US3795864A — Methods and apparatus for generating walsh functi…

Claim 1

Independent Claim 157 words

A method of generating a digital signal which is representative of the Kth Walsh function of order n, where n 2p, p > OR = 1, and 0 < OR = K < OR = n-1, comprising the steps of: ''''anding'''' each bit in the binary address of the K row of an n X n Hadamard array of the Walsh functions of order n, with the corresponding bit in the binary address of the mth column in said array, where 0 < OR = m < OR = n-1; generating a first signal if the number of ''''1''''s in the binary word resulting from said ''''anding'''' step is even, and a second signal if otherwise; and then reiterating said ''''anding'''' and said generating steps, seriatim, for the m+1th, m+2th, . . . n-1th, 0th, . . . m-1th column of the array, the sequence of first and second signals so produced comprising the desired digital signal.

Claim 2

Independent Claim 157 words

A method of generating a digital signal which is representative of the Kth Walsh function of order n, where n 2p, p > OR = 1, and 0 < OR = K < OR = n-1, comprising the steps of: ''''anding'''' each bit in the binary address of the K row of an n X n Hadamard array of the Walsh functions of order n, with the corresponding bit in the binary address of the mth column in said array, where 0 < OR = m < OR = n-1; generating a first signal if the number of ''''1''''s in the binary word resulting from said ''''anding'''' step is even, and a second signal if otherwise; and then reiterating said ''''anding'''' and said generating steps, seriatim, for the m+1th, m+2th, . . . n-1th, 0th, . . . m-1th column of the array, the sequence of first and second signals so produced comprising the desired digital signal.

Claim 3

Dependent Claim 28 words

The method according to claim 1 wherein said first and second signals are respectively representative of a numerical ''''1'''' and a numerical ''''-1'''' value in said Walsh function.

Claim 4

Independent Claim 212 words

A method of generating the Kth Walsh function of order n, where n 2p, p > or = 1, and 0 < or = K < or = n-1, comprising the steps of: a. generating a first binary signal representative of the number K; b. generating a second binary signal representative of a predetermined number m, where 0 < or = m < or = n-1; c. comparing each bit in said first binary signal with the corresponding bit in said second binary signal, thereby to generate a third binary signal, said third binary signal having a first signal condition in each bit position if the bits in the corresponding bit positions of said first and second binary signals are simultaneously ''''1''''s and a second signal condition if otherwise; d. counting the number of first signal conditions in said third binary signal; e. generating a fourth binary signal, comprising a third signal condition if the number of first signal conditions counted in said counting step is even, and a fourth signal condition if otherwise; and then f. reiterating steps (b) through (e), seriatim, for the numbers m+1, m+2, . . . , n-1, 0, . . . , m-1, the sequence of fourth binary signals so produced comprising the desired Walsh function.

Claim 5

Independent Claim 212 words

A method of generating the Kth Walsh function of order n, where n 2p, p > or = 1, and 0 < or = K < or = n-1, comprising the steps of: a. generating a first binary signal representative of the number K; b. generating a second binary signal representative of a predetermined number m, where 0 < or = m < or = n-1; c. comparing each bit in said first binary signal with the corresponding bit in said second binary signal, thereby to generate a third binary signal, said third binary signal having a first signal condition in each bit position if the bits in the corresponding bit positions of said first and second binary signals are simultaneously ''''1''''s and a second signal condition if otherwise; d. counting the number of first signal conditions in said third binary signal; e. generating a fourth binary signal, comprising a third signal condition if the number of first signal conditions counted in said counting step is even, and a fourth signal condition if otherwise; and then f. reiterating steps (b) through (e), seriatim, for the numbers m+1, m+2, . . . , n-1, 0, . . . , m-1, the sequence of fourth binary signals so produced comprising the desired Walsh function.

Claim 6

Dependent Claim 24 words

The method according to claim 3 wherein said first, second, third and fourth signal conditions respectively comprise a 1, 0, 1, and -1 signal.

