Digital signal synthesis system

Claim 2

A process for digital synthesis of a complex waveform having one or more sinusoidal components of arbitrary frequency, amplitude, and phase, comprising the steps of: spectrally describing each of said sinusoidal components in the frequency domain with a spectral description formed by: selecting for each of said sinusoidal components a set of spectral cells spaced-apart in order by a predetermined frequency, f c , each cell potentially representing any complex value in the frequency domain; determining for each of said spectral cells the magnitude and phase of a complex value according to a raised cosine modulation function, each value varying in dependence upon the order of the respective one of said spectral cells within its set; and, adding each complex value to the value represented by the respective one of said spectral cells; periodically transforming each said spectral description from the frequency domain to the time domain to provide successive samples forming segments of the respective said sinusoidal components; and, overlapping successive of said segments having an identical frequency by 50 percent of their period to provide unmodulated segments of each of the components.

Claim 3

The process as set forth in claim 1, further comprising the steps of: periodically combining one of each said unmodulated segments at each said arbitrary frequency.

Claim 4

The process set forth in claim 1 wherein said sinusoidal components are modulated in amplitude according to the formula: A.sub.m = 0.54 + 0.46 COSINE (2π f.sub.c t).

Claim 5

The process set forth in claim 1 wherein said sinusoidal components are modulated in amplitude according to the formula: A.sub.m = 0.5 + 0.5 COSINE (2π f.sub.c t).

Claim 6

A digital circuit for the electronic synthesis of a desired waveform having m sinusoidal components, comprising: a first buffer register for receiving and storing the relative amplitude, frequency, and phase of each of said m sinusoidal components; a second buffer register for receiving and storing in m sets of n spectral cells spaced apart by a predetermined frequency, f c , m·n complex values describing the frequency spectrum of a modulated segment of the desired waveform; a third buffer register for receiving and storing for each periodic transformation the last N samples of a sampled segment of a modulated waveform; and, computational means coupled between said first and second buffer registers, and between said second and third buffer registers, for determining for each of the m sinusoidal components, at each of n spaced-apart frequencies, a set of n complex values, W m (i), where i varies incrementally by one from (-n/2) + 1 to n,/2 for adding each of the m·n complex values in a prescribed sequence to a different one of said the spectral cells, for periodically performing an inverse discrete Fourier transformation upon the m·n complex values describing the frequency spectrum of a modulated segment of the desired waveform, providing 2N samples of a waveform segment of each of said sinusoidal components modulated in the domain, and for adding the last N samples of each waveform segment with the first N samples of the next waveform segment provided of the same one of the sinusoidal components.

Claim 7

A digital circuit for the electronic synthesis of a desired waveform having m sinusoidal components, comprising: a first buffer register for receiving and storing the relative amplitude, frequency, and phase of each of said m sinusoidal components; a second buffer register for receiving and storing in m sets of n spectral cells spaced apart by a predetermined frequency, f c , m·n complex values describing the frequency spectrum of a modulated segment of the desired waveform; a third buffer register for receiving and storing for each periodic transformation the last N samples of a sampled segment of a modulated waveform; and, computational means coupled between said first and second buffer registers, and between said second and third buffer registers, for determining for each of the m sinusoidal components, at each of n spaced-apart frequencies, a set of n complex values, W m (i), where i varies incrementally by one from (-n/2) + 1 to n,/2 for adding each of the m·n complex values in a prescribed sequence to a different one of said the spectral cells, for periodically performing an inverse discrete Fourier transformation upon the m·n complex values describing the frequency spectrum of a modulated segment of the desired waveform, providing 2N samples of a waveform segment of each of said sinusoidal components modulated in the domain, and for adding the last N samples of each waveform segment with the first N samples of the next waveform segment provided of the same one of the sinusoidal components.

Claim 8

The digital circuit set forth in claim 5 wherein W m (i) is determined according to the formula: ##EQU43## where n is a selected real, even integer, and m is an index initially equal to one.

Claim 9

The digital circuit set forth in claim 5 wherein said sinusoidal components are modulated in amplitude according to the formula: A.sub.m = 0.54 + 0.46 COSINE (2πf.sub.c t0).

Claim 10

The digital circuit set forth in claim 5 wherein said sinusoidal components are modulated in amplitude according to the formula: A.sub.m = 0.5 + 0.5 COSINE (2πf.sub.c t).

