WO1991014162A1 - Method and apparatus for acoustic signal compression - Google Patents

Method and apparatus for acoustic signal compression Download PDF

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Publication number
WO1991014162A1
WO1991014162A1 PCT/JP1990/000323 JP9000323W WO9114162A1 WO 1991014162 A1 WO1991014162 A1 WO 1991014162A1 JP 9000323 W JP9000323 W JP 9000323W WO 9114162 A1 WO9114162 A1 WO 9114162A1
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mwd
jδt
cos
sin
hπt
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PCT/JP1990/000323
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French (fr)
Inventor
Min-Shiung Lin
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Ichikawa, Kozo
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Priority to PCT/JP1990/000323 priority Critical patent/WO1991014162A1/en
Publication of WO1991014162A1 publication Critical patent/WO1991014162A1/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F1/00—Details not covered by groups G06F3/00 - G06F13/00 and G06F21/00
    • G06F1/02—Digital function generators
    • G06F1/03—Digital function generators working, at least partly, by table look-up

Definitions

  • RAM random access memory
  • the present invention is to provide a new storage technology which greatly reduces memory
  • a half-hour or longer acoustic signal can be stored in a RAM of 256 K bytes (8 bits for each byte, this high capacity of RAM has been commercialized). Therefore, it is capable of storing the data recorded in an existing cassette tape.
  • acoustic signals of musics and songs can be pre- stored in a ROM for commercial purpose to replace conventional recording tape.
  • equations (52) and (54) have been simulated through computer
  • a 0 a n and b n in the equations of (4)-1 and (4)-2 are respectively as follows: L(x)cos(n ⁇ 0 x)dx + R(x)cos(n ⁇ 0 x)dx L(x)sin(n ⁇ 0 x)dx+ R(x)sin(n ⁇ 0 x)dx in w hich ,
  • a c (S,t) D c (H,-t,0)+D sc (H,-t,0)
  • the second sign of the C C n (t) at the left side of the equation means "negative Sin", therefore the second item in the brackets at the right side of the equation is "-b n sin (n ⁇ 0 t)"; the third sign “C” of the C C n (t) expresses the "Cos(H ⁇ t)" at the right side of the equation; the lower mark “n” represents each n at the right side of the equation.
  • the rest of SS n (t), SCC n (t) and S n (t) may be inferred by analogy.
  • W s1 -H ⁇ R' (T-t)sin(H ⁇ T-H ⁇ t)-[R" (T-t) -(H ⁇ ) 2 R(T-t) + 1 (H ⁇ ) 2 ]
  • W c3 R(T-t)cos(H ⁇ T-H ⁇ t) 0 cos(H ⁇ T-H ⁇ t) ⁇ (24)-3 If to increa(se H value gradually, the value of ER (t) is relatively reducing. As soon as the value of H is increased to a certain extent, the value of ER (t) is reduced to become of little significance.
  • ⁇ s (t)+ ⁇ s (t) can be expressed by means of 4k items (this will be outlined further). Therefore, when S(t) is an acoustic signal function it can be expressed by means of 4k+6 items (the other six items are Z s S(0), Z s S' (0), Z s S" (0), W s1 S(T), W s S' (T), W s 3 S" (T)) That is meant that 4k+6 groups of memory will be sufficient for the storage of an acoustic signal S(t).
  • 2k+6 sets of memories in an embodiment of the present invention, each set contains 4 bytes) is capable of storing such an acoustic signal S(t).
  • a c (S,t) can be converted to :
  • a c (S,t) L(x)S(x+t)cos(H ⁇ x)dx+ ⁇ R(x)S(x+t)
  • ⁇ c (t) and ⁇ c (t) are respectively called as "cosine waveform function" of the cosine and sine of S(t), and the value of which are respectively as:
  • ⁇ c (t) + ⁇ c (t) ⁇ [a n cos(n ⁇ 0 t) -b n sin(n ⁇ 0 t))cos(H ⁇ t)
  • SCC n (t) [a n sin(n ⁇ 0 t)+b n cos(n ⁇ 0 t)]cos(H ⁇ t) ⁇ (33)-3
  • SCS n (t) [a n sin(n ⁇ 0 t)+b n cos(n ⁇ 0 t))sin(H ⁇ t) ⁇ (33)-4
  • C C n (t), C S n (t), SCC n (t) and SCS n (t) are respectively the same as those in the equations (15)-1 to (15)-4 ((33)-1 and (15) -1 are indeed the same).
  • the approximate expression (32) provides a significant meaning, that is ⁇ o (t)+ ⁇ o (t) can be expressed by means of 4k items. This will be outlined further.
  • Y c2 -L(0) +R(0) ⁇ (39)-2
  • Z c1 0 -L(-t)]H ⁇ sin(H ⁇ t)+L' (-t)cos(H ⁇ t) ⁇ (40)-1
  • a (t)+ ⁇ (t) can be expressed by means of 4k items (this will be explained further); therefore, if S(t) is an acoustic signal function, it can be expressed by means of 4k+4 items (the additional 4 items are Z c1 S(0), Z c2 S' (0), W c1 S(T), W c2 S' (T)). Actually, in an embodiment of the present invention, 2k+4 items are sufficient for such an expression. This will be described further. IV. ERROR:
  • EP k (t) is called Fourier error.
  • a c (s,t) a 0 [S s (H, -t,T-t) +S cc (H, -t,T-t)]
  • (47) is an identical equation and (34) is an approximate expression.
  • EP k (-t) L(-t)-P k (-t) ⁇ ( 49)-6 s c (T-t,t)cos(H ⁇ T-H ⁇ t) i
  • V s1 W + (H ⁇ ) 2 [R(T-t)-P k (T-t)]cos(H ⁇ T-H ⁇ t)
  • V 3 W 3 - [R(T-t) -P k (T-t)]cos(H ⁇ T-H ⁇ t) ⁇ (56)-6
  • V 1 W 1 + [R' (T-t)-P k ' (T-t)]cos(H ⁇ T-H ⁇ t)
  • V c2 W c2 + [R(T-t)-P k (T-t)]cos(H ⁇ T-H ⁇ t) ⁇ (55)-4 V.
  • the Q xn (CS,j), Q xn (CC,j), Q xn (SS,j) and Q xn (SC,j) in equations (14)-1 ⁇ (14)-4, and the Q n (CS,j), Q n (CC,j), Q n (SS,j) and Q n (SC,j) in equations (14) - 5 ⁇ (14)-8 are generally called "n times sound recording parameter at location j"; these sound recording parameters are further expressed by Q xn (CS,j), ⁇ Q xn (SC,j), and Q n (CS,j), ⁇ Q n (SC,j)
  • Equations (53)- 1 ⁇ (53) -6 and (55) - 1 ⁇ (55) -4 are called "End point sound reproduction parameter at location t" (It is a kind of sound reproduction parameter); these sound reproduction parameters are further expressed by Z s1 , ⁇ etc., respectively.
  • ⁇ s (t)+ ⁇ s (t) and ⁇ c (t)+ ⁇ c (t) finally contain only 4k items, in which each item is a product of a waveform data and a sound reproduction parameter, and each waveform data can be obtained for storage in RAM after acoustic signal S(t) (t ⁇ [0,T]) is completely presented.
  • the process to obtain a waveform data is a process to record a sound. For reproduction of sound, it is to read out waveform data from each set of RAM and multiply the corresponding sound reproduction parameter, as shown in expressions (16) or (32), by the waveform data thus obtained so as to seek for ⁇ s (t)+ ⁇ s (t) or ⁇ c (t)+ ⁇ c (t)
  • MQ xn (CC,j), MQ xn (SC,j), MQ n (CC,j) and MQ n (SC,j) are designated as memories for Q xn (CC,j), Q xn (SC,j), Q n (CC,j) and Q xn (CC,j) respectively.
  • MC S n (t) and MSCC n (t) are designated as memories for C S n (t) and SCC n (t)
  • End point sound reproduction parameter indicates
  • Mu 1 (t), Mu 2 (t), Mv 1 (t) and Mv 2 (t) are designated as memories for u 1 (t), u 2 (t), v 1 (t), and v 2 (t) respectively.
  • T the total number of acoustic signals. Because acoustic signal S(t) is 1 second, a 1 second of acoustic signal can be stored by means of 400 Bytes.
  • MWD 1 (n) and MWD 2 (n) are called “waveform data memories", they are used as a recording tape.
  • Storage method Sound recording method
  • a “derivative circuit” shall be prepared (the derivative circuit will be described further in Hardware Structure) to give an output for the voltage signal S' (t) of the derivative function of t as soon as an acoustic voltage signal S(t) enters.
  • One or two A/D converters shall also be prepared. When two A /D converters are used, they are respectively for converting S(t) and S' (t) into digital signals.
  • samples from S(t) and S' (t) are S(0) and S' (0).
  • Fig. 4 is a schematic drawing, illustrating the contents stored in a hybrid memory of Mu 1 (j ⁇ T),
  • Fig. 5 is a circuit diagram of a
  • Fig. 6 is a computing circuit for the
  • Fig. 7 is a computing circuit (sound recording circuit) diagram for computing the waveform data WD 1 (n) and WD 2 (n) of acoustic signal S(t), the result of which are sent through DW 1 and DW 2
  • Fig. 8 is a read-write control circuit diagram for MWD 1 (n) and MWD 2 (n);
  • Fig. 9 is a computing circuit diagram for the calculation of
  • Fig. 10 is a circuit diagram which can continuously complete the following operation
  • Fig. 11 is a partly view of a restoration circuit (sound reproduction circuit) diagram for the restoration of acoustic signal S(t);
  • Fig. 12 is a complete restoration circuit diagram for the restoration of acoustic signal S(t);
  • Fig. 13 is a complete "storage/restoration circuit" diagram
  • Fig. 14 is a control block diagram, in which a microprocessor is added to control the storage /restoration circuit. Description of the designated numerals:
  • 020 MQ n (CC.j).
  • 031 MSCC n (j ⁇ T).
  • 090 circuit for providing constant "64,000”.
  • 091 circuit for providing constant "(64,000 ⁇ ) 2 " .
  • timer (or called as "sound recording timer") for use in the process of the storage of acoustic signal S(t).
  • timer (or called as "sound reproduction timer") for use in the process of the reproduction of acoustic signal S(t).
  • 27,270,271 circuits as illustrated in Fig. 6.
  • 31,310,311 circuits as illustrated in Fig. 10.
  • 32 circuit as illustrated in Fig. 11.
  • resistors 112 -114 are R 11 , R 12 and R 1 ohm respectively;
  • inductance of inductor 115 is L Henry.
  • Amplifier's current i b 10 -9 is negligible; and (3) Amplifier's open-circuit gain is qenerally at D-C and can be as high as 10 8 .
  • amplifier 110 With respect to amplifier 110, assume its input voltage is e in (i.e. the voltage at terminal a in Fig. 5), the voltage at input connecting point is e x1 , the voltage at both inducing ends is e t , output voltage is e y 1 (i.e. the voltage at terminal y 1 in Fig. 5), input current is i 1 , feedback current is i 2 .
  • the input voltage of amplifier 111 is the output voltage e y1 of amplifier 110. Assume the voltage at its input connecting point is e x2 , the output voltage is e y2 , the input current is i 3 , the feedback current is i 4 , thus:
  • e y2 is the output through terminal b in Fig. 5, and e in is the input through terminal a. In case the input through
  • terminal a is an acoustic signal S(t)
  • the output through terminal b becomes S' (t)
  • this is a derivative of time for S(t).
  • amplifier 110 still can be regarded as in an open- circuit status when amplifier 111 is connected.
  • Fig. 6 is a computing circuit for the calculation of :
  • S' (0) and S' (0) from the digital signals of S' (t) that A/D converter 131 provides will be stored in memory 150 when the total time length of S(t) is one second.
  • the address data of memory 150 is provided by counter 101. Under this condition, a pulse enters clock input terminal CK 3 of counter 101 per every second, and "write control terminal" W 1 enters an input of High to complete storage operation when address data and S' (0) or S' (1) that A/D converter 131 provides become stable.
  • S(0) and S(l) from the digital signals of S(t) that A/D converter 130 provides are stored in memory 1511.
  • the address data of memory 151 is provided by counter 102.
  • a pulse enters CK 4 per every second, and "write control terminal" W 2 enters an input of High to complete storage operation when address data and digital signal S(0), S(1) become stable.
  • (6) 17 is a shift register.
  • 270 and 271 are the circuit 27 as
  • 010 is MQ xn (CC,j); 011 is MQ xn (SC,j);
  • 020 is MQ n (CC,j); 021 is MQn(SC,j).
  • Counter 103 is MQ n (CC,j); 021 is MQn(SC,j).
  • MWD 1 (n) 050 and MWD 2 (n) 051 are
  • 050 are R 1 and W 2 respectively, and of 051 are R 1 and W 2 respectively.
  • Counters 104 and 105 provide address data for 050 and 051 respectively, wherein 104 provides higher address data and 105 provides lower address data.
  • CK 1 and CK 2 are count pulse input terminals of 104 and 105 respectively, and CR is the common clear terminal.
  • 0512, ⁇ , 051q, and lower address are the address of every set of said every segment (each segment has 50 sets, therefore, lower address contains 5 Bits).
  • Address data can be freely set in advance (therefore, 104 and 105 here are special counters). During setting, the data to set is added to terminal ADS, and thereafter, a setting signal is added to terminal Sr.
  • address data can be freely set in advance, it is possible to start reading and writing from any segment in 050 and 051.
  • an external microprocessor is provided for selection control (by means of keyboard operation).
  • An acoustic signal S(t) is stored in said every segment of 050 and 051.
  • a one-hour acoustic signal is divided into 3600 segments and every segment equals to 1 second, 050 and 051 must have 3600 segments (for higher address 14 Bits is required) sufficient for the storage of the waveform data of an one-hour acoustic signal.
  • circuit herein is a computing circuit for the calculation of :
  • 0750-0751 are multipliers and 081 is an adder, they are provided for the calculation of above expression.
  • a High is added to terminal EN after the data in Data Bus DES 1 , DUV 1 ⁇ become stable. After a delayed duration through the circuit, the result thus obtained is sent for output through terminal D0.
  • the data to process are sent to terminals DW and DP.
  • Fig. 11 is a part of a restoration circuit which can restore an
  • Terminal DES is connected to terminal
  • CK 3 is added with a pulse
  • R 1 is added with High
  • CK 4 is added with a pulse
  • R 2 is added with High
  • said 4 pcs. of data can then be registered in buffers 1620, 1630, 1640 and 1650 respectively.
  • Counter 106 provides address data for 030 and 031.
  • DW 1 and DW 2 in Fig. 11 or Fig. 12 are respectively connected to DW 1 and DW 2 of circuit 29 in Fig. 8 (see Fig. 13), and DW 1 and DW 2 of circuit 29 (Fig. 8) are data input output terminals of MWD 1 (n) 050 and MWD 2 (n) 051. Therefore, what are presented through DW 1 and DW 2 here (Fig. 11 or Fig. 12) are waveform data of S(t). According to the description for Fig. 10, the output through 310 and 311 are
  • (2) 22 designates a timer for use in the calculation of waveform data of S(t) (i.e. during sound recording); 23 designates a timer for use in the restoration of S(t) (i.e. in reproduction of sound); in which TEN 1 is an Enable terminal to drive timer 22 to operate, and TEN 2 is an Enable terminal to drive timber 23 to operate.
  • Timer 22 includes T 1 - T 21 total 21 output control terminals; Timer 23 includes T 1 - T 32 total 32 output control terminals.
  • control terminal of timers 22 and 23 completes a circuit operation each after every output of High
  • timers 22 and 23 are of known art and not within the scope of the present invention, the circuit of which will not be described here.
  • Fig. 14 is a
  • control block diagram in which a microprocessor is provides to control storage/restoration circuit. It is detailed hereinafter.
  • 34 is the circuit in Fig. 13; 25 designates a keyboard; 26 designates a
  • (2) 24 designates a microprocessor, the I/0 of which includes:
  • one set of scanning output lines DSP 2 for selecting digit place to desplay when DSP 1 provides a 7 digits data to digital display 26;
  • one set of output lines ADS for providing the address data of MWD 1 (n) and MWD 2 (n) to circuit 34; one output line TEN 1 for selecting timer 22 of circuit 34 to operate;
  • one output line Sr for providing a control sihnal when the address data in MWD 1 (n) and MWD 2 (n) are set through ADS;
  • DK 2 one sets of "key-entry identification lines" DK 2 to judge and identify any key-entry then DK 1 provides scanning data to keyboard 25.
  • Digital display 26 provides two functions. One is to display the address data preset in MWD 1 (n) and MWD 2 (n) so that an user can know where to start recording or reproduction; the other is to display the duration of time during sound recording or reproduction so that an user can know how long has been consumed in sound recording or reproduction.
  • the first function is to set address data in MWD 1 (n) and MWD 2 (n); the second function is to select TEN 1 or TEN 2 to be High (both can not be High at the same time) for sound recording or reproduction; the third
  • function is to select the mode of display through digital display 26 (to display address data, or
  • Microprocessor 24 is of a known art and not within the scope of the present invention, the hardware and software structure of which will not be described here. However, further detail will be available when it is required.