Claim 7

Independent Claim 192 words

A method of generating a digital signal which is representative of the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, comprising the steps of: a. generating a first p bit binary signal representative of the number K; b. generating a second p bit binary signal representative of a number m, where 0 < or = m < or = n-1; c. generating a third signal representative of a first binary signal condition; d. for each of the p bit positions in said p bit binary signals, sequentially complementing said third signal to cause said signal to become representative of a second binary signal condition or said first binary signal condition, if the bits occupying corresponding bit positions in said first and second binary signals both simultaneously comprise a third binary condition, and maintaining said third signal constant if otherwise; e. reiterating steps (b) through (d), seriatim, for the numbers m+1, m+2, . . . , n-1, 0, 1, . . . , m-1, the sequence of sequentially complemented third signals so producEd comprising the desired Walsh function.

Claim 8

Independent Claim 192 words

A method of generating a digital signal which is representative of the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, comprising the steps of: a. generating a first p bit binary signal representative of the number K; b. generating a second p bit binary signal representative of a number m, where 0 < or = m < or = n-1; c. generating a third signal representative of a first binary signal condition; d. for each of the p bit positions in said p bit binary signals, sequentially complementing said third signal to cause said signal to become representative of a second binary signal condition or said first binary signal condition, if the bits occupying corresponding bit positions in said first and second binary signals both simultaneously comprise a third binary condition, and maintaining said third signal constant if otherwise; e. reiterating steps (b) through (d), seriatim, for the numbers m+1, m+2, . . . , n-1, 0, 1, . . . , m-1, the sequence of sequentially complemented third signals so producEd comprising the desired Walsh function.

Claim 9

Dependent Claim 32 words

The method according to claim 5 wherein said first and second binary signal conditions respectively comprise a numerical ''''1'''' and a numerical ''''-1,'''' respectively, and said third binary condition comprises a ''''1.''''

Claim 10

Independent Claim 188 words

A method of transmitting an intelligence signal from a first to a second location, comprising the steps of: at said first locations, a. periodically sampling said intelligence signal at a predetermined rate; b. generating an n term Walsh transform for each periodic sample of said intelligence signal; c. selecting the K largest terms of said n term Walsh transform, where K < or = n; and d. transmitting to said second location signals which are representative of the magnitude and Walsh function number of each of said K largest terms; and at said second location, a. generating a Walsh function for each of said K largest terms, the number of said function being determined by the corresponding Walsh function number signal received from said first location; b. multiplying said Walsh function by a factor which is proportional to the corresponding magnitude signal received from said first location; and c. summing said K multiplied Walsh functions to substantially reconstruct each periodic set of samples of said intelligence signal, whereby said intelligence signal itself may be substantially reconstructed at said second location by detecting successive ones of said periodic samples.

Claim 11

Independent Claim 188 words

A method of transmitting an intelligence signal from a first to a second location, comprising the steps of: at said first locations, a. periodically sampling said intelligence signal at a predetermined rate; b. generating an n term Walsh transform for each periodic sample of said intelligence signal; c. selecting the K largest terms of said n term Walsh transform, where K < or = n; and d. transmitting to said second location signals which are representative of the magnitude and Walsh function number of each of said K largest terms; and at said second location, a. generating a Walsh function for each of said K largest terms, the number of said function being determined by the corresponding Walsh function number signal received from said first location; b. multiplying said Walsh function by a factor which is proportional to the corresponding magnitude signal received from said first location; and c. summing said K multiplied Walsh functions to substantially reconstruct each periodic set of samples of said intelligence signal, whereby said intelligence signal itself may be substantially reconstructed at said second location by detecting successive ones of said periodic samples.

Claim 12

Dependent Claim 67 words

The method according to claim 7 wherein said transmitting step comprises: simultaneously generating K discrete p bit binary words, each word including q bits which are representative of the number of a corresponding Walsh function, and r bits which are representative of the magnitude of said function; assembling said K discrete binary words into a train; and encoding said train for serial transmission to said second location.

