 2M-points inverse fast Fourier transformer using a first half element coupled to an output of the 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points,
performing a second multiplication based on the first halving signal using a second multiplier coupled to an output of the first half element,
performing a third multiplication using a third multiplier coupled to the input of the first 2M-points fast Fourier transformer;
calculating a first exponential equation of exp(−jΠn 2 α) for n=0:M−1 using a first exponential block coupled to inputs of the second and third multipliers, the calculating being derived from the independent signal having a value α, and
where calculating the second 2M-points fast Fourier transform and calculating the first exponential equation are shared by the respective data streams; and
combining the independently extracted cyclic prefixes and the data symbols.
12. A method according to claim 11 , further comprising a second exponential block for calculating a value exp(jΠn 2 α) for n=0:M, derived from a signal having a value α; and a phase copy block having an input coupled to an output of the second exponential block for copying an output signal and having an output coupled to the second 2N-points fast Fourier transformer, with the second exponential block and the phase copy block being shared by the respective data streams.
13. An electronic device for performing an M-point Fractional Fourier Transform on an input signal, where M is a nonzero integer, the electronic device comprising:
a first 2M-points fast Fourier transformer having an input for receiving the input signal;
a second 2M-points fast Fourier transformer having an input for receiving an independent signal;
a first multiplier having respective inputs coupled to an output of said first 2M-points fast Fourier transformer, and to an output of said second 2M-points fast Fourier transformer;
a 2M-points inverse fast Fourier transformer having an input coupled to an output of said second multiplier;
a first half element coupled to an output of said 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points;
a second multiplier coupled to an output of said first half element and providing an output signal representing an M-point Fractional Fourier Transform of the input signal;
a first exponential circuit for calculating a value exp(jΠn 2 α) for n=0:M, where α is a value of the independent signal; and
a phase copy circuit having an input coupled to an output of said first exponential circuit for copying an output signal thereform, and having an output coupled to said second 2M-points fast Fourier transformer.
14. An electronic device according to claim 13 , further comprising:
a third multiplier coupled to the input of said first 2M-points fast Fourier transformer; and
a second exponential circuit coupled to inputs of said second and third multipliers for calculating exp(−jΠn 2 α) for n=0:M−1, derived from the independent signal having a value α.
15. An electronic device according to claim 13 , wherein the electronic device is configured as a transmitter.
16. An electronic device according to claim 13 , wherein the electronic device is configured as a receiver.
17. An electronic device according to claim 13 , wherein the electronic device is configured as a modem.
18. An electronic device according to claim 13 , further comprising a substrate; and
wherein said first and second 2M-points fast Fourier transformers, said first multiplier and said 2M-points inverse fast Fourier transformer are on said substrate so that the electronic device is an integrated circuit.
19. A receiver comprising:
a splitter for splitting a received multicarrier signal into first and second data paths, with the first data path providing a first data stream corresponding to data symbols and with the second data path providing a second data stream;
each respective data path comprising the following for processing the first and second data streams with different delays to independently extract cyclic prefixes and the data symbols therefrom
a first 2M-points fast Fourier transformer having an input for receiving the input signal,
a second 2M-points fast Fourier transformer having an input for receiving an independent signal,
a first multiplier having respective inputs coupled to an output of said first 2M-points fast Fourier transformer, and to an output of said second 2M-points fast Fourier transformer,
a 2M-points inverse fast Fourier transformer having an input coupled to an output of said first multiplier,
a first half element coupled to an output of said 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points,
a second multiplier coupled to an output of said first half element,
a first exponential block for calculating a value exp(jΠn 2 α) for n=0:M, derived from a signal having a value α,
a phase copy block having an input coupled to an output of said first exponential block for copying an output signal therefrom, and having an output coupled to an input of said second 2M-points fast Fourier transformer, and
with said second 2M-points fast Fourier transformer, said first exponential block and said phase copy block being shared by the respective data paths; and
a combiner for combining the independently extracted cyclic prefixes and the data symbols.
20. A receiver according to claim 19 , further comprising a second exponential block coupled to inputs of said second and third multipliers for calculating exp(−jΠn 2 α) for n=0:M−1, derived from the independent signal having a value α, with said second exponential block being shared by the respective data paths.
21. A method for processing a multicarrier signal comprising data symbols and cyclic prefixes, the method comprising:
splitting the multicarrier signal into a first data stream corresponding to the data symbols and into a second data stream corresponding to the cyclic prefixes;
processing each respective data stream with different delays to independently extract the cyclic prefixes and the data symbols therefrom, the processing comprising
calculating a first 2M-points fast Fourier transform using a first 2M-points fast Fourier transformer having an input for receiving an input signal, where M is a non-zero integer,
calculating a second 2M-points fast Fourier transform using a second 2M-points fast Fourier transformer having an input for receiving an independent signal,
performing a first multiplication of the first and second 2M-points fast Fourier transforms using a first multiplier having respective inputs coupled to an output of the first 2M-points fast Fourier transformer, and to an output of the second 2M-points fast Fourier transformer,
calculating a 2M-points inverse fast Fourier transform using a 2M-points inverse fast Fourier transformer having an input coupled to an output of the first multiplier,
calculating a first halving of a signal output by the 2M-points inverse fast Fourier transformer using a first half element coupled to an output of the 2M-points inverse fast Fourier transformer for reducing an output therefrom from 2M-points to M-points,
performing a second multiplication based on the first halving signal using a second multiplier coupled to an output of the first half element,
calculating a first exponential equation exp(jΠn 2 α) for n=0:M, derived from a signal having a value α,
copying an output signal from the second exponential block using a phase copy block, and providing an input to the second 2M-points fast Fourier transformer, and
with the second 2M-points fast Fourier transformer, the first exponential equation and the phase copy block being shared by the respective data streams; and
combining the independently extracted cyclic prefixes and the data symbols.
22. A method according to claim 21 , further comprising calculating a second exponential equation of exp(−jΠn 2 α) for n=0:M−1 using a second exponential block coupled to inputs of the second and third multipliers,
derived from the independent signal having a value α, and where calculating the second exponential equation is shared by the respective data streams.