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  • Theoretical Computer Science (AREA)
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Abstract

The present invention is related to a method for acoustic signal storage access with minimized memory capacity occupation and the related hardware equipment, and more particularly to the method which analyses and calculates the waveform data of an acoustic signal for storage in a memory and the related hardware equipment required for such storage access process.

Description

DESCRIPTION Method and apparatus for acoustic signal compression
BACKGROUND OF THE INVENTION
Conventional method to store acoustic signal electrically is to continuously sample
acoustic signals and turn the signals into digital signals for storage in a memory one after another by means of an A/D converter; for retrieval of acoustic signals, read out the data from the memory one after another in proper order according to the order they are originally stored (its reading rate is equal to sampling rate). According to the above-described
conventional method, a random access memory (RAM) of big capacity is generally required. For a sampling rate of 10kHz as an example, a capacity of 104 bytes is required for an acoustic signal of one second
(When 1024 bytes is calculated as 1 K bytes, a
capacity of 9.77 K bytes will be required). Therefore, a capacity of 3600 X 104 bytes = 35156.25 K bytes = 35.15625 M bytes will be required for the storage of an acoustic signal of 1 hour. For such a high
capacity of RAM, either in dynamic or static state, it is still not possible to build in a single chip through the knowm technology. If to barely design for the storage of an one hour's acoustic signal, several memory chips must be used. The present invention is to provide a new storage technology which greatly reduces memory
capacity occupation. According to the present
invention, a half-hour or longer acoustic signal can be stored in a RAM of 256 K bytes (8 bits for each byte, this high capacity of RAM has been commercialized). Therefore, it is capable of storing the data recorded in an existing cassette tape.
Since the capacity of a ROM can be much larger than a RAM under same I.C. manufacturing technology,
acoustic signals of musics and songs can be pre- stored in a ROM for commercial purpose to replace conventional recording tape.
In the following description, equations (52) and (54) have been simulated through computer
operation with satisfactory result.
PRINCIPLE:
I . EQUATIONS TO BE APPLIED:
1. Assume F(x) continues in real number interval
[a, b], and F' (x), F" (x), ··· F (n) (x) (n∈N) all exist, i then :
∫a b F(x)sin(H πx)dx = [F (2 i) (b)cos(bH π )
Figure imgf000004_0001
-F (2 i) (a)cos(aH π)]}
(b)sin(bH π)
Figure imgf000004_0002
-F (2 i -1 ) (a)sin(aH π)]}·············(1)-1 The above equation can be proved by means of partial integration (in which F(2 i) (x) and F(2 i-1)(x) are derivatives at 2i and 2i-1 times from x).
Assign that:
Figure imgf000004_0004
(H,a,b) = [F (2 i) (b)cos(bH π)
Figure imgf000004_0003
-F(2 i) (a)cos(aH π)]} ··························(2)-1 [F(2 i-1) (b)sin(bHπ)
Figure imgf000005_0001
-F(2 i-1) (a)sin(aHπ)]}···················(2)-2
Thus:
∫a bF(x)sin(Hπx)dx=F
Figure imgf000005_0006
(H,a,b) +
Figure imgf000005_0007
(H,a,b)···········(1)-2 In the same way:
∫a bF(x)cos(Hπx)dx= [F(2 i) (b)sin(bHπ)
Figure imgf000005_0002
-F(2 i) (a)sin(aHπ)]} [F(2 i-1) (b)cos(bHπ)
Figure imgf000005_0003
-F(2 i-1) (a)cos(aHπ)]}··········(1)-3 Now, letting: J [F(2 i) (b)sin(bHπ)
Figure imgf000005_0004
-F(2 i) (a)sin(aHπ))}·····················(2)-3 [F(2 i-1) (b)cos(bHπ)
Figure imgf000005_0005
-F(2 i-1) (a)cos(aHπ)]}····················(2)-4 Thus:
∫a b F(x)cos(Hπx)dx=
Figure imgf000005_0008
(H,a,b)+
Figure imgf000005_0009
cc(H,a,b)···········(1)-4 2. Define an "auxiliary function" in any real number interval [-M,M] (M>0) as follows:
L(x); when x∈[-M,0]
P(x) = ···············(3)
R(x); when x∈[0,M]
in which L(x) and R(x) are respectively called as
"left auxiliary function" and "right auxiliary
function", they are a continuous function in real number interval [-M,0] and [0,M], and L(n)(x) and R(n) (x) (n∈N) exist, L(0) = R(0). P(x) in interval [-M,M] can be expanded by means of Fourier series: [ancos(nω0x)+bnsin(nω0x)]
Figure imgf000006_0001
·········(4)-1
In above equation (4)-1, if n is taken to k, there is total 2k-1 items in the right side (some items may be zero). Then , use Pk(x) to express the sum of 2k- 1 items, thus: k [ancos(n ω0 x) +bnsin(n ω0x)]········ (4)-2
Figure imgf000006_0002
therefore, the value of a0 an and bn in the equations of (4)-1 and (4)-2 are respectively as follows:
Figure imgf000006_0003
L(x)cos(n ω0x)dx + R(x)cos(n ω 0x)dx
Figure imgf000006_0004
Figure imgf000006_0005
L(x)sin(n ω0x)dx+ R(x)sin(n ω0x)dx
Figure imgf000006_0006
Figure imgf000006_0007
in w hich ,
Figure imgf000006_0008
(4)-1 and (4)-2 can also be rewritten as f o l l ow s :
P(x) =c0 + (cncos(n ω0 x- θ n)]···························(4)-3
Figure imgf000007_0003
Pk (x) =c0 + [cncos(n ω0 x- θ n)]··························(4)-4
Figure imgf000007_0004
in which ,
Figure imgf000007_0001
In (4)-2 and (4)-4, to what extent the k shall be taken so that Pk(x) can approximate P(x) is determined according to L(x) and R(x) selected.
Generally, in interval [-M,M] when M has a fixed value, the more the points of extreme large and extreme small in L(x) and R(x), the bigger the value of k, and the closer the approximation of Pk(x) to P(x)
(this is a matter of mathematics and not within the scope of the present invention, further detail will be provided when it is required). II. "SINE WAVEFORM FUNCTION" AND ITS CALCULATION:
Function Ac(S,t)= p(x)S(x+t)sin(Hπx)dx·······(5)
Figure imgf000007_0002
It is called S(t)'s "sine waveform function"; in A,(S,t) the lower mark "s" means sine, in the parentheses ( ) the first character "s" means
function "S(t)", and the second character "t"
represents variable. Further, in this equation, P(x) is an "auxiliary function" as defined in equation (3), t∈[0,T], 0<T≤M, H is any real number. According to the definition of P(x) defined by means of equation (3), As(S,t) can also be rewritten as follows: Ac(S,t)= L(x)S(x+t)sin(H πx)dx
+ ∫ R(x)S(x+t)sin(H πx)dx
Figure imgf000008_0001
=
Figure imgf000008_0012
(H,-t,0)+Dsc(H,-t,0)
+E
Figure imgf000008_0013
(H,0,T-t)+
Figure imgf000008_0011
(H,0,T-t) when substitute equation (1)-2, thus:
Ac(S,t)=D
Figure imgf000008_0008
c(H,-t,0)+Dsc(H,-t,0)
+
Figure imgf000008_0009
(H,0,T-t)+E
Figure imgf000008_0010
(H,0,T-t)················(6) in which, we assign D(x,t) = L(x)S(x+t) and E(x,t) = R (x)S(x+t) (D and E here are respectively a function which contains two variables).
In equation (4)-2, if the value of k that we take is sufficient to permit Pk(x) to be a very close approximation to P(x), then, Ac(S,t) can be rewritten as follows:
Figure imgf000008_0014
A (S,t)
Figure imgf000008_0002
Pk(x)S(x+t)sin(Hπx)dx S(x+t)sin(Hπx)dx
Figure imgf000008_0003
[ancos(nω0x)+bnSin(nω0x)]
Figure imgf000008_0004
·S(x+t)sin(Hπx)dx
= [Scc(H, -t,T-t) +Scc(H, -t,T-t)]
Figure imgf000008_0005
S(x+t)cos(nω0x)sin(H πx)dx
Figure imgf000008_0006
1
S(x+t)sin(nω0x)sin(H πx)dx·····(7)-1
Figure imgf000008_0007
Figure imgf000009_0001
cc(H,-t,T-t)+
Figure imgf000009_0002
cc(H,-t,T-t)]
+ c(t)+ (t)···························( 7)-2 in which,
Figure imgf000009_0006
(t) and
Figure imgf000009_0007
(t) are respectively regarded as "sine waveform function" of the cosine and sine of S(t), and the value of which are respectively as follows: S(x+t)cos(nω0x)sin(Hπx)dx·····(8)-1
Figure imgf000009_0003
n=1 t
S(x+t)sin(nω0x)sin(Hπx)dx·····(8)-2
Figure imgf000009_0004
1 because:
S(x+t)cos(nω0x)sin(Hπx)dx
Figure imgf000009_0005
= ∫0 T S(x' )cos[nω0(x' -t)]sin(Hπ (x' -t)]dx
= ∫0 T S(x)cos(nω0x-nω0t)sin(Hπx-Hπt)dx
= ∫0 T S(x)[cos(nω0x)cos(nω0t)+sin(nω0x)sin(nω0t)] ·[sin(Hπx)cos(Hπt)-sin(Hπt)cos(Hπx)]dx =cos(nω0t)cos(Hπt)∫0 TS(x)cos(nω0x)sin(Hπx)dx
-cos(nω0t)sin(Hπt)∫0 TS(x)cos(nω0x)cos(Hπx)dx
+sin(nω0t)cos(Hπt)∫0 TS(x)sin(nω0x)sin(Hπx)dx -sin(nω0x)sin(Hπt)∫0 TS(x)sin(nω0x)cos(Hπx)dx
(9)-1 In the same manner, it can be obtained that: S(x+t)sin(nω0t)sin(Hπx)dx
Figure imgf000010_0001
=cos(nω0t)cos(Hπt)∫0 TS(x)sin(nω0x)sin(Hπx)dx
-cos(nω0x)sin(Hπx)∫0 TS(x)sin(nω0t)cos(Hπt)dx -sin(nω0x)cos(Hπx)∫0 TS(x)cos(nω0x)sin(Hπx)dx +sin(nω0x)sin(Hπx)∫0 T S(x)cos(nω0t)cos(Hπt)dx
(9)-2
When substituting equations (9)-1 and (9)-2 in
equations (8)-1 and (8)-2, respectively for
(t) +
Figure imgf000010_0002
(t), thus, we can obtain:
for
Figure imgf000010_0003
s (t)+
Figure imgf000010_0004
(t), thus, we can obtain: {[ancos(nω0t)-bnsin(nωot)]
Figure imgf000010_0005
1
·cos(Hπt) ∫0 TS(x)cos(nω0x)sin(Hπx)dx} {[-ancos(nω0t)+bnsin(nω0t)]
Figure imgf000010_0006
n 1 ·sin(Hπt)∫0 TS(x)cos(nω0x)cos(Hπx)dx} {[ansin(nω0t) +bncos(nω0t)]
Figure imgf000010_0007
·cos(Hπt)∫0 TS(x)sin(nω0x)sin(Hπx)dx} {[-ansin(nω0t)-bncos(nω0t)]
Figure imgf000010_0008
1
·sin(H πt)∫0 TS(x)sin(nω0x)cos(Hπx)dx}
(10) Assign T=m(ΔT); ΔT→0, m→∞ m∈NU{0}. In equations (5) ~ (10), each variable t which is
contained in interval [0,T] is assigned as j(ΔT) (j=0, 1, ···,m), i.e. t=j(ΔT), thus,
∫0 TS(x)cos(nω0t)sin(Hπx)dx
= S(x)cos(nω0x)sin(Hπx)d]···········(11)
Figure imgf000011_0001
j o
Since interval [j ( Δ T), (j+1) Δ T] is extremely small, the S(x) of the two end points which are connected to this interval (i.e. coordinates (x1, s(x1)) and (x2, s(x2))) is a straight line; here we
Figure imgf000011_0007
use Sj (x) to express this straight line, thus:
Figure imgf000011_0002
+(j+1)·S(j(ΔT))-j·S((j+1)ΔT)
=S' (j(ΔT))·x+(j+1)·S(j(ΔT))
-j·S((j+1)ΔT)··································(12)
Substitute equation (12) in equation (11), we can obtain an approximate expression as follows:
∫0 T S(x)cos(nω0x)sin(Hπx)dx (j(ΔT)) xcos(nω0x)sin(Hπx)dx]
Figure imgf000011_0003
Figure imgf000011_0006
{[(j+1) ·S(j(ΔT))-j·S((j+1)ΔT)]
Figure imgf000011_0004
j 0 cos(nω0x)sin(Hπx)dx···················(13)
Figure imgf000011_0005
In the same manner, it can be obtained that:
∫0 T S(x)cos(n ω0x)cos(H πx)dx (j(ΔT)) cos(nω0x)cos(H πx)dx)
Figure imgf000012_0001
Figure imgf000012_0002
{[(j+1) ·S(j(ΔT))-j ·S((j+1)ΔT))
Figure imgf000012_0003
cos(nω0x)cos(Hπx)dx}······················(13)
Figure imgf000012_0004
∫0 T S(x)sin(nω0x)sin(H πx)dx [ (j(ΔT)) sin(nω0x)sin(H πx)dx)
Figure imgf000012_0005
Figure imgf000012_0006
{[(j+1) ·S(j(ΔT))-j ·S((j+1)ΔT))
Figure imgf000012_0007
sin(nω0x)sin(Hπx)dx}··················(13)-1
Figure imgf000012_0008
∫0 TS(x)sin(nω0x)cos(Hπx)dx (j(ΔT)) x sin(nω0x)cos(Hπx)dx]
Figure imgf000012_0009
Figure imgf000012_0010
[(j+1) ·S(j(ΔT))-j -S((j+1)ΔT))
Figure imgf000012_0011
sin(nω0x)cos(Hπx)dx}························(13)-2
Figure imgf000012_0012
Then, assign that:
Qxn(CS,j)= cos(nω0x)sin(Hπx)dx·················(14)-1
Qxn(CC,j)= cos(nω0x)cos(Hπx)dx·················(14)-2
Qxn(SS,j)= sin(nω0x)sin(Hπx)dx·················(14)-3
Figure imgf000012_0013
Qxn (SC,j)= x sin(nω0x)cos(Hπx)dx···············(14)-4 Qn (CS,j)=∫ cos(nω0x)sin(Hπx)dx···············( 14)-5 Qn (CC,j)=∫ cos(nω0x)cos(Hπx)dx···············( 14)-6 Qn (SS,j)=∫ sin(nω0x)sin(H πx)dx···············( 14)-7 Qn(SC,j)= sin(nω0x)cos(Hπx)dx···············( 14)-8
Figure imgf000013_0001
Then, assign that:
Figure imgf000013_0002
Cn(t)= [ancos(nω0t)-bnsin(nω0t)] cos(Hπt)··········(15)-1
Figure imgf000013_0003
n(t)= [-ancos(nω0t)+bnsin(nω0t)] sin(Hπt)··········(15)-2
SCCn(t)= [ansin(nω0t) +bnCos(nω0t)) cos(H πt)··········(15)-3
Figure imgf000013_0004
n(t)= [-ansin(nω0t)-bncos(nω0t)) sin(Hπt)··········(15)-4 in which, the first sign "C" of the C
Figure imgf000013_0005
Cn(t) at the left side of the equation means "positive Cos", therefore, in the brackets at the right side of the equation (15)-1, the first item is "+ancos(nω0t)";
the second sign
Figure imgf000013_0006
of the C
Figure imgf000013_0007
Cn (t) at the left side of the equation means "negative Sin", therefore the second item in the brackets at the right side of the equation is "-bn sin (n ω0t)"; the third sign "C" of the C
Figure imgf000013_0008
Cn(t) expresses the "Cos(Hπt)" at the right side of the equation; the lower mark "n" represents each n at the right side of the equation. The rest of
Figure imgf000013_0009
SSn(t), SCCn(t) and
Figure imgf000013_0010
Sn(t) may be inferred by analogy.
Now, substitute equations (14) - 1 to (14) - 8 in equations (13) - 1 to (13)-4 respectively, and then substitute in equation (11), together with equations (15) - 1 to (15) -4 in equation (10); thus, the
following approximate expressions can be obtained: c c { n [ (j(ΔT))Qxn(CS,j)
Figure imgf000014_0001
+ [(j+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(CS,j)]} + n [ ' (j(ΔT))Qxn(CC,j)
Figure imgf000014_0002
n=1 j
+ [(j+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(CC,j)]}
1
n [ (j(ΔT))Qxn(SS,j)
Figure imgf000014_0003
1
+[(d+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(SS,j)]}
1
{ n [ (j(ΔT))Qxn(SC,j)
Figure imgf000014_0004
1
+[(j+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(SC,j))}
····························(16)
In the approximate expression (16), there is contained a significant meaning, i.e. α c(t)+ β c (t) can be expressed by means of 4k items, this will be outlined further.