Claim 13

Dependent Claim 112 words

The method according to claim 7 further comprising, at said second location, decoding said train of K encoded binary words, as they are received from said first location; storing said words in a shift register until the K word has been fully decoded; and then feeding the K groups of p bits stored in said register, in parallel, to K Walsh function generators, thereby to generate said K Walsh functions, and feeding the K groups of r bits to K digital-to-analog converters, each receiving the output of a corresponding Walsh function generator, thereby to multiply said K Walsh functions by factors which are proportional to the magnitude of said K largest terms.

Claim 14

Dependent Claim 252 words

Apparatus for generating the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, which comprises: p cascaded, conditional-complementing stages, the output of each stage comprising the input to the immediately succeeding stage; means for supplying a first binary signal condition to the input of the first conditional-complementing stage, the output from the last such stage comprising the desired Walsh function; means for supplying a first p bit binary signal representative of the number K to said conditional-complementing stages, the least significant through most significant bits of said signal being respectively connected to the first through last ones of said conditional-complementing stages; means for supplying a second p bit binary signal to said conditional-complementing stages, said signal being representative of a predetermined number m, where 0 < or = m < or = n-1, the least significant through most significant bits of said signal being respectively connected to the first through last ones of said stages, each said stage complementing the signal applied to the input thereof if the corresponding bits from said first and second signal sUpplying means both simultaneously comprise a second binary signal condition; and means, connected to said second signal supplying means, for incrementing said second binary signal so that it successively represents the numbers m+1, m+2, . . . , n-1, 0, 1, . . . , m-1, whereby the output from the last one of said complementing stages comprises a desired Walsh function.

Claim 15

Dependent Claim 252 words

Apparatus for generating the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, which comprises: p cascaded, conditional-complementing stages, the output of each stage comprising the input to the immediately succeeding stage; means for supplying a first binary signal condition to the input of the first conditional-complementing stage, the output from the last such stage comprising the desired Walsh function; means for supplying a first p bit binary signal representative of the number K to said conditional-complementing stages, the least significant through most significant bits of said signal being respectively connected to the first through last ones of said conditional-complementing stages; means for supplying a second p bit binary signal to said conditional-complementing stages, said signal being representative of a predetermined number m, where 0 < or = m < or = n-1, the least significant through most significant bits of said signal being respectively connected to the first through last ones of said stages, each said stage complementing the signal applied to the input thereof if the corresponding bits from said first and second signal sUpplying means both simultaneously comprise a second binary signal condition; and means, connected to said second signal supplying means, for incrementing said second binary signal so that it successively represents the numbers m+1, m+2, . . . , n-1, 0, 1, . . . , m-1, whereby the output from the last one of said complementing stages comprises a desired Walsh function.

Claim 16

Dependent Claim 85 words

Apparatus according to claim 10 wherein said first signal supplying means comprises: a p stage register, said register receiving the first binary signal from an external source, the output from each stage of said register being connected to a corresponding conditional-complementing stage; said second signal supplying means comprises a p stage binary counter, the output from each stage thereof being connected to a corresponding conditional-complementing stage; and means, connected to said binary counter, for establishing an initial count therein representative of the predetermined number m.

Claim 17

Dependent Claim 25 words

Apparatus according to claim 11 wherein said incrementing means comprises a clock circuit connected to said binary counter for successively advancing the count stored therein.

Claim 18

Dependent Claim 222 words

Apparatus for generating the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, which comprises: means for supplying a first p bit binary signal representative of the number K; means for supplying a second p bit binary signal representative of a predetermined number m, where 0 < or = m < or = n-1; means, connected to said first and second signal supplying means, for comparing each of the p bit positions in said first binary signal with a corresponding one of the p bit positions in said second binary signal to generate a first binary signal condition for each such comparison wherein the corresponding bit positions both simultaneously comprise a second binary signal condition, and a third binary signal condition if otherwise; means, connected to said comparing means, for counting the number of first binary signal conditions so generated and for generating a fourth binary signal condition if said count is even, and a sixth binary signal condition if otherwise; and means, connected to said second signal supplying means, for causing said second signal to successively represent the numbers m+1, m+2, . . . n-1, 0, 1, . . . l m-1, whereby the sequence of third and fourth binary signal conditions comprises the desired Walsh function.