Claim 11

A process for digital synthesis of a complex, composite time wave form having M sinusoidal components S m (t) of relative frequency F m , and relative amplitude A m , where M is a positive, real integer having a value equal to or greater than one, and m is an integer index varying in value from one to M, comprising the steps of: defining a set of N fixed spectral cell frequencies spaced apart by f c Hertz the band between zero and (N-1)f c includes each said frequency F m for all said sinusoidal components; determining for each of M said sinusoidal components two frequency parameters, C m and CF m respectively, the integer part and the fractional part of the quotient of F m to f c ; loading the frequency parameters C m and CF m , and the amplitude A m of each of said M sinusoidal components into the memory of a first buffer register; determining the phase α m of each of the corresponding said M sinusoidal components at the beginning of said time waveform; storing the phase α m corresponding to each of said M sinusoidal components in the memory of said first buffer register; generating in a digital computer adapted to read said frequency parameters, said amplitude, and said phase of each of said M sinusoidal components from the memory of a buffer, a set of n complex values by performing an interative routine comprising the seven steps of: (1) computing the value W m (i) where: ##EQU44## where n is a selected real, even integer, i is an index of n having a value equal to (-n/2) + q, q is an index initially equal to one, and m is an index initially equal to one; (2) adding W m (i) to the contents of that one of N said spectral cells in the memory of a second buffer register having an index of (C m + i) to form the frequency spectral cells in the memory of a second buffer register having an index of (C m + i) to form the frequency spectra of said time waveform; (3) incrementing the value of q by one; (4) repeating the preceeding three steps until the value of q exceeds the value of n; (5) incrementing the current phase α m by π(C m + CF m ) radians; (6) incrementing the value of m by one; and, (7) repeating the steps set forth in the preceding six paragraphs until the value of m exceeds the value of M; applying in said digital computer an inverse discrete Fourier transform to the contents of the N cells containing said frequency spectra to produce a modulated waveform segment having a set of 2N real time samples, TS rp , for which r varies in value by successive increments of one; adding in said digital computer the first N real time samples belonging to the set TS rp , for which r varies in value from one to N, to the last N real time samples belonging to the set TS r (p-1), for which r varies in value from N+1 to 2N, to form an unmodulated segment of said time waveform; storing the last N real time samples belonging to the set TS rp , for which r varies in value from N+1 to 2N, in the memory of a third register; incrementing the value of p; and, repeating the steps set forth in the preceding 11 paragraphs whereby an output waveform of successive segments of N real time samples is digitally synthesized.

Claim 12

A process for digital synthesis of a complex, composite time wave form having M sinusoidal components S m (t) of relative frequency F m , and relative amplitude A m , where M is a positive, real integer having a value equal to or greater than one, and m is an integer index varying in value from one to M, comprising the steps of: defining a set of N fixed spectral cell frequencies spaced apart by f c Hertz the band between zero and (N-1)f c includes each said frequency F m for all said sinusoidal components; determining for each of M said sinusoidal components two frequency parameters, C m and CF m respectively, the integer part and the fractional part of the quotient of F m to f c ; loading the frequency parameters C m and CF m , and the amplitude A m of each of said M sinusoidal components into the memory of a first buffer register; determining the phase α m of each of the corresponding said M sinusoidal components at the beginning of said time waveform; storing the phase α m corresponding to each of said M sinusoidal components in the memory of said first buffer register; generating in a digital computer adapted to read said frequency parameters, said amplitude, and said phase of each of said M sinusoidal components from the memory of a buffer, a set of n complex values by performing an interative routine comprising the seven steps of: (1) computing the value W m (i) where: ##EQU44## where n is a selected real, even integer, i is an index of n having a value equal to (-n/2) + q, q is an index initially equal to one, and m is an index initially equal to one; (2) adding W m (i) to the contents of that one of N said spectral cells in the memory of a second buffer register having an index of (C m + i) to form the frequency spectral cells in the memory of a second buffer register having an index of (C m + i) to form the frequency spectra of said time waveform; (3) incrementing the value of q by one; (4) repeating the preceeding three steps until the value of q exceeds the value of n; (5) incrementing the current phase α m by π(C m + CF m ) radians; (6) incrementing the value of m by one; and, (7) repeating the steps set forth in the preceding six paragraphs until the value of m exceeds the value of M; applying in said digital computer an inverse discrete Fourier transform to the contents of the N cells containing said frequency spectra to produce a modulated waveform segment having a set of 2N real time samples, TS rp , for which r varies in value by successive increments of one; adding in said digital computer the first N real time samples belonging to the set TS rp , for which r varies in value from one to N, to the last N real time samples belonging to the set TS r (p-1), for which r varies in value from N+1 to 2N, to form an unmodulated segment of said time waveform; storing the last N real time samples belonging to the set TS rp , for which r varies in value from N+1 to 2N, in the memory of a third register; incrementing the value of p; and, repeating the steps set forth in the preceding 11 paragraphs whereby an output waveform of successive segments of N real time samples is digitally synthesized.

Claim 13

The process as set forth in claim 9 wherein said waveform segment is modulated in amplitude according to the formula: A.sub.m = 0.5 + 0.5 COSINE (2πf.sub.c t).

Claim 14

The process as set forth in claim 9 wherein said waveform segment is modulated in amplitude according to the formula: A.sub.m = 0.54 + 0.46 COSINE (2πf.sub.c t).

Claim 15

The process as set forth in claim 9 wherein n equals 4.

Claim 16

The process as set forth in claim 9 wherein n equals 6.