In comparing equation (6) with approximate expression (7)-2, we can obtain an approximate
expression as:
Figure imgf000014_0006
c (t) +
Figure imgf000014_0007
c (t)
Figure imgf000014_0005
cc (H, -t,0) +
Figure imgf000014_0008
sc (H, -t,0) +
Figure imgf000014_0009
ss (H,0,T-t)
Figure imgf000014_0011
sc(H,0,T-t) a0[ cs(H,-t,T-t)
Figure imgf000014_0010
Figure imgf000014_0012
+ sc(H,-t,T-t)]·····························(17) by means of equations (2)-1 and (2)-2, and because D (x, t)=L (x)S (x+ t) and E (x, t)=R (x)S (x+ t), it can be obtained that: (Hπ)3
Figure imgf000015_0004
sc(H,-t,0) (0,t)sin(0-Hπ)
Figure imgf000015_0001
Figure imgf000015_0002
(-t,t)sin((-t)Hπ))}
=HπDx' (-t,t)sin(Hπt) / (-t,t)sin(Hπt)]
Figure imgf000015_0003
=Hπ[L' (-t)S(0)+L(-t)S' (0)]sin(Hπt)+DERcs(t)
···················································································(18)-1
(Hπ)3(sc(H,-t,0)
(0,t)cos(0·Hπ)
Figure imgf000015_0005
i 0
Figure imgf000015_0006
+ (-t,t)cos(Hπt)]}
= (Hπ)2[D(0,t)-D(-t,t)cos(Hπt))-[Dx" (0,t) -Dx" (-t,t)cos(Hπt)]+ J x (0,t)
Figure imgf000015_0007
Figure imgf000015_0008
(-t,t)cos(Hπ)]}
= (Hπ)2[L(0)S(t)-L(-t)S(0)cos(Hπt)]
-[L" (0)S(t)+2L' (0)S' (t)+L(0)S" (t)]
+[L" (-t)S(0)+2L' (-t)S' (0)+L(-t)S" (0)]
· cos(Hπt) +DERsc(t)······························(18)-2 (Hπ)3Ecs(H,0,T-t) (T-t,t)sin(HπT-Hπt)
Figure imgf000016_0001
Figure imgf000016_0002
(0,t)sin(0,H,π)]}
=HπEx' (T-t,t)sin(HπT-Hπt) (T-t,t)sin(HπT-Hπt)]
Figure imgf000016_0003
=Hπ[R' (T-t)S(T)+R(T-t)S' (T)]
· sin(HπT-Hπt)+EERcs(t)··································(18)-3
(Hπ)3Esc(H,0(T-t) (T-t,t)cos(HπT-Hπt)
Figure imgf000016_0004
Figure imgf000016_0005
(0,t)cos(0·Hπ)]}
= (Hπ)2[E(T-t,t)cos(HπT-Hπt)-E(0,t)]
-[Ex" (T-t,t)cos(HπT-H πt)-Ex" (0,t)] λ W (T-t,t)cos(HπT-Hπt)
Figure imgf000016_0006
Figure imgf000016_0007
(0,t)]}
=(Hπ)2[R(T-t)S(T)cos(HπT-Hπt)-R(0)S(t)]
-[R" (T-t)S(T)+2R' (T-t)S' (T)+R(T-t)S" (T)]
·cos(HπT-Hπt) + [R" (0)S(t)+2R' (0)S' (t)
+R(0)S" (t)]+EERsc(t)······································(18)-4 (Hπ)3Scs(H,-t,T-t)
(T)sin(HτcT-Hπt)
Figure imgf000017_0001
-S(2i-1) (0)sin((-t)Hπ)]}
=Hπ[S' (T)sin(HπT-Hπt)+S' (0)sin(Hπt)]
+SER
Figure imgf000017_0006
s (t)·························································(18)-5
(Hπ)3S (H,-t,T-t)
Figure imgf000017_0007
(T)cos(HπT-Hπt)
Figure imgf000017_0002
-S(2 i) (0)cos(Hπt)]}
= (Hπ)2[S(T)cos(HπT-Hπt)-S(0)cos(Hπt)]
-[S" (T)cos(HπT-Hπt)-S" (O)cos(Hπt)]
+SERsc (t)·························································(18)-6In the equations from (18)-1 to (18)-6, cs (-t,t)sin(Hπt))··········(19)-1
Figure imgf000017_0003
( sc 0 ( (-t, t)
Figure imgf000017_0004
·cos(Hπt)]}···································(19)-2 sc (T-t,t)sin(HπT-Hπt)]
Figure imgf000017_0005
····································································(19)-3 sc Λ (T-t,t)cos(HπT-Hπt)
Figure imgf000018_0001
Figure imgf000018_0021
(0,t)]}·································(19)-4
[ i (T)sin(HπT-Hπt)
Figure imgf000018_0002
+S(2i-1) (0)sin(Hπt)]}·····················(19)-5 so [ (2 i (T)cos(HπT-Hπt)
Figure imgf000018_0003
-S(2 i) (0)cos(Hπt)]}·························(19)-6
Now, multiply both the left side and the right side of the approximate expression (17) by (Hπ)3, and substitute (18)-1 to (18)-6 to obtain the following:
Figure imgf000018_0004
c1S(t)+
Figure imgf000018_0005
c2S' (t)+
Figure imgf000018_0006
c3S" (t)
=Z
Figure imgf000018_0007
s1S(0) +
Figure imgf000018_0008
s2S' (0)+Z
Figure imgf000018_0009
s3S" (0)+
Figure imgf000018_0010
Ws1S(T)+
Figure imgf000018_0011
s2 " (T)
+W
Figure imgf000018_0012
a3S" (T) + (Hπ)3[α
Figure imgf000018_0013
s(t)+ β
Figure imgf000018_0014
s(t)]-DER
Figure imgf000018_0015
cs(t)
-DER
Figure imgf000018_0016
sc(t)-EER
Figure imgf000018_0017
ss(t)-EER
Figure imgf000018_0018
sc(t) 0 as(t)]
Figure imgf000018_0019
[ sc ]
=Z
Figure imgf000018_0022
1S(0)+Z
Figure imgf000018_0023
S' (0)+Z
Figure imgf000018_0024
S" (0)+W
Figure imgf000018_0025
S(T)+W
Figure imgf000018_0026
S' (T)
+W
Figure imgf000018_0027
3S" (T) + (Hπ)3[α
Figure imgf000018_0028
(t)+β
Figure imgf000018_0029
(t)]+ER
Figure imgf000018_0030
(t)············(20) in which,
ER
Figure imgf000018_0031
(t) = -DER
Figure imgf000018_0032
(t) -DER
Figure imgf000018_0033
(t) -EER
Figure imgf000018_0034
(t) -EER
Figure imgf000018_0035
(t)
=ya0[SER (t)+SER (t)]······················(21) Y
Figure imgf000019_0001
c1 = (Hπ)2L(0)-L" (0)+R" (0)-(Hπ)2R(0)···············(22)-1
Y
Figure imgf000019_0002
c =2R' (0)-2L' (0)···········································(22)-2
Y
Figure imgf000019_0003
c =R(0)-L(0)·························································( 22)-3
Z
Figure imgf000019_0004
c1 = -HπL' (-t)sin(Hπt)-[L" (-t) -(Hπ)2L(-t) 0 1 (Hπ)2]cos(Hπt)······················(23)-1
Figure imgf000019_0010
Z
Figure imgf000019_0005
s2=-HπL(-t)sin(Hπt)-2L' (-t)cos(Hπt) 0H π sin (H π t)·····································(23)-2
Figure imgf000019_0011
Z
Figure imgf000019_0006
s3=-L(-t)cos(Hπt) 0cos(Hπt)····················(23)-3
Figure imgf000019_0012
W
Figure imgf000019_0007
s1=-HπR' (T-t)sin(HπT-Hπt)-[R" (T-t) -(Hπ)2R(T-t) + 1 (Hπ)2]
Figure imgf000019_0013
· cos (H π T -H π t)·········································(24)-1
W
Figure imgf000019_0008
s = [ -HπR(T-t)]sin(HπT-Hπt)
Figure imgf000019_0014
-2R' (T-t)cos(HπT-Hπt)······················(24)-2
W
Figure imgf000019_0009
c3=R(T-t)cos(HπT-Hπt) 0cos(HπT-Hπt)··········(24)-3
Figure imgf000019_0015
If to increa(se H value gradually, the value of ER
Figure imgf000019_0016
(t) is relatively reducing. As soon as the value of H is increased to a certain extent, the value of ER
Figure imgf000019_0017
(t) is reduced to become of little significance. If we select properly a "left auxiliary function" L(x) and a "right auxiliary function" R(x) so that R(0)=L(0) and R' (0)=L' (0) but R"(0)≠L"(0) (for example, select L(x)=X2, R(x)=-X2; or L(x)=Sin2X, R(x)=-Sin2X, thus, R(0)=L(0) and R' (0)=L' (0) but R" (0)≠L" (0)), thus we can obtain (when H is extremely large) the following:
Figure imgf000020_0001
C () ()) s1S(0)+Z
Figure imgf000020_0002
s2S' (0)+Zs
Figure imgf000020_0003
3S" (0)
-W
Figure imgf000020_0004
s1S(T)+Ws2S' (T)+Ws S" (T)
4-(Hπ)3[αs(t)+βs(t)]}···························(25)
In the above approximate expression, α
Figure imgf000020_0005
s(t)+ β s (t) can be expressed by means of 4k items (this will be outlined further). Therefore, when S(t) is an acoustic signal function it can be expressed by means of 4k+6 items (the other six items are Z
Figure imgf000020_0006
s S(0), Zs S' (0), Z
Figure imgf000020_0007
s S" (0), W
Figure imgf000020_0008
s1S(T), W
Figure imgf000020_0009
s S' (T), Ws
Figure imgf000020_0010
3S" (T)) That is meant that 4k+6 groups of memory will be sufficient for the storage of an acoustic signal S(t). In an embodiment of the present invention, 2k+6 sets of memories (in an embodiment of the present invention, each set contains 4 bytes) is capable of storing such an acoustic signal S(t).
III. "COSINE WAVEFORM FUNCTION" AND ITS CALCULATION:
Function A
Figure imgf000020_0012
c(S,t)=∫ P(x)S(x+t)cos(Hπx)dx············(26)
Figure imgf000020_0011
is called a "cosine waveform function" of S (t); in A
Figure imgf000020_0013
c(S,t) the lower mark "c" means "cosine", and the others are same as those in As(S,t), P(x) is an "auxiliary function" as defined in equation (3), 0≤t≤T, 0<T≤M, H is any real number.
According to the definition of equation (3), Ac(S,t) can be converted to : A
Figure imgf000020_0014
c(S,t)= L(x)S(x+t)cos(Hπx)dx+∫ R(x)S(x+t)
Figure imgf000020_0015
Figure imgf000020_0016
· cos(Hπx)dx
=D
Figure imgf000020_0017
cc(H, -t,0) +D
Figure imgf000020_0018
cc(H, -t,0) +E
Figure imgf000020_0019
cs (11,0, T-t)
+Ecc(H,0,T-t)Ecs(H,0,T-t)+E
Figure imgf000020_0020
cc(H,0,T-t) ;
when substitute equation (1)-3, thus: A
Figure imgf000021_0006
(S,t)=D
Figure imgf000021_0007
cs(H,-t,0) +Dcc(H,-t,0)+E
Figure imgf000021_0008
cs(H,0,T-t)
+E
Figure imgf000021_0009
cc(H,0,T-t)·········································(27) in which , D (x, t) =L (x) S (X+t ) and E (x, t)=R (x)S (x+t); D and E are a function which contains two variables. In equation (4)-2, if the value of k that we take is so sufficient that Pk(x)→P(x), thus: c S(x+t)cos(Hπx)dx
Figure imgf000021_0001
[ancos(nω0x) +bnsin(nω0x)]
Figure imgf000021_0002
n 1
· S (x +t)cos (Hπx)dx
0[S
Figure imgf000021_0010
s(H,-t,T-t)+Scc(H,-t,T-t)]
Figure imgf000021_0003
+ α
Figure imgf000021_0012
c(t)+ β
Figure imgf000021_0011
c(t)·····································(28) in which, α
Figure imgf000021_0013
c(t) and β
Figure imgf000021_0014
c(t) are respectively called as "cosine waveform function" of the cosine and sine of S(t), and the value of which are respectively as:
S(x +t)cos(nω0x)cos(Hπx)dx···········(29)-1
Figure imgf000021_0004
c S(x +t)sin(nω0x)cos(Hπx)dx···········(29)-2
Figure imgf000021_0005
n 1
Same as the derivation in equations (9)-1 and (9)-2, we can obtain: S(x+t)cos(nω0x)cos(Hπx)dx
Figure imgf000022_0001
=cos(nω0t)cos(Hπt) 0 TS(x)cos(nω0x)cos(Hπx)dx +cos(nω0t)sin(Hπt)∫0 TS(x)cos(nω0x)sin(Hπx)dx
Figure imgf000022_0002
+sin(nω0t)cos(Hπt)∫0 T S(x)sin(nω0x)cos(Hπx)dx
Figure imgf000022_0003
+sin(nω0t)sin(Hπt)∫0 T S(x)sin(nω0x)sin(Hπx)dx
Figure imgf000022_0004
········ ······························································ ······························ (30)-1
S(x+t)sin(nω0x)cos(Hπx)dx
Figure imgf000022_0005
=cos(nω0t)cos(Hπt) ∫0 TS(x)sin(nω0x)cos(Hπx)dx
Figure imgf000022_0006
+cos(nω0t)sin(Hπt)∫0 TS(x)sin(nω0x)sin(Hπx)dx
Figure imgf000022_0007
-sin(nω0t)cos(Hπt)∫0 TS(x)cos(nω0x)cos(Hπx)dx
Figure imgf000022_0008
-sin(nω0t)sin(Hπt)∫0 T S(x)cos(nω0x)sin(Hπx)dx
Figure imgf000022_0009
········ ······························································ ······························ (30)-2
When substitute (30)-1 and (30)-2 in (29)- 1 and (29) -2 for a o (t)+ βo (t), we can obtain:
αc (t) + βc (t) = {[ancos(nω0t) -bnsin(nω0t))cos(Hπt)
n 1
Figure imgf000022_0010
·∫0 T S(x)cos(nω0x)cos(Hπx)dx}
Figure imgf000022_0011
{[ancos(nω0t)-bnsin(nω0t)]sin(Hπt) 1 ·∫0 T (x)cos(nω0x)sin(Hπx)dx} {[ansin(nω0t) +bncos(nω0t)]cos(Hπt) 1 ·∫0 T (x)sin(nω0x)cos(Hπx)dx} {[ansin(nω0t)+bncos(nω0t)]sin(Hπt) 1 ·∫0 T (x)sin(nω0t)sin(Hπt)dx}··········(31)
Figure imgf000023_0001
Same as the derivation in approximate expression (16), we can obtain an approximate expression as the
following: c c [ (j(ΔT)Qxn(CC,j)
Figure imgf000023_0002
1
+ [(j+1)·S(j(ΔT))-j·S((j+1)ΔT)Qn(CC,j)]}
1
{ n [S (j(ΔT))Qxn(CS,j)
Figure imgf000023_0003
1
+ [(j +1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(CS,j)]}
1
{ [ (j(ΔT))Qxn(SC,j)
Figure imgf000023_0004
1
+[(j+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(SC,j)]}
1
{ n [ (j(ΔT))Qxn(SS,j)
Figure imgf000023_0005
1
+ [(j+1)·S(j(ΔT))-j·S((j+1)ΔT)]Qn(SS,j)]} ········ ······························································ ·······················(32) in which;
Cn(t)=[ancos(nω0t)-bnsin(nω0t)]cos(Hπt)············(33)-1
Figure imgf000024_0001
n (t ) = [ancos(nω0t)-bnsin(nω0t)]sin(Hπt)············(33)-2
SCCn (t)=[ansin(nω0t)+bncos(nω0t)]cos(Hπt)············(33)-3 SCSn (t) = [ansin(nω0t)+bncos(nω0t))sin(H πt)············(33)-4
In the above equations, C
Figure imgf000024_0006
Cn(t), C
Figure imgf000024_0007
Sn(t), SCCn(t) and SCSn(t) are respectively the same as those in the equations (15)-1 to (15)-4 ((33)-1 and (15) -1 are indeed the same). Same as approximate expression (16), the approximate expression (32) provides a significant meaning, that is α o(t)+ β o(t) can be expressed by means of 4k items. This will be outlined further.