Claim 19

Dependent Claim 222 words

Apparatus for generating the Kth Walsh function of order n, where n 2p, p > or = 1, 0 < or = K < or = n-1, which comprises: means for supplying a first p bit binary signal representative of the number K; means for supplying a second p bit binary signal representative of a predetermined number m, where 0 < or = m < or = n-1; means, connected to said first and second signal supplying means, for comparing each of the p bit positions in said first binary signal with a corresponding one of the p bit positions in said second binary signal to generate a first binary signal condition for each such comparison wherein the corresponding bit positions both simultaneously comprise a second binary signal condition, and a third binary signal condition if otherwise; means, connected to said comparing means, for counting the number of first binary signal conditions so generated and for generating a fourth binary signal condition if said count is even, and a sixth binary signal condition if otherwise; and means, connected to said second signal supplying means, for causing said second signal to successively represent the numbers m+1, m+2, . . . n-1, 0, 1, . . . l m-1, whereby the sequence of third and fourth binary signal conditions comprises the desired Walsh function.

Claim 20

Dependent Claim 45 words

The apparatus according to claim 13 wherein said first and second binary signal conditions are logical ''''1''''s, said third binary signal condition is a logical 0, said fourth binary signal condition is a numerical 1, and said fifth binary signal condition is a numerical -1.

Claim 21

Dependent Claim 233 words

The apparatus according to claim 13 wherein said first signal supplying means comprises a register receiving said first p bit binary signal from an external source; said second signal supplying means comprises a p bit binary counter storing in each stage thereof respective bits in said second binary signal; said comparing means comprises: p/2 comparing stages, each stage including first and seond AND-gates, said first AND-gate having its input connected to a predetermined stage of said register, and the corresponding stage of said counter, said second AND-gate having its input correspondingly connected to the next most significant stages of said register and counter; third and fourth AND-gates, said third AND-gate having its input connected to the outputs of said first and second AND-gates, said fourth AND-gate having its inputs connected, via first and second inverter stages, to the outputs of said first and second AND-gates; and a first OR-gate connected to the outputs of said third and fourth AND-gates; and for each pair of comparing stages, a fifth and sixth AND-gate, said fifth AND-gate having its inputs connected to the outputs of the two first OR-gates in said pair of comparing stages, said sixth AND-gate having its inputs connected, via a third and a fourth inverter stage, to the outputs of said pair of first OR-gates; and a second OR-gate having its inputs connected to the output of said fifth and sixth AND-gates.

Claim 22

Dependent Claim 262 words

A transmission system for transmitting intelligence signals from a first to a second location which comprises: means for periodically sampling the analog signal to be transmitted to the second location, at a predetermined rate; means for converting each such sample into a digital signal; computing means for generating an n term Walsh transform representative of each of said n samples, and for selecting the K largest of said n terms; and means for transmitting to said second location a signal which is representative of the magnitude and Walsh function number of each of the K terms in each of said n periodic samples; and at said second location, means for recovering the signals transmitted by the transmitting means at said first location; a shift register connected to said recovering means for temporarily storing said signals, as received, until a signal representative of a complete sample has been stored; K Walsh function generators connected to said shift register for generating K Walsh functions in accordance with the signals representative of the Walsh function numbers of each of said K terms transmitted from said first location; K converter stages connected to corresponding ones of said K Walsh function generators, and to said shift register, for amplifying the outputs of the Walsh function generators in accordance with the signals representative of the magnitude of each of said K transforms transmitted from said first location and for converting said amplified Walsh functions into analog form; and means for summing the outputs of each of said K converter stages thereby to substantially reconstruct each of said samples.

