High-speed multiplier to multiply a digital signal by a periodic signal
First Claim
1. A method for the multiplication of a digital signal SN by a sine waveform using a digital phase φ
- varying periodically in a sawtoothed form, wherein said method comprises the operations consisting in;
applying this phase to the input of a decoder using, as a decoding function, a table of N approximate integer values Ai of N numbers K sine 2iπ
/N, i being an index from 0 to N-1, and K being any number that is identical for all the indices i, the approximate integer values Ai being algebraic sums of one or more positive integer powers of 2 to which a sign is assigned, at least some of the values being sums of several different powers of two,multiplying the digital signal SN, for each index i corresponding to a phase 2iπ
/N, by the various powers of 2 that form the number Ai, under the control of the decoder,and obtaining the algebraic sums of the signals thus multiplied to form a digital value that is the product of SN by the approximate value Ai.
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Accused Products
Abstract
Disclosed is a digital multiplication circuit to multiply a digital signal SN by a periodic waveform that is, in principle, a sine waveform. This circuit uses a phase digital generator φ varying in saw-toothed form and it uses an approximation of the samples of a function K sine φ by algebraic sums of positive integer values of two for each phase value, K being a coefficient identical for all the phase values. The product of SN by these sums is rapid and easy to obtain and does not require a sine table. A decoder receiving the phase φ defines the powers of two to be set up, and a routing circuit carries out the operation of multiplication by powers of two under the control of the decoder. One or two adders obtain the sums of powers of two. The result is an approximate result of the product SN.K. sine φ.
23 Citations
14 Claims
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1. A method for the multiplication of a digital signal SN by a sine waveform using a digital phase φ
- varying periodically in a sawtoothed form, wherein said method comprises the operations consisting in;
applying this phase to the input of a decoder using, as a decoding function, a table of N approximate integer values Ai of N numbers K sine 2iπ
/N, i being an index from 0 to N-1, and K being any number that is identical for all the indices i, the approximate integer values Ai being algebraic sums of one or more positive integer powers of 2 to which a sign is assigned, at least some of the values being sums of several different powers of two,multiplying the digital signal SN, for each index i corresponding to a phase 2iπ
/N, by the various powers of 2 that form the number Ai, under the control of the decoder,and obtaining the algebraic sums of the signals thus multiplied to form a digital value that is the product of SN by the approximate value Ai. - View Dependent Claims (2, 3, 4, 5)
- varying periodically in a sawtoothed form, wherein said method comprises the operations consisting in;
-
6. A method for the multiplication of a digital signal SN by a periodic waveform F(φ
- ), using a digital phase φ
varying periodically in a sawtoothed form and taking successive values φ
i during a period, i being an index from 0 to N-1, where N represents the number of phase samples used during one period, wherein said method comprises the operations consisting in;applying this phase to the input of a decoder using, as a decoding function, a table of N approximate integer values Ai of N numbers KF(φ
i), K being any number that is identical for all the indices i, the approximate integer values Ai being algebraic sums of one or more positive integer powers of 2 to which a sign is assigned, at least certain values Ai being sums of several different powers of two,multiplying the digital signal SN, for each index i corresponding to a phase φ
i, by the various powers of 2 that form the number Ai, under the control of the decoder,obtaining the algebraic sums of the signals thus multiplied to form a digital value that is the product of SN by the approximate value Ai.
- ), using a digital phase φ
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7. A digital multiplication circuit for the periodic multiplication of a digital value SN by a sine waveform, wherein said circuit comprises:
-
a means to produce a periodic digital phase φ
varying in sawtoothed form,a decoder receiving the phase φ and
bringing about the correspondence, with any value 2iπ
/N of the phase φ
, where i is an index varying from 0 to N-1, of one or more positive integer powers of 2 to which a sign is assigned, the algebraic sum Ai of which is an approximate value of K sine 2iπ
/N, K having the same value for all the values of Ai,routing means activated by the decoder when it receives a phase 2iπ
/N to give one or more signals SNij from the signal SN, the signal SNij representing the signal SN multiplied by one of the powers of two that are assigned a sign and are used in the sum Ai,means of addition activated by the decoder and capable of receiving and adding the signals SNij given by the routing means when the decoder receives a phase 2iπ
/N,the circuit giving, at one output, a signal SN.Ai that represents the multiplication of the signal by a waveform which is an approximate value of the sine waveform K sine φ
. - View Dependent Claims (8, 9, 10, 11, 13, 14)
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12. A digital multiplication circuit for the periodic multiplication of a digital signal SN by a periodic waveform F(φ
- ), using a digital phase φ
varying periodically in a sawtoothed form and taking successive values φ
i during a period, i being an index from 0 to N-1, where N represents the number of phase samples used during one period, wherein said circuit comprises;a means to produce a periodic digital phase φ
varying in sawtoothed form,a decoder receiving the phase φ and
bringing about the correspondence, with any value φ
i of the phase φ
, of the sum Ai of one or more positive integer powers of 2 to which a sign is assigned, i being an index varying from 0 to N-1, each number Ai being equal to an approximate value of KF(φ
i), K having the same value for all instances of Ai, and at least certain values of Ai being constituted by sums of several different powers of two,routing means activated by the decoder when it receives a phase φ
i to give one or more signals SNij from the signal SN, the signal SNij being the signal SN multiplied by one of the powers of two that are assigned a sign and are used in the sum Ai,means of addition activated by the decoder and capable of receiving and adding the signals SNij given by the routing means when the decoder receives a phase φ
i,the circuit giving, at one output, a signal SN.Ai that represents the multiplication of the signal by a waveform which is an approximate value of the periodic waveform K(φ
).
- ), using a digital phase φ
Specification