In comparing equation (27) with equation (28), it can be obtained that: αc(t)+βc(t)
Figure imgf000024_0002
Dcs(H,-t,0)+Dcc(H,-t,0)+Ecs(H,0,T-t)
+Ecc(H,0,T-t)- [Scs(H,-t,T-t)
Figure imgf000024_0005
+Scc(H,-t,T-t)}······················(34)
By means of (2)-3 and (2)-4, and because D(x,t)=L(x)S (x+ t) and E(x, t)=R (x)S (x, t), we can obtain that:
(Hπ)2Dcs(H,-t,0) [ (0,t)sin(0·Hπ)
Figure imgf000024_0003
Figure imgf000024_0004
i (-t,t)sin((-t)Hπ)]}
=HπL(-t)S(0)sin(Hπt)+DERcs(t)·················(35)-1 (Hπ)2Dcc(H,-t,0) (0,t)cos(0·Hπ)
Figure imgf000025_0001
i 1
Figure imgf000025_0002
( i-1 (-t,t)cos(Hπt)]}
=L' (0)S(t)+L(0)S' (t)-[L' (-t)S(0)
+L(-t)S' (0)]cos(Hπt)+DERcc(t)···············(35)-2
(Hπ)2Ecs(H,0,T-t) n (T-t,t)sin(HπT-Hπt)
Figure imgf000025_0003
Figure imgf000025_0004
(2i) (0,t)sin(0·Hπ)]}
=HπR(T-t)S(T)sin(HπT-Hπt) +EERcs(t)···········(35)-3 (Hπ)2Ecc(H,0,T-t) (T-t,t)cos(HπT-Hπt)
Figure imgf000025_0005
Figure imgf000025_0006
(0,t)cos(0·Hπ )]}
= [R' (T-t)S(T)+R(T-t)S' (T)]cos(HπT-Hπt)
-[R' (0)S(t)+R(0)S' (t)]+EERcc(t)··············(35)-4 (Hπ)2Scs(H,-t,T-t) [ i) (T)sin(H πT-Hπt)
Figure imgf000025_0007
0
+S(2 i) (0)sin(Hπt)]}
=Hπ[S(T)sin(HπT-Hπt)+S(0)sin(Hπt)]
+SERcs(t)·························································(35)-5 (Hπ)2Scc(H,-t,T-t) [ i ) (T)cos(HπT-Hπt)
Figure imgf000026_0001
-S(2 i-1) (0)cos(Hπt)]}
=S' (T)cos(HπT-Hπt)-S' (0)cos(Hπt)+SERcc(t) ········ ······························································ ······························ ( 35)-6 in which: cs (-t,t)sin(Hπt)]············(36)-1
Figure imgf000026_0002
cc i-1) (-t,t)cos(Hπt)]
Figure imgf000026_0003
········ ······························································ ······························ ( 36)-2 cs (T-t,t)sin(HπT-Hπt)]····(36)-3
Figure imgf000026_0004
cc (T-t,t)cos(HπT-Hπt)
Figure imgf000026_0005
1)
Figure imgf000026_0008
(0,t)]}·······························(36)-4 [ i) (T)sin(HπT-Hπt)
Figure imgf000026_0006
+S(2 i) (0)sin(Hπt)]}·························(36)-5 [ 2i-1) (T)cos(HπT-Hπt)
Figure imgf000026_0007
-S(2i-1) (0)cos(Hπt)]}······················(36)-6 Multiply the both sides of the equations. (24) by
(Hπ)2, and substitute (35)-1 to (35) - 6 respectively, thus, we can obtain:
Yc1S(t)+Yc2S' (t)
=Zc1S(0)+Zc2S' (0)+Wc1S(T)+Wc2S' (T)
-DERcs(t)+(Hπ)2[αc(t)+βc(t)]-DERcc(t)
-EERc s (t) -EERc c (t) + 0 [SERc s (t) +SERc c (t)]
Figure imgf000027_0001
=Zc 1S(0) +Zc2S' (0) +Wc1S(T) +Wc2S' (T)
+ (H π )2 [ α c (t) + β c (t) ] +ERc (t) ······················(37) i n whi ch ,
ERc (t) = -DERcs (t) -DERcc (t) -EERcs (t) -EERcc (t) 0 [SERcs (t) +SERcc (t)]······························(38)
Figure imgf000027_0002
Yc1 = -L' (0)+R' (0)······················································(39)-1
Yc2 =-L(0) +R(0)············································································(39)-2 Zc1 = 0-L(-t)]Hπsin(H πt)+L' (-t)cos(Hπt)········(40)-1
Figure imgf000027_0003
Zc2= 0+L(-t)]cos(Hπt)···························································(40)-2
Figure imgf000027_0004
Wc1= -R(T-t)]Hπsin(HπT-Hπt)
Figure imgf000027_0005
-R' (T-t)cos(H πT-Hπt)·········································(41)-1
Wc2= -R(T-t))cos(HπT-Hπt)···································(41)-2
Figure imgf000027_0006
When H value is increasing gradually, the value of ERc (t) is relatively reducing. As soon as H value is increased to a certain extent, ERc(t) becomes of little significance. When we take such "left
auxiliary function" L(x) and "right auxiliary function" R(x) that R(0)=L(0) but R' (0)≠L' (0) (for example, we select L(x)=x, and R(x)=0; or, select L(x)=SInx and R(x)=-x), thus we can obtain (when the value of H is extremely large): {Zo1S(0)+Zc2S' (0)+Wc1S(T)
Figure imgf000028_0001
+Wc2S' (T) +(Hπ)2[αc(t)+βc(t)]}···················· (42)
In the above approximate expression (42), a
Figure imgf000028_0004
(t)+ β
Figure imgf000028_0005
(t) can be expressed by means of 4k items (this will be explained further); therefore, if S(t) is an acoustic signal function, it can be expressed by means of 4k+4 items (the additional 4 items are Zc1S(0), Zc2S' (0), Wc1S(T), Wc2S' (T)). Actually, in an embodiment of the present invention, 2k+4 items are sufficient for such an expression. This will be described further. IV. ERROR:
In addition to ERc(t) and ERc(t), there is still another error in expressions (25) and (42) which is caused to happen when P(x) is substituted by Fourier series Pk(x). Letting:
P(x) = Pk(x)+EPk(x)
in which EPk(t) is called Fourier error.
thus,
P(x)= Pk(x)
Figure imgf000028_0002
that is, EPk(t) =0
Figure imgf000028_0003
In actual practice, it is not possible to obtain an infinitely great for k, and the finite value that we take for k has a great concern with the "left
auxiliary function" L(x) and the "right auxiliary function" R(x). For example, given that: L(x)=x and R(x)=0, thus P50(x) has a very close approximation to P(x) when 50 is taken for k. Although P(x)-P50(x) is very small, it is still not infinitely small. For accuracy's sake P(x)-P50(x) must be taken into account. With respect to equation (5) regarding the definition As(s,t):
As(s,t)=
Figure imgf000029_0001
P(x)S(x+t)sin(Hπx)dx = Pk(x)S(x+t)sin(Hπx)dx
Figure imgf000029_0002
+∫ -tEPk(t)S(x+t)sin(Hπx)dx
Figure imgf000029_0003
0 [S
Figure imgf000029_0010
c (H, -t,T-t) +Scc(H, -t,T-t)) + α
Figure imgf000029_0011
c (t)
Figure imgf000029_0004
+ β
Figure imgf000029_0012
(t) + / tEPk(t)S(x+t)sin(Hπx)dx;
Figure imgf000029_0005
in which, / EPk(t)S(x+t)sin(Hπx)dx is
Figure imgf000029_0006
called "Fourier sine integral error of S(t)" and expressed by SE
Figure imgf000029_0009
(t), that is :
SE
Figure imgf000029_0008
(t)= EPk(b)S(x+t)sin(Hπx)dx
Figure imgf000029_0007
letting:
G(x,t) =EPk(x)S(x + t) according to equations (1)-1, (2)-1 and (2)-2, it is obtained that:
SE
Figure imgf000030_0019
s(t)=G
Figure imgf000030_0018
c(H, -t,T-t) +G
Figure imgf000030_0020
(H, -t,T-t)···(43)-1 thus, A
Figure imgf000030_0021
(s,t) ya0[S
Figure imgf000030_0022
(H,-t,T-t) +S
Figure imgf000030_0023
(H,-t,T-t))
Figure imgf000030_0001
+ α
Figure imgf000030_0003
s (t) + β
Figure imgf000030_0024
(t) +G
Figure imgf000030_0025
(H, -t,T-t)
+G
Figure imgf000030_0002
sc(H,-t,T-t)·······································································( 44)
Letting:
SE
Figure imgf000030_0026
(t)= EPk(t)S(x+t)cos(Hπx)dx
Figure imgf000030_0004
thus:
SE
Figure imgf000030_0027
(t)=G
Figure imgf000030_0005
cc(H,-t,T-t)+G
Figure imgf000030_0028
(H,-t,T-t)···(43)-2 and thus:
Ac(s,t) = a0 [S
Figure imgf000030_0007
s (H, -t,T-t) +Scc(H, -t,T-t)]
Figure imgf000030_0006
+ αc (t) + βc (t) +G
Figure imgf000030_0029
(H, -t,T-t)
+G
Figure imgf000030_0008
cs(H,-t,T-t)············································································(45)
In comparing equation (6) with equation (44), it can be obtained that: α
Figure imgf000030_0009
c (t) + β
Figure imgf000030_0010
s
Figure imgf000030_0011
(t) =Dsc (H, -t,0) +D
Figure imgf000030_0012
sc (H, -t,0) +E
Figure imgf000030_0013
sc (H,0,T-t) +E
Figure imgf000030_0016
sc(H,0,T-t) ya0[S
Figure imgf000030_0015
sc(H,-t,T-t)
Figure imgf000030_0014
+Ssc(H,-t,T-t)]-Gsc(H,-t,T-t)
-G
Figure imgf000030_0017
sc(H,-t,T-t)····································································(46)
In comparing equation (46) with expression (17), (46) is an identical equation and (17) is an approximate expression. In comparing equations (27) with (45), it can be obtained that: αc(t)+βc (t) =Dcs (H, -t,0) +Dcc (H, -t,0)
+Ecs(H,0,T-t)+Ecc(H,0,T-t)
Figure imgf000031_0001
y0[Scc(H,-t,T-t)+Scs(H,-t,T-t)]
-Gcc(H,-t,T-t)-Gcs(H,-t,T-t)···········(47)
In comparing (47) with (34), (47) is an identical equation and (34) is an approximate expression.
Since: (Hπ)3Gsc(H,-t,T-t) (T- t,t)cos(HπT- Hπt)
Figure imgf000031_0002
Figure imgf000031_0003
(-t,t)cos(Hπt)]}
= (Hπ)2[G(T-t,t)cos(HπT-Hπt)
-G(-t,t)cos(Hπt)]-[Gx" (T-t,t)cos(HπT-Hπt) -Gx" (-t,t)cos(Hπt)]+ (T-t,t)
Figure imgf000031_0004
· cos(HπT-Hπt) -Gx (2 i) (-t,t)cos(Hπt)]}
= (Hπ)2[EPk(T-t)S(T)cos(HπT-Hπt)
-EPk(-t)S(0)cos(Hπt)]-{[EPk" (T-t)S(T) + 2EPk' (T-t)S' (T)+EPk(T-t)S" (T)]
·cos(HπT-Hπt)-[EPk" (-t)S(0) +2EPk' (-t)S' (0)
+EPk (-t)S" (0)]cos(Hπt)} +GERsc (t)················(48)-1 (Hπ)3G
Figure imgf000032_0007
(H,-t,T-t) Gx (2 i-1) (T-t,t)sin(HπT-Hπt)
Figure imgf000032_0001
Figure imgf000032_0002
x ( i-1) (-t,t)sin(Hπt)]}
= (Hπ){[EPk' (T-t)S(T)+EPk(T-t)S' (T)]
·sin(HπT-Hπt) + [EPk' (-t)S(0)+EPk(-t)S' (0))
·sin(Hπt)}+GER
Figure imgf000032_0008
(t)··············································(48)-2 in which:
EPk" (T-t)=P" (T-t)-Pk" (T-t)=R" (T-t)-Pk" (T-t) (49)-1
EPk' (T-t)=R' (T-t)-Pk' (T-t)·····································(49)-2 EPk(T-t)=R (T-t)-Pk(T-t)··············································(49)-3
EPk" (-t)=P" (-t)-Pk" (-t)=L" (-t)-Pk" (-t)······(49)-4
EPk' (-t)=L' (-t)-Pk' (-t)·········································(49)-5
EPk(-t)=L(-t)-Pk(-t)·······································································( 49)-6 sc (T-t,t)cos(HπT-Hπt)
Figure imgf000032_0003
i
Figure imgf000032_0004
-Gx (2 i) (-t,t)cos(Hπt)]}·····································(50)-1 cs [Gx (2 i-1) (T-t,t)sin(HπT-Hπt)
Figure imgf000032_0005
Figure imgf000032_0006
Gx (2 i-1) (-t,t)sin(Hπt)])··································(50)-2
Substitute (49)-1 ~ (49)-6 into (48)-1, (48)-2, then multiply both sides of the equation (46) by (Hπ)3 and then substitute (48) - 1, (48) - 2 or together with (18)-1 ~ (18)-6 into the equation of (46) after it is multiplied by (Hπ)3. Thus, it is obtained that: Y
Figure imgf000033_0002
s1S(t)+Y
Figure imgf000033_0003
s S' (t)+Ys S" (t)
= {Zs1-(Hπ)2[L(-t)-Pk(-t)]cos(Hπt)
-[L" (-t)-Pk" (-t))cos(Hπt)+(Hπ)[L' (-t)
-Pk' (-t)]sin(Hπt)}S(0)+{Zs2 +2[L" (-t)-Pk" (-t)] ·cos(Hπt)+(Hπ)[L(-t)-Pk(-t)]sin(Hπt)}S' (0) +{Z
Figure imgf000033_0004
c3+[L(-t)-Pk(-t)]cos(Hπt)}S" (0) + {W
Figure imgf000033_0005
s1+(Hπ)2[R(T-t)-Pk(T-t)]cos(HπT-Hπt)
-[R" (T-t)-Pk" (T-t)]cos(HπT-Hπt)
+ (Hπ)[R' (T-t)-Pk' (T-t))sin(HπT-Hπt)}S(T) +{W
Figure imgf000033_0006
s -2[R" (T-t)-Pk" (T-t)]cos(HπT-Hπt)
+ (H π) [R(T-t) -Pk(T-t)]sin(HπT-Hπt)}S' (T)
+ {W
Figure imgf000033_0007
c3-[R(T-t)-Pk(T-t))cos(HπT-Hπt)S" (T)
+ (Hπ)3 [ α
Figure imgf000033_0008
s (t) + β
Figure imgf000033_0009
s (t)] +ER
Figure imgf000033_0010
s (t) +GER
Figure imgf000033_0011
sc (t) +GER
Figure imgf000033_0012
sc (t) ············· ··············· ······························································ ·····(51) Thus, when H is extremely great, ERs(t)
+GERsc (t) +GERss (t) is extremely small; Letting L(0)=R (0) and L' (0)=R' (0), but L" (0)≠R" (0), (51) can be rewritten as:
{U
Figure imgf000033_0013
s1S(0)+U
Figure imgf000033_0014
s2S' (0)+U
Figure imgf000033_0015
s3S" (0)
Figure imgf000033_0001
+V
Figure imgf000033_0016
s1S(T) +V
Figure imgf000033_0017
s2S' (T)+V
Figure imgf000033_0018
s3S" (T)
+(Hπ)3[α
Figure imgf000033_0019
s(t)+β
Figure imgf000033_0020
s(t)]}····························································· ·· ···· ·(52)
in which, U
Figure imgf000034_0002
=Z
Figure imgf000034_0003
1-(Hπ)2[L(-t)-Pk(-t)]cos(Hπt)-[L" (-t)
-Pk" (-t)]cos(Hπt) + (Hπ)[L' (-t)-Pk' (-t)]sin(Hπt) ············· ··············· ······························································ ·····( 53) 1
U
Figure imgf000034_0004
=Z
Figure imgf000034_0005
+2[L" (-t)-Pk" (-t)]cos(Hπt) +(Hπ)[L(-t)
-Pk(-t)]sin(Hπt)····························································· ·· ···· ·· ·( 53)-2
U
Figure imgf000034_0006
=Z
Figure imgf000034_0007
s3+[L(-t)-Pk(-t)]cos(Hπt)···················································(53)-3
V
Figure imgf000034_0008
s1=W
Figure imgf000034_0009
+ (Hπ)2[R(T-t)-Pk(T-t)]cos(HπT-Hπt)
-[R" (T-t)-Pk" (T-t)]cos(HπT-Hπt)
+ (Hπ)[R' (T-t)-Pk' (T-t)]sin(HπT-Hπt)··········(53)-4 V
Figure imgf000034_0010
2=Ws
Figure imgf000034_0011
-2[R" (T-t)-Pk" (T-t))cos(HπT-Hπt)
+(Hπ)[R(T-t)-Pk(T-t)]sin(HπT-Hπt)····················(53)-5
V
Figure imgf000034_0012
3 =W
Figure imgf000034_0013
3 - [R(T-t) -Pk (T-t)]cos(HπT-Hπt)·······················(56)-6
Therefore, when H is extremely great, L(0)=R(0) but L' (0)≠R' (0), thus, S {Uc1S(0)+Uc2S' (0)+Vc1S(T)
Figure imgf000034_0001
+V
Figure imgf000034_0014
2S' (T) + (Hπ)2[α c(t)+ βc(t)]}·····························(54) in which:
U
Figure imgf000034_0015
1=Z
Figure imgf000034_0016
1-[L' (-t)-Pk' (-t)]cos(Hπt)+Hπ[L(-t)
-Pk(-t)]sin(Hπt)····················································(55)-1 U
Figure imgf000034_0017
c2 =Z
Figure imgf000034_0018
- [L(-t) -Pk(-t))cos(Hπt)··································(55)-2
V
Figure imgf000034_0019
1=W
Figure imgf000034_0020
1 + [R' (T-t)-Pk' (T-t)]cos(HπT-Hπt)
+Hπ [R(T-t)-Pk(T-t)]sin(HπT-Hπt)······················(55)-3
Vc2=Wc2 + [R(T-t)-Pk(T-t)]cos(HπT-Hπt)······················(55)-4 V. SOUND RECORDING AND REPRODUCTION PARAMETER:
The Qxn(CS,j), Qxn(CC,j), Qxn(SS,j) and Qxn (SC,j) in equations (14)-1 ~ (14)-4, and the Qn(CS,j), Qn(CC,j), Qn(SS,j) and Qn(SC,j) in equations (14) - 5 ~ (14)-8 are generally called "n times sound recording parameter at location j"; these sound recording parameters are further expressed by Qxn(CS,j), ··· Qxn (SC,j), and Qn(CS,j), ··· Qn(SC,j)
The C
Figure imgf000035_0001
Cn(t),
Figure imgf000035_0002
SSn(t) ··· in equations (15)-1 ~(15)-4 and (33)-1 ~ (33)-4 (wherein (15) - 1 is
identical to (33) - 1) are called "sound reproduction parameter at location t"; these sound reproduction parameters are further expressed by CSCn(t), CSSn(t) ··· etc. The U
Figure imgf000035_0003
1~U
Figure imgf000035_0004
, V
Figure imgf000035_0005
1~V
Figure imgf000035_0006
, U
Figure imgf000035_0007
1, U
Figure imgf000035_0008
, V
Figure imgf000035_0009
1 and V
Figure imgf000035_0010
2 in equations (53)- 1 ~ (53) -6 and (55) - 1 ~ (55) -4 are called "End point sound reproduction parameter at location t" (It is a kind of sound reproduction parameter); these sound reproduction parameters are further expressed by Zs1, ··· etc., respectively.