Claim 23

Dependent Claim 262 words

A transmission system for transmitting intelligence signals from a first to a second location which comprises: means for periodically sampling the analog signal to be transmitted to the second location, at a predetermined rate; means for converting each such sample into a digital signal; computing means for generating an n term Walsh transform representative of each of said n samples, and for selecting the K largest of said n terms; and means for transmitting to said second location a signal which is representative of the magnitude and Walsh function number of each of the K terms in each of said n periodic samples; and at said second location, means for recovering the signals transmitted by the transmitting means at said first location; a shift register connected to said recovering means for temporarily storing said signals, as received, until a signal representative of a complete sample has been stored; K Walsh function generators connected to said shift register for generating K Walsh functions in accordance with the signals representative of the Walsh function numbers of each of said K terms transmitted from said first location; K converter stages connected to corresponding ones of said K Walsh function generators, and to said shift register, for amplifying the outputs of the Walsh function generators in accordance with the signals representative of the magnitude of each of said K transforms transmitted from said first location and for converting said amplified Walsh functions into analog form; and means for summing the outputs of each of said K converter stages thereby to substantially reconstruct each of said samples.

Claim 24

Dependent Claim 23 words

The system according to claim 16 wherein each of said Kth Walsh function generators comprises the Walsh function generator claimed in claim 13.

Claim 25

Dependent Claim 23 words

The system according to claim 16 wherein each of said Kth Walsh function generators comprises the Walsh function generator claimed in claim 10.

Claim 26

Dependent Claim 276 words

A receiver for use at a receiving loaction in a transmission system of the type which transmits intelligence signals from a transmitting location to the receiving location, the transmitting location, including means for periodically sampling the analog signal to be transmitted to the receiving location, at a predetermined rate; means for converting each such sample into a digital signal; computing means for generating an n term Walsh transform representative of each of said n samples, and for selecting the K largest of said n terms; and means for transmitting to said receiving location a signal which is representative of the magnitude and Walsh function number of each of the K terms in each of said n periodic samples, wherein the receiver comprises: means for recovering the signals transmitted by the transmitting means at said first location; a shift register connected to said recovering means for temporarily storing said signals, as received, until a signal representative of a complete sample has been stored; K Walsh function generators connected to said shift register for generating K Walsh functions in accordance with the signals representative of the Walsh function numbers of each of said K terms transmitted from said transmitting location; K converter stages connected to corresponding ones of said K Walsh function generators, and to said shift register, for amplifying the outputs of the Walsh fuNction generators in accordance with the signals representative of the magnitude of each of said K transforms transmitted from said transmitting location and for converting said amplified Walsh functions into analog form; and means for summing the outputs of each of said K converter stages thereby to substantially reconstruct each of said samples.

Claim 27

Dependent Claim 276 words

A receiver for use at a receiving loaction in a transmission system of the type which transmits intelligence signals from a transmitting location to the receiving location, the transmitting location, including means for periodically sampling the analog signal to be transmitted to the receiving location, at a predetermined rate; means for converting each such sample into a digital signal; computing means for generating an n term Walsh transform representative of each of said n samples, and for selecting the K largest of said n terms; and means for transmitting to said receiving location a signal which is representative of the magnitude and Walsh function number of each of the K terms in each of said n periodic samples, wherein the receiver comprises: means for recovering the signals transmitted by the transmitting means at said first location; a shift register connected to said recovering means for temporarily storing said signals, as received, until a signal representative of a complete sample has been stored; K Walsh function generators connected to said shift register for generating K Walsh functions in accordance with the signals representative of the Walsh function numbers of each of said K terms transmitted from said transmitting location; K converter stages connected to corresponding ones of said K Walsh function generators, and to said shift register, for amplifying the outputs of the Walsh fuNction generators in accordance with the signals representative of the magnitude of each of said K transforms transmitted from said transmitting location and for converting said amplified Walsh functions into analog form; and means for summing the outputs of each of said K converter stages thereby to substantially reconstruct each of said samples.

Claim 28

Dependent Claim 23 words

The receiver according to claim 19 wherein each of said K Walsh function generators comprises the Walsh function generator claimed in claim 13.

Claim 29

Dependent Claim 23 words

The receiver according to claim 19 wherein each of said K Walsh function generators comprises the Walsh function generator claimed in claim 10.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1977-03-04	1977-09-03	1978-03-05	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1981-03-04	1981-09-03	1982-03-05	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1985-03-04	1985-09-03	1986-03-05	$7700.00	Window Closed / Lapsed

Methods and apparatus for generating walsh functions

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