Since the foregoing sound recording and reproduction parameters have nothing to do with S(t) (S(t) is an acoustic signal to store), they can be calculated and pre-stored in ROM for ready use. VI. WAVEFORM DATA:
In approximate expressions (13)-1~(13)-4, ∫0 TS(x)cos(nω0x)sin(Hπx)dx ; ∫0 T S(x)cos(nω0x)cos(Hπx)dx ; ∫0 T S(x)sin(n ω0x)sin(H πx)dx ; and ∫0 T S(x)sin(n ω0x)cos(Hπx)dx ;
These are called "n times waveform data" of S(t). The calculation of these data can be
understood directly from equations (13)-1~(13)-4.
It is to sample m times from S(t) in interval [0,T] and proceed a calculation each time a sample S(j(ΔT)) (j=0, 1, ···, m-1, Δ T=T/m) is drawn.
Because sampling is proceedes from n to k, after m times of sampling on S(t) is completed, a 4k number is obtained. Therefore, a 4k waveform data can be obtained. As shown in expressions (16) and (32), αs (t)+ βs (t) and αc (t)+ βc (t) finally contain only 4k items, in which each item is a product of a waveform data and a sound reproduction parameter, and each waveform data can be obtained for storage in RAM after acoustic signal S(t) (t∈[0,T]) is completely presented.
There are total 4k sets of RAM which are equivalent to a recording tape. The process to obtain a waveform data is a process to record a sound. For reproduction of sound, it is to read out waveform data from each set of RAM and multiply the corresponding sound reproduction parameter, as shown in expressions (16) or (32), by the waveform data thus obtained so as to seek for αs(t)+βs(t) or αc(t)+ βc (t) The result thus obtained is substituted into expression (52) (When L(x) and R(x) are selected to permit R(0)=L(0), R' (0)=L' (0) but L " (0)≠R" (0)) or expression (54) (When L(x) and R(x) are selected to permit R(0)=L(0) but R' (0)≠L' (0) to seek for S(t)).
METHOD OF THE INVENTION
The method of the present invention to record and reproduce a sound will be described by way of example as hereinafter. Either expression (52) or expression (54) can be used for performing the method of the present invention. Hereby expression (54) is taken for explanation, and letting:
L(x) = x;
R(x) = 0;
[-M,M] = [-2,2], i.e. M = 2 seconds;
T = 1 second;
H = 64,000;
m = 64,000.
thus, according to the definition of P(x) as defined in equation (3), when it is expanded by Fourier series in interval [-2,2], it can be obtained that: ∫0 T x dx= -1;
Figure imgf000037_0001
cos(nω0x)dx = - v [1-(-1)n);
Figure imgf000037_0002
Figure imgf000037_0003
sin(nω0x)dx= -
Figure imgf000037_0005
Figure imgf000037_0004
in which,
Figure imgf000037_0006
After P(x) is expanded by Fourier series, and 50 is taken for n, thus:
k = 50 In the above, m=64,000 represents that acoustic signal S(t) in interval [0,1] (T=1 second) has been sampled for 64,000 times, that is to sample from S(t) at a sampling frequency of 64RHz. Now, during reproduction of sound, assume time point t of each sound reproduction is just the same as the
original sampling time point (r = 0, 1 , ···, 63, 999),
Figure imgf000038_0001
thus: sin(Hπt)=sin(64,000X π X )=sin(rπ)=0
Figure imgf000038_0002
cos(Hπt)=cos(64,000X π X =cos(rπ)
Figure imgf000038_0003
= (-1)r; r=64,000t
Assume the time point of each sound reproduction t= thus:
Figure imgf000038_0004
sin(Hπt)=sin(rπ+ =(-1)r; r=64,000t
Figure imgf000038_0005
cos(Hπt) =cos(rπ + =0
Figure imgf000038_0006
Now, the former is selected.
According to the above selection,
expression (54) can be rewritten as:
S(t)
Figure imgf000038_0007
(-1)r{Pk' (-t)S(0) + [ +Pk(-t)]S' (0)-Pk' (1-t)
Figure imgf000038_0008
·S(1)-[y+Pk(1-t)]S' (1)} + (64,000π)2[αc(t) + βc(t)]
Figure imgf000038_0009
············· ··············· ······························································ ·····( 56) in which, αc(t)+βc(t)= n [S (jΔT)Qxn(CC,j)
Figure imgf000039_0001
1 1
+ [(j+1)S(jΔT)-j·S((j+1)ΔT)]
·Qn(CC,j)]}+ n [S' (jΔT)
1
Figure imgf000039_0002
·Qxn(SC,j) + [(j +1)S(jΔT)
-j·S((j + 1)ΔT)]Qn(SC,j)))····························(57) n 0 0 sin(nω0t)](-1)r··(58)-1
Figure imgf000039_0003
SCCn(t) = cos(nω0t)](-1)r··(58)-2
Figure imgf000039_0004
Qxn(CC,j)=∫ x cos(nω0x)cos(64,000πx)dx···········(59)-1 Qxn (SC,j) =∫ x sin(nω0x)cos(64,000πx)dx···········(59)-2
Qn(CC,j)= cos(nω0x)cos(64,000πx)dx···········( 59)-3
Qn(SC,j)=
Figure imgf000039_0005
) sin(nω0x)cos(64,000πx)dx·················(59)-4
r = 64,000t, 0 = = ' =
Figure imgf000039_0006
Because ΔT is not infinitely small, the S' (j Δ T) here differs from the S' (j Δ T) in expression (16) or (32).
The expression (56) is taken for the
present embodiment. In expression (57) a number of 2k =2X50=100 (i.e. 2k=100 waveform data) is sufficient to express αc (t)+ βc (t)°
As per above example, the method of the present invention is outlined hereinafter. 1. SOUND RECORDING PARAMETER AND "SOUND RECORDING
PARAMETER MEMORY"
In the present embodiment, Qxn(CC,j), Qxn(SC, j), Qn(CC,j) and Qn(SC,j) as what indicated in (59) -1 ~ (59)-4 are sound recording parameters. Because n=1, 2, ···,50, and j=0, 1,···, 63999, there are total 4X50X 64000=1.28X107 recording parameters. These
parameters are calculated through computer and stored in ROM which we call "Sound recording parameter
memory".
Hereby, MQxn(CC,j), MQxn(SC,j), MQn(CC,j) and MQn(SC,j) are designated as memories for Qxn(CC,j), Qxn(SC,j), Qn(CC,j) and Qxn(CC,j) respectively.
2. SOUND REPRODUCTION PARAMETER AND "SOUND
REPRODUCTION PARAMETER MEMORY"
(1) Main sound reproduction parameter
In the present embodiment, the "main sound reproduction parameter" indicates CSCn(t) and SCCn(t) as shown in equations (58)-1 and (58)-2. Because n=1, 2,···,50, and ···, therefore, there
Figure imgf000040_0001
are total 2X50X64,000=6.4X106 parameters. These parameters are calculated through computer and stored in ROM which we call "main sound reproduction
parameter memory". Hereby, MC
Figure imgf000040_0002
Sn(t) and MSCCn(t) are designated as memories for C
Figure imgf000040_0003
Sn(t) and SCCn (t)
respectively.
(2) End point sound reproduction parameter In the present embodiment, "end point sound reproduction parameter" indicates
(-1)rPk' (-t), (-1) [ k(-t)], -(-1)rPk' (1-t)
Figure imgf000041_0001
and - (-1)r [y k(1-t)] as shown in expression (56).
Figure imgf000041_0002
Because
Figure imgf000041_0003
theref ore , t here are tot a l 4 X 64 , 000= 2 . 56 X 105
parameters. These parameters are calculated through computer and stored in ROM which we call "end point sound reproduction parameter memory", in which
r=64,000t, Hereby, letting: u1(t) = (-1)rPk' (t); u2(t) = (-1)r[ k(-t)];
Figure imgf000041_0004
v1(t) = -(-1)rPk' (1-t); and v2(t) = -(-1)r[ κ(1-t)] °
Figure imgf000041_0005
Thus, Mu1(t), Mu2(t), Mv1(t) and Mv2 (t) are designated as memories for u1 (t), u2(t), v1(t), and v2 (t) respectively.
3. WAVEFORM DATA, WAVEFORM DATA MEMORY (RECORDING TAPE) AND SOUND RECORDING METHOD
In the following description, a sign (X) will be used, in which X represents a certain memory, and (X) represents the data in the memory X. Further, in case Y is a memory, thus:
Y ← (X)
It means to store the data from memory X to memory Y. In general condition, the right side of the arrow "← " represents a number, and the left side represents a memory. For example, Y ← (X1 ) + (X2) · (X3) +3
It means to store in memory Y the number which is obtained from the product of the data in memories X2 and X3, plus the data in memory X 1 and plus 3. (1). Waveform data and waveform data memory
(recording tape)
Letting:
WD1(n)= {S' (jΔT)Qxn(CC,j)+[(j+1)S(jΔT)
Figure imgf000042_0001
j 0
-jS((j+1)ΔT)]Qn(CC,j)}·····································(60)-1 WD2(n)= {S' (jΔT)Qxn(SC,j) + [(j+1)S(jΔT)
Figure imgf000042_0002
0
-jS((j+1)ΔT)]Qxn(SC,j)}···································(60)-2 thus, (57)-1 can be rewritten as: α c (t) + β c (t) = [C
Figure imgf000042_0004
Cn (t) · WD1 (n) +SCCn (t)
Figure imgf000042_0003
1
· WD2 (n)]·················································(57)-2 in which WD1 (n) and WD2 (n) are called waveform data. Because n= 1 , 2, ···, 50; there are total 2X50= 100
waveform data.
When MWD1 (n) and MWD2 (n) are respectively designated as RAM (random access memories) for WD1 (n) and WD2(n), there are totally 2X50=100 sets of RAM here. If each set of RAM contains 4 sets of Bytes (1 Byte = 8 Bits), there will be totally 400 Bytes.
According to the present embodiment, T=1. Because acoustic signal S(t) is 1 second, a 1 second of acoustic signal can be stored by means of 400 Bytes.
The foregoing MWD1 (n) and MWD2 (n) are called "waveform data memories", they are used as a recording tape. (2). Storage method (Sound recording method)
A "derivative circuit" shall be prepared (the derivative circuit will be described further in Hardware Structure) to give an output for the voltage signal S' (t) of the derivative function of t as soon as an acoustic voltage signal S(t) enters. One or two A/D converters shall also be prepared. When two A /D converters are used, they are respectively for converting S(t) and S' (t) into digital signals.
When single A/D converter is used, S(t) and S' (t) are commonly converted into digital signals
therethrough. The sound recording method according to the present invention is outlined hereinafter:
(i) clear MWD1 (n) and MWD2(n), then, sample S(t) and S' (t) when (i.e. t=0). The
Figure imgf000043_0001
samples from S(t) and S' (t) are S(0) and S' (0). Pre
-store S(0) and S' (0) in two sets of Data RAM which are designated MS(0) and MS' (0).
(ϊ) Sample S(t) when and the
Figure imgf000043_0002
,
sample is S(ΔT); After converting into
Figure imgf000043_0003
digital signal through A/D converter, the following calculations and operations are performed in proper sequence:
MWD1(1)← <MWD1(1)>+S' (0·ΔT)Qx1(CC,0)
+[S(0· ΔT) -0·S(1· ΔT)]Q1 (CC,0) MWD1 (2)← <MWD1 (2)>+S' (0· ΔT)QX2 (CC,0)
+ [S(0· ΔT) -0-S(1· ΔT)]Q2 (CC,0)
:
:
Figure imgf000044_0001
:
MWD1 (50)← <MWD1 (50)>+S' (0· ΔT)Qx50 (CC,0)
+ CS(0· ΔT) -0·S(1· ΔT)]Q50 (CC,0)
MWD2 (1)← <MWD2 (1)>+S' (0· ΔT)Qx1 (SC,0)
+ [S(0· ΔT) -0·S(1· ΔT)]Q1 (SC,0)
MWD2 (2)← <MWD2 (2)>+S' (0· ΔT)Qx2 (SC,0)
+ [S(0· ΔT) -0·S(1· ΔT)]Q2 (SC,0)
Figure imgf000044_0002
MWD2 (50)← <MWD2 (50)>+S' (0· ΔT)Qx50 (SC,0)
+ [S(0· ΔT) -0·S(1· ΔT)]Q50 (SC,0)
(iii) when repeat
Figure imgf000044_0003
64,000 64,000
Figure imgf000044_0006
the process of (ii), the final data in MWD1 (n) and MWD2
(n) (n=1, 2, ··· , 50) are the waveform data.
And, the samples of S(1) and S' (1) which are obtained when t= =1 are respectively stored in
Figure imgf000044_0004
,
two Data RAM MS(1) and MS' (1).
Thus, the final data in MWD1 (n), MWD2(n) (n=
1,2,···,50), MS(0), MS' (0). MS(1) and MS' (1)
represents a one second acoustic signal S(t). In the above calculations and operations, every procedure must be completed within second
Figure imgf000044_0005
= 15,625ns, and which is performed by means of
addition circuit and multiplication circuit matching with timing circuit. This will be described further. 4. METHOD OF RESTORATION (METHOD FOR REPRODUCTION OF SOUND)
The method to reproduce sound in accordance with the present invention is outlined hereinafter. (1) Read out the data from MS(0) directly when t= =0 this data is S(0).
Figure imgf000045_0001
(2) When t= do the following
Figure imgf000045_0002
calculations:
(i) First calculate the following: 1 > X <MWD1 (1) >
> X <MWD1 (2) > > X <MWD1 (3) > 50 ) > X <MWD1 (50) >
1 > X <MWD2 (1) >
> X <MWD2 (2) >
> X <MWD2 (3) > ) > X <MWD2 (50) >
Figure imgf000045_0003
(ii) Then, calculate the following: (64,000π)2 n >X<MWD1(n)>
Figure imgf000046_0001
n 1
+<MSCCn > X <MWD2 (n) >
Figure imgf000046_0002
(iii) And then, calculate the following:
Figure imgf000046_0003
Figure imgf000046_0004
X<MS' (0)> + <Mv1 )>X<MS(1)>
Figure imgf000046_0005
+ <Mv2 >X<MS' (1)>
Figure imgf000046_0006
(iv) Calculate the sum of the result
obtained from (ii) and (iii), and the sum thus obtained is:
Figure imgf000046_0007
(3) Repeat the calculation (2) when t=
Figure imgf000046_0008
thus, we can obtained respectively:
Figure imgf000046_0009
(4) Read out the data in MS(1) directly when t= 1 hour, which data is S(1).
Figure imgf000046_0010
Every procedure above-described shall also be completed within 15,625ns. This will be described further in Hardware Structure. HARDWARE STRUCTURE OF THE INVENTION
An embodiment of hardware structure in
accordance with the present invention for the
operation of the foregoing method will be fully
understood from the following detailed description, with reference to the annexed drawings, in which:
1. Brief Description of the Drawings:
Fig. 1 is a schematic drawing, illustrating the contents of (a) and (b) which are re s pect ively stored in MQxn(CC,j) and MQn(CC,j) (j=0, 1, ···, 63999) according to address sequence;
Fig. 2 is a schematic drawing, illustrating the contents of (a) and (b) which are respectively stored in MQxn(SC,j) and MQn(SC,j) (j=0, 1, ···, 63999) according to address sequence;
Fig. 3 is a schematic drawing, illustrating the contents of (a) and (b) which are respectively stored in MC
Figure imgf000047_0003
Cn(jΔT) and MSCCn(jΔT) (j=0, 1,···, 63999, according to address sequence;
Figure imgf000047_0001
Fig. 4 is a schematic drawing, illustrating the contents stored in a hybrid memory of Mu1 (j Δ T),
Mu2(jΔT), Mvx(jΔT), Mv2(jΔT) (j= 1, 2, ···, 63999, Δ T= according to address sequence;
Figure imgf000047_0002
Fig. 5 is a circuit diagram of a
"derivative circuit" according to the present
invention, in which an output of S' (t) is provided through terminal b when an input of acoustic signal S
(t) enters through terminal a (t is differentiated);
Fig. 6 is a computing circuit for the
calculation of
64,000[(DS2)-(DS1))X(DQx)+[j(DS1)-(j-1)(DS2)]X(DQ)+(DW); In which (DS1), (DS2), (DQx), (DQ) and (DW) represent the data in Data Bus DS1, DS2, DQx, DQ and DW (the others may be inferred by analog); j=0, 1,···, 63999; the value of j is counted by Counter 100. The calculation result is finally sent for output through DO (beyond the dotted line);
Fig. 7 is a computing circuit (sound recording circuit) diagram for computing the waveform data WD1 (n) and WD2 (n) of acoustic signal S(t), the result of which are sent through DW1 and DW2
respectively for output;
Fig. 8 is a read-write control circuit diagram for MWD1 (n) and MWD2 (n);
Fig. 9 is a computing circuit diagram for the calculation of
(DES1)X(DUV1)+(DES2)X(DUV2)+(DES3)X(DUV3)+(DES4)X(DUV4)
Fig. 10 is a circuit diagram which can continuously complete the following operation;
(1) to calculate (DW) X (DP)
(2) to read the data from accumulator 18 and add to the product obtained from (1) for further storage in accumulator 18 again, or simultaneously to multiply the result by a constant (64,000 π)2 for further output through D0;
Fig. 11 is a partly view of a restoration circuit (sound reproduction circuit) diagram for the restoration of acoustic signal S(t);
Fig. 12 is a complete restoration circuit diagram for the restoration of acoustic signal S(t);
Fig. 13 is a complete "storage/restoration circuit" diagram;
and
Fig. 14 is a control block diagram, in which a microprocessor is added to control the storage /restoration circuit. Description of the designated numerals:
010 : MQxn(CC,j). 021 : MQn(SC,j). 011 : MQxn(SC,j). 030 : MC
Figure imgf000049_0002
Cn(jΔT).
020 : MQn(CC.j). 031 : MSCCn(jΔT).
04 : hyprid memory of Mu1 (j Δ T), Mu2 (j Δ T), Mv1
(jΔT), Mv2 (jΔT). in the above, j=0, 1, 63999; Δ T=
Figure imgf000049_0001
050 : MWD1 (n);n= 1, 2, ···,50.
0500~050q : q+1 segments of MWD1(n),each segment contains 50 sets (because n= 1, 2, ···, 50).
051: MWD2 (n); n=1, 2, ···, 50.
0510-051q : q+1 segments of MWD2 (n), each segment contains 50 sets (because n=1, 2, ···, 50).
060,063 : subtracter for subtracting the data at input terminal DI1 from the data at input terminal DI2 for further output through D0.
061 : subtracter for subtracting 1 from the data at input terminal DI.
070-074, 0750-0753, 076, 077 : multiplier for the calculation of (DI1) X (DI2).
080 and 083 : adder for the calculation of (DI1) +(DI2)+(DI3).
081 : adder for the calculation of (DI1)+(DI2)+ (DI3)+(DI4)
082 : adder for the calculation of (DI1)+(DI2).
090 : circuit for providing constant "64,000". 091: : circuit for providing constant "(64,000 π)2 " .
100 counter for counting the value of "j", in which CK is a count pulse input end, and CR is a clear end.
101-107 : to provide address data for counter of memory device, in which CK is a count pulse input end, and CR is a clear end. 11 : "derivative circuit".
110,111 : high gain operational amplifier.
112-114 : resistors.
115 : inductor.
120,121 : electronic switch for use in
sampling acoustic signal S(t), in which Cr is the ON -OFF control end, and it becomes ON when Cr is High or it becomes OFF when Cr is Low.
130,131 : A/D converter.
14 : D/A converter.
150 : hybrid memory of MS' (0) and MS' (1).
151 : hybrid memory of MS(0) and MS(1).
160,161,1620,1621,1630,1631,1640,1641,1650,1651: buffers.
17 : shift register, in which the output data at D0 is the last input data at DI.
18 : accumulator for use in the process of the restoration of acoustic signal S(t).
19 : power amplifier.
20 : speaker.
210,211 : 0R gate group.
22 : timer (or called as "sound recording timer") for use in the process of the storage of acoustic signal S(t).
23 : timer (or called as "sound reproduction timer") for use in the process of the reproduction of acoustic signal S(t).
24 : microprocessor.
25 : keyboard.
26 : digital display.
27,270,271 : circuits as illustrated in Fig. 6.
28 : circuit as illustrated in Fig. 7.
29 : circuit as illustrated in Fig. 8.
30 : circuit as illustrated in Fig. 9.
31,310,311 : circuits as illustrated in Fig. 10. 32 : circuit as illustrated in Fig. 11.
33 : circuit as illustrated in Fig. 12.
34 : circuit as illustrated in Fig. 13.
2. Detailed Description of the Drawings:
1). Figs. 1 through 4
As previously described, these drawings illustrate the contents in the memories concerned.
2). Fig. 5
It is a "derivative circuit". As
illustrated, assume the resistance of resistors 112 -114 are R11, R12 and R1 ohm respectively; the
inductance of inductor 115 is L Henry. For the
selection of operational amplifiers 110 and 111, the following three terms must be taken into account: (1) The relative relation among amplifier's output
voltage e0, voltage eb at input connecting point and amplifier's gain K must be e0=-Keb; (2) Amplifier's current ib
Figure imgf000051_0003
10-9 is negligible; and (3) Amplifier's open-circuit gain is qenerally at D-C and can be as high as 108.
With respect to amplifier 110, assume its input voltage is ein (i.e. the voltage at terminal a in Fig. 5), the voltage at input connecting point is ex1, the voltage at both inducing ends is et, output voltage is e y 1 (i.e. the voltage at terminal y1 in Fig. 5), input current is i1, feedback current is i2.
Because the current at amplifier 110 is as small as
10-9, it is negligible and can be regarded as 0.
thus,
i1 +i2
Figure imgf000051_0002
0
and (because ey1=- Kex1,
Figure imgf000051_0001
and K is extremely great, therefore ex1 → 0) i2
i1'
i1
Figure imgf000052_0001
' i2' '
that is, L ein'
Figure imgf000052_0002
the voltage e. at both inducing ends can also be expressed by:
eL = ey1-ex1
Figure imgf000052_0003
ey1
therefore:
e 1 n'
Figure imgf000052_0004
r1
With respect to amplifier 111, the input voltage of amplifier 111 is the output voltage ey1 of amplifier 110. Assume the voltage at its input connecting point is ex2, the output voltage is ey2, the input current is i3, the feedback current is i4, thus:
3 i i4
Figure imgf000052_0005
therefore, eyz =
Figure imgf000053_0001
Wh en said e y 1 is su b stit ut ed ,
Figure imgf000054_0002
i2 1
When the value of Ri1, Ri2, Ri and L are selected to let i 2 i 1
Figure imgf000054_0001
t hus , ey2
Figure imgf000054_0003
= ei n
In the above expression, ey2 is the output through terminal b in Fig. 5, and ein is the input through terminal a. In case the input through
terminal a is an acoustic signal S(t), the output through terminal b becomes S' (t), and this is a derivative of time for S(t).
Because the input resistance in regular operational amplifiers is generally infinitely great, amplifier 110 still can be regarded as in an open- circuit status when amplifier 111 is connected.
3). Fig. 6
As foregoing statement, Fig. 6 is a computing circuit for the calculation of :
64,000[(DS2)-(DS1)]X(DQx)+[j(DS1)-(j-1)(DS2)]X(DQ)+(DW)
When the data at Data Bus DW, DS1, DS2, DQx and DQ become stable and a High signal enters through Enable terminal EN, the result from said calculation will be sent for output through terminal DO after a duration delayed by the circuit itself. Before each calculation or before adding High to EN, a pulse input is sent through terminal CK to drive counter 100 to produce a new value of "j". Further, an input signal of clear must be sent through terminal CR while proceeding with first calculation process, permitting the value of "j" to start from 0.
4). Fig. 7
Therein illustrated is a computing circuit for the calculation of waveform data of acoustic signal S(t), and the operation of which is outlined hereinafter.
(1) Acoustic signal S(1) enters from terminal S through "derivative circuit" 11, to provide electronic switch 121 with S' (t).
(2) At the same time, S(t) enters electronic switch 120 directly.
(3) S(t) and S' (t) are continuously sampled for converting into digital signals by A/D converters 130 and 131 respectively (the frequency at Cr is 64,000Hz) when the instant is High at terminal Cr.
(4) S' (0) and S' (0) from the digital signals of S' (t) that A/D converter 131 provides will be stored in memory 150 when the total time length of S(t) is one second. The address data of memory 150 is provided by counter 101. Under this condition, a pulse enters clock input terminal CK3 of counter 101 per every second, and "write control terminal" W1 enters an input of High to complete storage operation when address data and S' (0) or S' (1) that A/D converter 131 provides become stable.
(5) S(0) and S(l) from the digital signals of S(t) that A/D converter 130 provides are stored in memory 1511. The address data of memory 151 is provided by counter 102. Similarly, a pulse enters CK4 per every second, and "write control terminal" W2 enters an input of High to complete storage operation when address data and digital signal S(0), S(1) become stable.
(6) 17 is a shift register. When a fist High enters terminal SF the input data from terminal DI is shifted to a register prepared in 17. As soon as a second High enters terminal SF the data in said register is shifted to terminal D0 and the data at DI is shifted to said register. Therefore, the data at terminals DS2, DS1, in circuit blocks 270 and 271 are constantly the same: the data at DS is existing S(t), and the data at DS1 is the last S(t). That is to say: DS1 is S((j-1)ΔT) when DS2 is S(jΔT), in which j=0, 1,···, 63, 999; Δ T .
Figure imgf000056_0001
(7) 270 and 271 are the circuit 27 as
illustrated in Fig. 6.
(8) 010 is MQxn(CC,j); 011 is MQxn(SC,j);
020 is MQn(CC,j); 021 is MQn(SC,j). Counter 103
provides address data for these memories, and "Read control terminals" are concomitantly controlled by R3.
(9) According to the description of Fig. 6, it is apparent that the data presented in DW1 and DW2 after last S(t) is presented (i.e. after termination of 1 second) are the waveform data:
{S' (jΔT)Qxn(CC,j) + [(j+1)S(jΔT)-jS((j+1)ΔT)]Qn(CC,j)};
Figure imgf000056_0002
0
and
9
{S' (jΔT)Qxn(SC,j) + [(j+1)S(jΔT)-jS((j+1)ΔT)]Qn(SC,j)};
Figure imgf000056_0003
0
in which, S' (j Δ T) = 64, 000 [S((j + 1) Δ T) - S (j Δ T)]
1
Δ T = (please refer to equation (57)-1); n=1,2,
Figure imgf000056_0004
···,50. Therefore, DW1 and DW2 will respectively provide an output of 50 waveform data. 5 ) . Fig . 8
Therein illustrated is a read-write control circuit for controlling MWD1 (n) and MWD2(n), and the operation of which is outlined hereinafter:
(1) MWD1(n) 050 and MWD2 (n) 051 are
respectively partitioned into q+1 segments 0500-050q and 0510-051q, in which each segment includes 50 sets permitting each set to store therein a WD1 (n) and a WD2(n) (n= 1,2,-,50).
(2) The read and write control terminals of
050 are R1 and W2 respectively, and of 051 are R1 and W2 respectively.
(3) Counters 104 and 105 provide address data for 050 and 051 respectively, wherein 104 provides higher address data and 105 provides lower address data. CK1 and CK2 are count pulse input terminals of 104 and 105 respectively, and CR is the common clear terminal.
(4) Higher address are the address of every segment of 0500, 0501, 0502, ···, 050q and 0510, 0511,
0512, ···, 051q, and lower address are the address of every set of said every segment (each segment has 50 sets, therefore, lower address contains 5 Bits).
(5) Address data can be freely set in advance (therefore, 104 and 105 here are special counters). During setting, the data to set is added to terminal ADS, and thereafter, a setting signal is added to terminal Sr.
(6) Because address data can be freely set in advance, it is possible to start reading and writing from any segment in 050 and 051.
(7) For address data free setting, an external microprocessor is provided for selection control (by means of keyboard operation).
(8) An acoustic signal S(t) is stored in said every segment of 050 and 051. When a one-hour acoustic signal is divided into 3600 segments and every segment equals to 1 second, 050 and 051 must have 3600 segments (for higher address 14 Bits is required) sufficient for the storage of the waveform data of an one-hour acoustic signal.
(9) The circuit in Fig. 8 is actually
equivalent to a "recording tape".
6). Fig. 9
As previously described, the circuit herein is a computing circuit for the calculation of :
(DES1)X(DUV1)+(DES2)X(DUV2)+(DES3)X(DUV3)+(DES4)X(DUV4)
Because 0750-0751 are multipliers and 081 is an adder, they are provided for the calculation of above expression. During computation, a High is added to terminal EN after the data in Data Bus DES1, DUV1 ··· become stable. After a delayed duration through the circuit, the result thus obtained is sent for output through terminal D0.
7). Fig. 10
The operational sequence of the circuit herein is outlined hereinafter:
(1) The data to process are sent to terminals DW and DP.
(2) After the data at DW and DP become stable, High is added to terminals EN1 and R. After delayed duration through the circuit, an output of (DW) X(DP) is added from D0 of multiplier 076 to DI of adder 082, and the data in accumulator 18 is read out and added to DI of adder 082.
(3) After the data at DI1 and DI2 of adder 082 become stable, High is added to EN2 and the sum from its two input terminals is sent for output
through D0 of adder 082.
(4) After the output from adder 082 becomes stable, High is added to terminal W so as to store the sum from (3) back to accumulator 18.
(5) Repeat the operation from (1) through (4) for 50 times.
(6) Then, add High to ST so as to register
"final result" in buffer 166.
(7) 091 is a circuit to provide constant (64,000π)2. When High is finally added to EN3, said "final result" can be multiplied by (64,000 π)2
before output (since 077 is a multiplier).
8). Fig. 11 and Fig. 12
As previously described, Fig. 11 is a part of a restoration circuit which can restore an
acoustic signal S(t), and Fig. 12 is a complete
restoration circuit (sound reproduction circuit).
Both drawings are concomitantly described hereinafter.
(1) In Fig. 12, 32 designates Fig. 11; In Fig. 11 designates Fig. 9, and 310 and 311 designate 31 in Fig. 10.
(2) In Fig. 12, 04 designates hybrid memory of Mu1(jΔT), Mu2(jΔT), Mv1(jΔT) and MV2(jΔT); 107 designates a counter to provide address data. From the allocation of the storage contents in Fig. 4, when 4 pcs. of data is continuously read out from 04 each time, such 4 pcs. of data are u1 (j Δ T), u2 (j Δ T), v1(jΔT) and v2(jΔT) (j= 1, 2, ···, 63999; Δ
Figure imgf000059_0001
After ST2, ST3, ST4 and ST5 in Fig. 11 become
synchronous and are respectively added with High in proper sequence, said 4 pcs. of data can then be registered in Buffers 1621, 1631, 1641 and 1651 properly.
(3) Terminal DES is connected to terminal
DES of circuit 28 in Fig. 7 (see Fig. 13). In Fig. 7, the following operations are performed in proper sequence :
CK3 is added with a pulse;
R1 is added with High;
ST1 is added with High ----- under this
condition, S' (0) is presented at DES;
CK4 is added with a pulse;
R2 is added with High;
ST2 is added with High ---- under this
condition, S(0) is presented at DES;
Repeat above operation twice permitting S'
(1) and S(1) to be presented at DES in proper sequence.
(4) Return to Fig. 11 now. According to (3), 4 pcs. of data S' (0), S(0), S' (1) and S(1) can be continuously presented through DES. When ST2, ST3, ST4 and ST5 become synchronous and are added with
High in proper sequence, said 4 pcs. of data can then be registered in buffers 1620, 1630, 1640 and 1650 respectively.
(5) After output data from buffers 1620, 1621, 1630, 1631, and etc., become stable, EN4 (in Fig.
11) is added with High, and then output can be sent through 30 (see Fig. 9): u1(jΔT)S' (0)+u2(jΔT)·S(0) +v1(jΔT)S' (1)+v2(jΔT)S(1).
(6) 310 and 311 in Fig. 11 designates 31 in Fig. 10; 030, 031 in Fig. 12 designate MC
Figure imgf000060_0002
Cn(jΔT) and MSCCn(jΔT) (j= 1, 2, ···, 63999; Δ the
Figure imgf000060_0001
allocation of the contents of which is as shown in Fig.
3. Counter 106 provides address data for 030 and 031.
Therefore, when pulse enters CK1 in Fig. 12 and High is given to terminal R1 after the address data each time provided become stable, C
Figure imgf000060_0003
C1 (jΔT), C
Figure imgf000060_0004
C2 (jΔT), ··· and SCC1 (jΔT), SCC2 (j Δ T), ··· are respectively continuously presented through terminals DP1 and DP2
(see the allocation of the contents of 030 and 031 in Fig . 3 ) .
(7) DW1 and DW2 in Fig. 11 or Fig. 12 are respectively connected to DW1 and DW2 of circuit 29 in Fig. 8 (see Fig. 13), and DW1 and DW2 of circuit 29 (Fig. 8) are data input output terminals of MWD1 (n) 050 and MWD2 (n) 051. Therefore, what are presented through DW1 and DW2 here (Fig. 11 or Fig. 12) are waveform data of S(t). According to the description for Fig. 10, the output through 310 and 311 are
respectively as:
(64,000π)2 [<MC
Figure imgf000061_0002
SCn(jΔT)>X<MWD1(n)>]; and
1
(64,000π)2 [<MSCCn(jΔT)>X<MWD2(n)>]
Figure imgf000061_0001
1 in which, j= 1, 2, ··· 63999.
(8) Because 083 is an adder, the output from 083 is the sum of the output from 310, 311 and 30, and such sum is S(jΔT). Under this condition, S(jΔT) is a digital signal which can be converted into
analog signal through D/A converter.
9). Fig. 13
Therein illustrated is a "storage/ restoration circuit" which incorporates the circuit which stores S(t) and the circu. which restores S(t), and the operation of which is outlined hereinafter.
(1) In the drawing, 28 designates the
circuit in Fig. 7, 33 designates the circuit in Fig. 12, 29 designates the circuit in Fig. 8, and in which S is an acoustic signal input terminal, ADS and Sr are equivalent to that in Fig. 8.
(2) 22 designates a timer for use in the calculation of waveform data of S(t) (i.e. during sound recording); 23 designates a timer for use in the restoration of S(t) (i.e. in reproduction of sound); in which TEN1 is an Enable terminal to drive timer 22 to operate, and TEN2 is an Enable terminal to drive timber 23 to operate.
(3) Timer 22 includes T1 - T21 total 21 output control terminals; Timer 23 includes T1 - T32 total 32 output control terminals. Each output
control terminal of timers 22 and 23 completes a circuit operation each after every output of High
(pulse) signal therethrough. The sequence of output from timers 22 and 23 and the duration of each output therefrom are respectively designed according to the above-described operational routine of the circuit.
(4) Because timers 22 and 23 are of known art and not within the scope of the present invention, the circuit of which will not be described here.
However, further detail will be available when it is required.
10). Fig. 14
As previously described, Fig. 14 is a
control block diagram, in which a microprocessor is provides to control storage/restoration circuit. It is detailed hereinafter.
(1) In the drawing, 34 is the circuit in Fig. 13; 25 designates a keyboard; 26 designates a
digital display.
(2) 24 designates a microprocessor, the I/0 of which includes:
one set of output lines DSP1 for sending a 7 digits data to digital display 26;
one set of scanning output lines DSP2 for selecting digit place to desplay when DSP1 provides a 7 digits data to digital display 26;
one set of output lines ADS for providing the address data of MWD1 (n) and MWD2 (n) to circuit 34; one output line TEN1 for selecting timer 22 of circuit 34 to operate;
one output line Sr for providing a control sihnal when the address data in MWD1 (n) and MWD2 (n) are set through ADS;
one sets of "read keyboard scanning line" DK 1 for providing scanning data to keyboard 25 during keyboard reading; and
one sets of "key-entry identification lines" DK2 to judge and identify any key-entry then DK1 provides scanning data to keyboard 25.
(3) Digital display 26 provides two functions. One is to display the address data preset in MWD1 (n) and MWD2 (n) so that an user can know where to start recording or reproduction; the other is to display the duration of time during sound recording or reproduction so that an user can know how long has been consumed in sound recording or reproduction.
(4) Keyboard 25 provides three functions.
The first function is to set address data in MWD1 (n) and MWD2 (n); the second function is to select TEN1 or TEN2 to be High (both can not be High at the same time) for sound recording or reproduction; the third
function is to select the mode of display through digital display 26 (to display address data, or
duration of time in sound recording or reproduction).
(5) Microprocessor 24 is of a known art and not within the scope of the present invention, the hardware and software structure of which will not be described here. However, further detail will be available when it is required.

Claims

1. A method for the storage access of acoustic signal S(t) defined within [0,T] (t∈[0,T]), including:
a first procedure to define an "auxiliary function" P(x) as:
L(α) ; when X ∈ [-M,0]
R(α) ; when X ∈ [0,M]
in which M M), 0 ≤ t ≤ M, L(x) is "left auxiliary function", R(x) is "right auxiliary
function", R(0) = L(0);
a second procedure to express acoustic signal S(t) by means of approximate expression as: {U
Figure imgf000064_0002
S(0)+Us
Figure imgf000064_0003
S' (0)+U S" (0)
Figure imgf000064_0001
+V
Figure imgf000064_0005
S(T)+V S' (T)+V
Figure imgf000064_0007
S" (T)
+(Hπ)3[α
Figure imgf000064_0008
(t)+β
Figure imgf000064_0009
(t)]}··············(52) in which H is a number of high absolute value, U
Figure imgf000064_0010
1S(0), U
Figure imgf000064_0011
S' (0), U
Figure imgf000064_0012
3S" (0), V
Figure imgf000064_0013
S(T), V
Figure imgf000064_0014
S' (T) and Vs3S" (T) are as described in the expressions (53) - 1 - (53) -6 of the specification, and α
Figure imgf000064_0015
(t)+ β
Figure imgf000064_0016
(t) is as described in expression (16);
a third procedure to calculate Qxn(CS,j),
Qxn(CC,j), Qxn(SS,j), Qxn(SC,j), Qn(CS,j), Qn(CC,j),
Qn(SS,j) and Qn(SC,j) (n=1, 2, ···, k; j=0, 1, ···, m-1; k is the highest number of harmonic wave after expansion of P(x) through Fourier series; m is the number of segments which are partitioned from interval [0,T]) and to store the result thus obtained in permanent memory MQxn(CS,j), MQxn(CC,j), MQxn(SS,j), MQxn(SC,j), MQn(CS,j), MQn(CC,j), MQn(SS,j) and MQn(SC,j)
respectively, in which Qxn(CS,j), Qxn(CC,j), Qxn(SS,j), Qxn(SC,j), Qn(CS,j), Qn(CC,j), Qn(SS,j) and Qn(SC,j) are as described in the equations (14)-1~(14)-8 of the specification;
a fourth procedure to prepare 4k sets of Data RAM MWD1 (n), MWD2 (n), MWD3 (n), MWD4 (n) and 6 sets of Data RAM MS(0), MS' (0), MS" (0), MS(T), MS' (T) and MS" (T), in which n=1, 2, ···,k; and
a fifth procedure to proceed with following jobs:
(1) clearing MWD1 (n), MWD2 (n), MWD3 (n), MWD4 (n) to zero;
(2) sampling S(t), S' (t) and S" (t) to have samples S(0), S' (0) and S" (0) when t=0 · Δ T ( Δ T
Figure imgf000065_0002
and storing S(0), S' (0) and S" (0) in MS(0), MS' (0) and MS" (0) respectively;
(3) sampling S(t) to have sample S(jΔT) when t=j· Δ T (j=1, 2, ··· m, Δ T , and then proceeding:
Figure imgf000065_0001
MWD1(1) ← <MWD1(1)>+S' ((j-1)ΔT)
X<MQx1(cs,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(cs,j-1)>;
MWD1(2) ← <MWD1(2)>+S' ((j-1)ΔT)
X<MQx2(cs,j-1)>+[js((j-1)ΔT)
(j-1)S(jΔT)]X<MQ2(cs,j-1)>;
: :
: :
: :
MWD1(n) ← <MWD1(n)>+S' ((j-1)ΔT)
X<MQx1(cs,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQn(cs,j-1)>; MWD2(1) ← <MWD2(1)>+S' ((j-1)ΔT)
X<MQx1(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(cc,j-1)>;
MWD2(2) ← <MWD2(2)>+S' ((j-1)ΔT)
X<MQx2(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ2(cc,j-1)>;
: :
: :
: :
MWD2(n) ← <MWD2(n)>+S' ((j-1)ΔT)
X<MQxn(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]x<MQn(cc,j-1)>;
MWD3(1) ← <MWD3(1)>+S' ((j-1)ΔT)
X<MQx1(ss,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(ss,j-1)>;
MWD3(2) ← <MWD3(2)>+S' ((j-1)ΔT)
X<MQx2(ss,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]x<MQ2(ss,j-1)>;
: :
: :
: :
MWD3(n) ← <MWD3(n)>+S' ((j-1)ΔT)
X<MQxn(ss,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQn(ss,j-1)>;
MWD4(1) ← <MWD4(1)>+S' ((j-1)ΔT)
XMQx1(sc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(sc,j-1)>; MWD4(2) ← <MWD4(2)>+S' ((j-1)ΔT)
X<MQx2(sc,j-1)>+[js(j-1)ΔT- (j-1)S(jΔT)]X<MQ2(sc,j-1)>;
: :
: :
: :
MWD4(n) ← <MWD4(n)>+S' ((j-1)ΔT)
X<MQx2(sc,j-1)>+[js(j-1)ΔT- (j-1)S(jΔT)]X<MQn(sc,j-1)>; in which,
S' ((j-1)ΔT) =
Figure imgf000067_0001
ΔT
(4) storing samples S(T), S' (T) and S" (T) in MS(T), MS' (T) and MS" (T) respectively when t=m Δ T =T.
2. A method for the storage access of
acoustic signal S(t) defined within [0,T] (t∈[0,T]), including:
a first procedure to define an "auxiliary function" P(x) as:
L(x) ; when X ∈ [-M,0]
P(x) =
R(x) ; when X ∈ [0,M]
in which M > 0, 0 ≤ t ≤ M, L(x) is "left auxiliary function", R(x) is "right auxiliary
function", R(x) is "right auxiliary function", R(0) = L(0);
a second procedure to express acoustic signal S(t) by means of approximate expression as: {Uc1S(0)+U
Figure imgf000067_0003
S' (0)+Vc1S(T)
Figure imgf000067_0002
+Vc2S' (T) +(Hπ)2[αc(t)+β-(t)]}····(54) in which, H is a number of high absolute value, Uc1S (0), Uc2S' (0), Vc1S(T), Vc2S' (T) are as described in the equations (55) - 1 - (55) -4, and αc(t)+ βx(t) is as described in the approximate expressoin (32) of the specification;
a third procedure to calculate Qxn(CS,j), Qxn(CC,j), Qxn(SS,j), Qxn(SC,j), Qn(CS,j), Qn(CC,j), Qn(SS,j) and Qn(SC,j) (n= 1, 2, ···, k; j=0, 1, ···, m-1; k is the highest number of harmonic wave after expansion of P(x) through Fourier series; m is the number of segments which are partitioned from interval [0,T]) and to store the result thus obtained in permanent memory MQxn(CS,j), MQxn(CC,j), MQxn(SS,j), MQxn(SC,j), MQn(CS,j), MQn(CC,j), MQn(SS,j) and MQn(SC,j),
respectively, in which Qxn(CS,j), Qxn(CC,j), Qxn(SS,j), Qxn(SC,j), Qn(CS,j), Qn(CC,j), Qn(SS,j) and Qn(SC,j) are as described in the equations (14) - 1 - (14) - 8 of the specification;
a fourth procedure to prepare 4k sets of Data RAM MWD1 (n), MWD2 (n), MWD3 (n), MWD4 (n) and 4 sets of Data RAM MS(0), MS' (0), MS(T), MS' (T), in which n=1,2,···,k; and
a fifth procedure to proceed with following jobs :
(1) clearing MWD1 (n), MWD2 (n), MWD3(n), MWD4 (n) to zero;
(2) sampling S(t) and S' (t) to have samples S(0) and S' (0) when t=0· Δ T ( Δ T
Figure imgf000068_0001
and storing S(0) and S' (0) in MS(0) and MS' (0) respectively;
(3) sampling S(t) to have sample S(jΔT) when t=j·ΔT (j= 1,2, ···m, Δ and then proceeding:
Figure imgf000068_0002
MWD1(1) ← <MWD1(1)>+S' ((j-1)ΔT)
X<MQx1(cs,j-1)>+[Js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(cs,j-1)>;
MWD1(2) ← <MWD1(2)>+S' ((j-1)ΔT)
X<MQx2(cs,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ2(cs,j-1)>;
: :
: :
: :
MWD1(n) ← <MWD1(n)>+S' ((j-1)ΔT)
X<MQx1(cs,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]x<MQn(cs,j-1)>;
MWD2(1) ← <MWD2(1)>+S' ((j-1)ΔT)
X<MQx1(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT))X<MQ1(cc,j-1)>;
MWD2(2) ← <MWD2(2)>+S' ((j-1)ΔT)
X<MQx2(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQ2(cc,j-1)>;
MWD2(n) ← <MWD2(n)>+S' ((j-1)ΔT)
X<MQxn(cc,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]X<MQn(cc,j-1)>;
MWD3(1) ← <MWD3(1)>+S' ((j-1)ΔT)
X<MQx1(ss,j-1)>+[ds((j-1)ΔT)- (j-1)S(jΔT)]X<MQ1(ss,j-1)>;
MWD3(2) ← <MWD3(2)>+S' ((j-1)ΔT)
X<MQx2(ss,j-1)>+[js((j-1)ΔT)- (j-1)S(jΔT)]x<MQ2(ss,j-1)>; MWD3(n) ← <MWD3(n)>+S' ((j-1)ΔT)
X<MQxn(ss,j-1)>+[js((j-1)ΔT)-
(j-1)S(jΔT)]x<MQn(ss,j-1)>;
MWD4(1) ← <MWD4(1)>+S' ((j-1)ΔT)
XMQx1(sc,j-1)>+[js((j-1)ΔT)-
(j-1)S(jΔT)]X<MQ1(sc,j-1)>;
MWD4(2) ← <MWD4(2)>+S' ((j-1)ΔT)
X<MQx2(sc,j-1)>+[js((j-1)ΔT)-
(j-1)S(jΔT)]x<MQ2(sc,j-1)>; MWD4(n) ← <MWD4(n)>+S' ((j-1)ΔT)
X<MQx2(sc,j-1)>+[js((j-1)ΔT)-
(j-1)S(jΔT)]X<MQn(sc,j-1)>; in which,
S, ((i-1) ΔT) =
Figure imgf000070_0001
(4) storing samples S(T) and S' (T) in MS(T) and MS' (T) respectively when t=mΔT=T.
3. A method according to claim 1 or 2, which includes a process, as described in said second procedure, to express the stored acoustic signal S(t) as the approximate expression of (52) or (54) in the specification.
4. A method according to claim 1 or 2, which includes a tequnical process as described in said third procedure.
5. A method according to claim 1 or 2, which includes a process as described in said fourth procedure.
6. A method according to claim 1 or 2, which includes a process as described in said fifth procedure.
7. A method according to claim 1 or 2 which is characterized by its process in defining an
"auxiliary function" P(x) as expressed in equation (3); expressing P(x) by means of Fourier series Pk(x) in which k is the number of times of the highest
harmonic wave in Fourier series, and considering
∫ L(x)S(x+t)sin(Hπx)dx+∫ R(x)S(x+t)sin(Hπx)dx
Figure imgf000071_0001
Figure imgf000071_0002
Figure imgf000071_0003
∫ Pk(x)S(x+t)sin(Hπx)dx ;
or
L(x)S(x+t)cos(Hπx)dx+∫ R(x)S(x+t)cos(Hπx)dx
Figure imgf000071_0004
Figure imgf000071_0005
∫ Pk(α)S(x+t)cos(Hπx)dx ;
Figure imgf000071_0006
as well as selecting "left auxiliary function" L(x) and "right auxiliary function"
properly so as to obtain an approximate expression (52) or (54)for S(t).
8. A method according to claim 7, which is to alternatively select "left auxiliary function" L(x) and "right auxiliary function" R(x) so as to obtain a respective approximate expression for S(t).
9. A method according to claim 1 or 2, which is characterized by its process in continuously sampling acoustic signal S(t) within interval [0,T] before its termination so as to complete the
calculation of : ∫0 T S(x)cos(nω0x)sin(Hπx)dx ; ∫0 T S(x)cos(nω0x)cos(Hπx)dx ; ∫0 T S(x)sin(nω0x)sin(Hπx)dx ; and ∫0 T S(x)sin(nω0x)cos(Hπx)dx ; in which n= 1,2,···,k; k is the number of times of the highest harmonic wave obtained from the expansion of P (x) through Fourier series; ; H is a number of
Figure imgf000072_0001
high absolute value.
10. A method according to claim 1, which includes a process to replace approximate expression (52) by: {Z
Figure imgf000072_0003
s1S(0)+Z
Figure imgf000072_0004
s2S' (0)+Z
Figure imgf000072_0005
s3S" (0)
Figure imgf000072_0002
+W
Figure imgf000072_0006
s1S(T)+W s2S' (T)+W
Figure imgf000072_0008
s3S" (T) + (Hπ)3[α
Figure imgf000072_0009
s(t)+ β
Figure imgf000072_0010
s(t)]} ············· ··············· ······························································ ···(25) in which, H is a number of high absolute value; Zs1, Z 2, Z
Figure imgf000072_0011
3, W
Figure imgf000072_0012
, W
Figure imgf000072_0013
, W
Figure imgf000072_0014
are respectively as
illustrated in equations (23) - 1 - (23)-3 and (24) - 1 - (24) - 3; and α
Figure imgf000072_0015
(t)+ β
Figure imgf000072_0016
(t) is as illustrated in
approximate expression (16).
11. A method according to claim 2, which, includes a process to replace approximate expression (54) by: ' {Zc1S(0)+Zc2S' (0)+Wc1S(T)
Figure imgf000073_0001
+Wc1S' (T) + (Hπ)2[αc(t)+βe(t)]}··················(42) in which, H is a number which has a high absolute value; Zc1, Zc2, and Wc1, Wc2 are respectively as illustrated in equations (40) - 1, (40) - 2, (41) - 1 and
(41) - 2 ; and αc(t)+ βc(t) is as illustrated in
approximate expression (32).
12. A method according to claim 9. which is characterized by its process in representing acoustic signal S(t) by means of a value which is obtained from its calculation, said value being: ∫0 TS(x)cos(nω0x)sin(Hπx)dx ; ∫0 T S(x)cos(nω0x)cos(Hπx)dx ; ∫0 T S(x)sin(nω0x)sin(Hπx)dx ; ∫0 T S(x)sin(nω0x)cos(Hπx)dx ; in which, H is a number of high absolute value; n=1, 2,
···, k; k is the number of times of the highest
harmonic wave obtained from the expansion of
"auxiliary function" P(x) through Fourier series;
Figure imgf000073_0002
13. A method according to claim 1, which includes a process to restore an acoustic signal S(t) defined within [0,T] by utilizing the waveform data stored in MWD1(n), MWD2(n), MWD3(n) and MWD4(n) (n= 1,2,
···, k; k is the number of times of the highest
harmonic wave obtained from the expansion of
"auxiliary function" P(x)), said process being
performed according to the following procedures:
(1). to calculate the value of Us1, Us2, Us3, Vs1, Vs2 and Vs3 of the approximate expression (52) and store respective result in permanent memories MUs1 (t), MUs2(t), MUs3(t), MVs1(t), MVs2(t) and MVs3(t);
(2). to calculate the value of C
Figure imgf000074_0001
Cn(t),
Figure imgf000074_0002
SSn
(t), SCCn(t) and
Figure imgf000074_0003
CSn(t) (t=0·ΔT, 1·ΔT, ··· (m-1)ΔT; m is a number of great positive integer) of
Figure imgf000074_0004
the equation (15) - 1 - (15) -4 in the specification and to store respective result in permanent memories MC
Figure imgf000074_0005
Cn
(t), M
Figure imgf000074_0006
SSn(t), MSCCn(t) and M
Figure imgf000074_0007
CCn(t) respectively;
(3). to execute following jobs:
(1) to clear MWD1 (n) ~MWD4 (n) to zero; n= 1, 2 , ···, k,
(2) to read out the data in MS(0)
directly when t=0 so as to obtain S(0);
(3) to start following calculations when t = j Δ T ( j=1, 2, ··· , m-1, Δ T= at first to calculate.
Figure imgf000074_0008
Φ1n=<MC
Figure imgf000074_0009
Cn(jΔT)>X<MWD1(n)> ;
Φ2n=<M
Figure imgf000074_0010
SSn(jΔT)>X<MWD2(n)> ;
Φ3n=<MSCCn(jΔT)>X<MWD3(n)> ;
Φ4n=<M
Figure imgf000074_0011
Cn(jΔT)>X<MWD4(n)> ; in which, n = 1, 2, ···, k; then, to calculate:
Φ=(Hπ) (Φ1 n+Φ2n+Φ3n+Φ4 n)
Figure imgf000075_0001
1
and then, to calculate: θ=<MUs1(jΔT)>X<MS(0)>+<MUs2(jΔT)>
X<MS' (0)>+<MUs3(jΔT)>X<MS" (0)>
+<MVs1(jΔT)>X<MS(T)>+<MVs2(jΔT)>
+<MS' (T)>+<MVs3(jΔT)>X<MS" (T)>
and final, to calculate ψ + θ , hereby ψ + θ equals to S(j Δ T);
(4) to read out the data in MS(T) directly when t=mΔ T=T so as to obtain S(T).
14. A method according to claim 2, which includes a process to restore an acoustic signal S(t) defined within [0,T] by utilizing the waveform data stored in MWD1(n), MWD2(n), MWD3 (n) and MWD4(n) (n= 1,2,
···,k; k is the number of times of the highest
harmonic wave obtained from the expansion of
"auxiliary function" P(x)), said process being
performed according to the following procedures:
(1) to calculate the value of Uc1, Uc2, v1 and Vc2 of the approximate expression (54) and store respective result in permanent memories MUc1(t), MUc2 (t), MVc1(t) and MVc2 (t);
(2) to calculate the value of C
Figure imgf000075_0002
SCn(t), C
Figure imgf000075_0004
Sn
(t), SCCn(t) and SCSn(t) (t=0·ΔT, 1 · Δ T, ··· (m-1) ΔT; Δ T= ; m is a number of great positive integer) of
Figure imgf000075_0003
the equations (33) - 1 - (33) -4 in the specification and to store respective result in permanent memories
MCSCn(t), MCSSn(t), MSCCn(t) and MSCSn(t) respectively:
(3) to execute following jobs:
(i) to clear MWD1 (n) ~MWD4 (n) to zero; n= 1, 2, ···, K ;
(ii) to read out the data in MS(0)
directy when t=0 so as to obtain S(0);
(iii) to start following calculations when t=jΔT (j= 1,2, ···, m-1; Δ
Figure imgf000076_0001
at first to calculate:
Φ1n = <MCSCn(t)>X<MWD1(n)> ; Φ 2n = <MC
Figure imgf000076_0002
SSn(t)>X<MWD2(n)> ; Φ3n = <MSCCn(t)>X<MWD3(n)> ; Φ 4n = <MSCSn(t)>X<MWD4(n)> ; it which, n=1, 2, ···, k; then, to calculate:
Ψ=(H π)2 (Φ1n+Φ2n+Φ3n+Φ4n)
Figure imgf000076_0003
1
and then, to calculate: θ=<MUc1(jΔT)>X<MS(0)>+<MUc2(jΔT)>
X<MS' (0)>+<MVex(jΔT)>X<MS(T)> +MVc2(jΔT)>X<MS' (T)> ; and final, to calculate: ψ+ θ , herein ψ + θ=S(jΔT);
(iv) to read out the data in MS(T) directly when t = mΔT=T so as to obtain S(T).
15. A method according to claim 13 or 14, which includes a process as described in said
procedure (1).
16. A method according to claim 13 or 14, which includes a process as described in said
procedure (2).
17. A method according to claim 13 or 14, which includes a process as described in said
procedure (3).
18. A method according to claim 13 or 14, which includes a process as described in the job (iii) of said procedure (3).
19. A method according to claim 1 through 18, which includes a process to let m=|H| (|H| is the absolute value of H) and to let -jΔT (j=0, 1, ···, m, ΔT= during restoration of acoustic signal S(t), so as to have
Figure imgf000077_0003
CSSn(t),
Figure imgf000077_0004
Sn(t) in the equations (15) - 2, (15)
-4 or C
Figure imgf000077_0005
Sn(t), SCSn(t) in the equations (33)-2, (33) -4 of the specification be constantly 0.
20. A method according to claim 1 through 18, which includes a process to let m=|H| (|H| is the absolute value of H) and to let [j Δ T+ (j+ 1) Δ T)
Figure imgf000077_0001
(j=0, 1, 2, ···, m; Δ during restoration of acoustic
Figure imgf000077_0002
signal S(t), so as to have C
Figure imgf000077_0006
Cn(t), SCCn (t) in the equations (15) - 1, (15) -3 or C
Figure imgf000077_0007
Cn(t), SCC (t) in
equations (33) - 1, (33) - 3 be constantly 0.
21. A method according to claim 19, which includes a process to let m= τ |H| (τ is a positive integer ≥ 2).
22. A method according to claim 20, which includes a process to let m= τ |H| ( τ is a positive integer ≥ 2).
23. The equipment according to claim 1 or 2, which includes:
k.m sets of permanent memories MQxn(CS,j) for the storage of Qxn(CS,j);
k.m sets of permanent memories MQxn(CC,j) for the storage of Qxn(CC,j);
k.m sets of permanent memories MQxn(SS,j) for the storage of Qxn(SS,j);
k.m sets of permanent memories MQxn(SC,j) for the storage of Qxn(SC,j);
k.m sets of permanent memories MQn(CS,j) for the storage of Qn(CS,j);
k.m sets of permanent memories MQn(CC,j) for the storage of Qn(CC,j);
k.m sets of permanent memories MQn(SS,j) for the storage of Qn(SS,j);
k.m sets of permanent memories MQn(SC,j) for the storage of Qn(SC,j);
4k sets of RAM MWD1 (n), MWD2 (n), MWD3 (n) and MWD4(n) respectively for the storage of waveform data WDx(n), WD2 (n), WD3 (n) and WD4 (n) of the
acoustic signal S(t);
6 sets of RAM MS(0), MS' (0), MS" (0), MS(T), MS' (T) and MS" (T), or 4 sets of RAM MS(0), MS' (0), MS(T) and MS' (T) respectively for the storage of S(0), S' (0), S" (0), S(T), S' (T) and S" (T), or S(0), S' (0), S(T) and S' (T); one set of circuit for performing the
operation of :
MWD1(n) ← <MWD1(n)>+S' ((j-1)ΔT)
X<MQxn(CS,j-1)>+[jS((j-1)ΔT)
-(j-1)S(jΔT)]X<MQn(CS,j-1)>
MWD2(n) ← <MWD2(n)>+S' ((j-1)ΔT)
X<MQxn(CC,j-1)>+[jS((j-1)ΔT)
-(j-1)S(jΔT)]X<MQn(CC,j-1)>
MWD3(n) +- <MWD3(n)>+S' ((j-1)ΔT)
X<MQxn(SS,j-1)>+[jS((j-1)ΔT)
-(j-1)S(jΔT)]X<MQn(SS,j-1)>
MWD4(n) ← <MWD4(n)>+S' ((j-1)ΔT)
X<MQxn(SC,j-1)>+[jS((j-1)ΔT)
-(j-1)S(jΔT)]x<MQn(SC,j-1)> in which, k is the number of times of the highest harmonic wave obtained from the "auxiliary function" P
(x) of the equation (3) after its expansion through
Fourier series; n= 1, 2, ···, k; j=0, 1, ···, m-1; S(t) is an acoustic signal defined within [0,T]; ΔT= ;
Figure imgf000079_0001
S' ((j-1) ΔT) = [S(jΔT)-S((j-1) ΔT)]/ΔT ;
one or more A/D converters; and
one "primary derivative circuit", or one
"primary derivative circuit" and one "secondary
derivative circuit".
24. An equipment for performing the method as claimed in claim 13 or 14, including:
4k X m sets of permanet memories MC
Figure imgf000079_0002
Cn(jΔT), M SSn(jΔT), MSCCn(jΔT) and M
Figure imgf000080_0001
Sn (j Δ T) for the storage of C
Figure imgf000080_0002
Cn(jΔT), SSn(jΔT), SCCn(jΔT) and
Figure imgf000080_0003
CSn (j Δ T); or permanent memories MC
Figure imgf000080_0004
Cn(jΔT), MC
Figure imgf000080_0005
Sn(jΔT), MSCCn(jΔT) and MSCSn (j Δ T) for the storage of C
Figure imgf000080_0006
SCn (j
ΔT), C
Figure imgf000080_0007
Sn(jΔT), SCCn(jΔT) and SCSn(jΔT);
6m sets of permanent memories MUs1(jΔT), MUs2(jΔT), MUs3(jΔT), MVs1(jΔT), MVs2(jΔT) and MVs3(jΔT) for the storage of Us1, Us2, Us3, Vs1, Vs2 and Vs3 when t in expression (52)=jΔT ; or 4 sets of 4m sets of permanent memories MUc1(jΔT), MUc2(jΔT), MVc1(jΔT), MVc2(jΔT) for the storage of Uc1, Uc2, Vc1 and Vc2 when t in expression (54) = j Δ T ;
one set of computing circuit for
calculating Φ1n, Φ2 n, Φ 3 n and Φ4n in which
Φ1n=<MC
Figure imgf000080_0008
Sn(jΔT)>X<MWD1(n)>, Φ2n=<MC
Figure imgf000080_0009
SSn(jΔT)> X<MWD2(n)>or<MC
Figure imgf000080_0010
SSn(jΔT)>X<MWD2(n)>, Φ3n= MSCCn(jΔT)>X<MWD3(n)>, Φ4n=<M
Figure imgf000080_0011
CCn(jΔT)>X <MWD4(n)>or<MSCSn(jΔT)>X<MWD4(n)>;
one set of computing circuit for
calculating ψ value, in which ψ=(Hπ)3 (Φ1n+ Φ2n+ Φ3n+ Φ4 n) or
Figure imgf000080_0012
1
k
(Hπ)2 (Φ1n+Φ2n+Φ3n+Φ 4n);
Figure imgf000080_0013
1 one set of computing circuit for
calculating θ value, in which θ=<MUs1(jΔT)>X<MS(0)>+<MUs2(jΔT)>X<MS' (0)> +<MUs3(jΔT)>X<MS" (T)>or<MUc1(jΔT)>X<MS(0)> +<MUc2(jΔT)>X<MS' (0)>+<MVc1(jΔT)>X<MS(T)> +<MVc2(jΔT)>X<MS' (T)>; one set of computing circuit for calculating ψ + θ ;
one D/A converter for converting the digital signal of ψ + θ into an analog signal;
a power amplifier to amplify the output of said D/A converter; and
a speaker;
wherein said k, n, j, ΔT are same as that claimed in claim 23, and said H is a number of high absolute value.
25. An equipment which is to incorporate the equipment as claimed in claim 23 with the
equipment as claimed in claim 24.
26. A controlling device including a microprocessor for controlling the equipment as claimed in claim 25 to select the operation of the equipment as claimed in claim 23 or the operation of the equipment as claimed in claim 24.
27. The controlling device as claimed in claim 26, wherein said microprocessor is capable of performing the free setting of the initial address of MWD1 (n) ~ MWD4 (n) of the equipment as claimed in claim 23 or 24.
28. The controlling device as claimed in claim 26, wherein said microprocessor includes a display for the indication of the duration of time and the data of the initial address preset in MWD1 (n) ~MWD4(n) during the operation of the equipment as claimed in claim 23 or 24.
PCT/JP1990/000323 1990-03-13 1990-03-13 Method and apparatus for acoustic signal compression WO1991014162A1 (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0605348A2 (en) * 1992-12-30 1994-07-06 International Business Machines Corporation Method and system for speech data compression and regeneration
WO1997016818A1 (en) * 1995-10-31 1997-05-09 Motorola Inc. Method and system for compressing a speech signal using waveform approximation

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1987001851A1 (en) * 1985-09-17 1987-03-26 Compusonics Video Corporation Audio and video digital recording and playback system
WO1988001811A1 (en) * 1986-08-29 1988-03-10 Brandenburg Karl Heinz Digital coding process
WO1989003574A1 (en) * 1987-10-06 1989-04-20 Fraunhofer Gesellschaft Zur Förderung Der Angewand Digital adaptive transform coding process

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1987001851A1 (en) * 1985-09-17 1987-03-26 Compusonics Video Corporation Audio and video digital recording and playback system
WO1988001811A1 (en) * 1986-08-29 1988-03-10 Brandenburg Karl Heinz Digital coding process
WO1989003574A1 (en) * 1987-10-06 1989-04-20 Fraunhofer Gesellschaft Zur Förderung Der Angewand Digital adaptive transform coding process

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0605348A2 (en) * 1992-12-30 1994-07-06 International Business Machines Corporation Method and system for speech data compression and regeneration
EP0605348A3 (en) * 1992-12-30 1996-03-20 Ibm Method and system for speech data compression and regeneration.
WO1997016818A1 (en) * 1995-10-31 1997-05-09 Motorola Inc. Method and system for compressing a speech signal using waveform approximation

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