An FM modulator

Abstract: An FM modulator comprises a delaying means (2,4) for delaying an input signal x(n), a multiplying means (5,6) for multiplying a delayed input signal by multiplying coefficients, and an adding means (1) for adding a delayed and multiplied input signal and an input signal. The adding means (1) produces a frequency modulation signal which may be further delayed and multiplied by multiplying coefficients. At least one of the multiplying coefficients varies in its value in regard of time so that the frequency modulation signal is produced.

Description: The invention relates to an FM modulator,and more particularly to an FM modulator in which a frequency modulation signal is produced in accordance with the processing of digital signals. One of conventional FM modulators comprises a ROM (Read Only Memory) for storing amplitude values of a quarter period of a sine wave at addresses based on phases thereof, and a signal processor for controlling the reading of a signal from the ROM. The FM modulator in which a frequency modulation signal is produced in accordance with the processing of digital signals can be applied to a sound source for a musical synthesizer. A frequency modulation wave of a peak amplitude P is expressed in the equation (1), where the carrier and modulation wave are sine curves. e(t)=Psin(αt+Isinβt) In the equation (1), e is the instantaneous amplitude of the modulated carrier, α is the carrier frequency in rad/s, I is the modulation index which is the ratio of the peak deviation to the modulating frequency, and β is the modulating frequency. In operation, a phase is calculated at a sampling time t in the signal processor in accordance with the equation (1) so that a stored signal is read from the ROM at an address thereof which corresponds to the calculated phase. Such signals are sequentially read from the ROM to produce a frequency modulation wave. According to the conventional FM modulator, however, a large capacity of ROM is necessary to be included, when the interval of sampling times t is shortened. In such a case, an external ROM has been added to the signal processor because there is resulted a shortage in the storing capacity for an internal ROM of the signal processor. On the other hand, a general purpose signal processor is not generally adopted to use an external ROM. Therefore, a special purpose signal processor has been adopted in the conventional FM modulator. Further, a supplemental calculation is performed to decrease the distortion of an output wave between sampled values. A system in which the supplemental calculation is performed is required to include a large scale of a signal processor as a hardware because a high speed summation and multiplication must be made therein. Electronics, vol. 53, no. 3, 31st January 1980, pages 102-107, New York, US; M.E. HOFF et al.: "Software makes a big talker out of the 2920 microcomputer", discloses a device having all features of the preamble of claim 1. However, this device is used as a speech synthesizer and not as an FM modulator. It is an object of the invention to provide an FM modulator in which a memory for storing for instance a sine wave is not necessary to be included. It is a further object of the invention to provide an FM modulator in which a large capacity of ROM is not required. It is still a further object of the invention to provide an FM modulator in which a frequency modulation wave is produced in accordance with only the processing of digital signals in a general purpose signal processor. This object is achieved by an FM modulator as defined in claim 1; the dependent claims are related to further developments of the invention. The invention will be explained in more detail in accordance with following drawings wherein, Fig. 1 is a block diagram showing a recursive digital filter on which an FM modulator according to the invention is based, Figs. 2 to 4 are block diagrams showing FM modulators in first to third embodiments according to the invention, and Fig. 5 is a block diagram showing another recursive digital filter on which an FM modulator according to the invention is based. Before describing an FM modulator in an embodiment according to the invention, there will be explained a recursive digital filter on which the FM modulator of the invention is based. Fig. 1 shows the recursive digital filter which comprises a first adding circuit 1 to one of input terminals Ti of which an input impulse signal X(n) is applied (n=0,1,2 -----), a second adding circuit 2 for producing an output to be applied to the other input terminal of the first adding circuit 1, a first delaying circuit 3 for delaying the output W(n) of the first adding circuit 1 by a predetermined time, for instance, one clock signal, a second delaying circuit 4 for further delaying the output of the first delaying circuit 3 by a predetermined time, for instance, a further one clock signal, a multiplying circuit 5 for multiplying the output of the second delaying circuit 4 by a first multiplying coefficient "-1", a second multiplying circuit 6 for multiplying the output of the first delaying circuit 3 by a second multiplying coefficient "2cosA", and a third multiplying circuit 7 for multiplying the output of the first delaying circuit 3 by a third multiplying coefficient "sinA" to produce a fixed sine wave Y(n) at an output terminal To. The fixed sine wave Y(n) is expressed in the equation (2). Y(n)=sinAn= 1 2j (e jAn - e -jAn ) The Z-conversion Y(Z) of the equation (2) is expressed in the equation (3). Fig. 1 is a block diagram wherein the above mentioned circuits 1 to 7 are included in accordance with the equation (3). Therefore, the fixed sine wave Y(n) is produced at the output terminal To, when a predetermined level of the impulse signal X(n) is applied to the input terminal Ti. In the recursive digital filter shown in Fig. 1, the amplitude of the fixed sine wave Y(n) is decided dependent on the parameter "sinA" of the multiplying circuit 7, while the outputs of the first adding circuit 1 and first delaying circuit 3 are respectively delayed by a delaying factor Z -1 which is predetermined to delay the outputs thereof by a sampling period. In Fig. 2, there is shown an FM modulator in a first embodiment according to the invention. The FM modulator comprises all of the circuit 1 to 6 except the multiplying circuit 7 shown in Fig. 1 wherein the second multiplying coefficient "2cosA" of the second multiplying circuit 6 is replaced by "f(n)" which is a function varying in regard to "time". As a result, such an FM modulator as shown in Fig. 2 which is defined only by the denominator of the equation (3), that is to say, " 1 1-2cosA·Z -1 +Z -2 " is obtained. At the output terminal To, a digital analog (D/A) converter 8 is provided to convert a digital frequency modulation wave into an analog signal. An amplifier 9 for amplifying the output signal of the D/A converter 8 is connected thereto, and a speaker 10 is connected to the amplifier 9. Here, the relation between the function "f(n)" and output W(n) is expressed in the equation (4), W(n)+W(n-2)=f(n)·W(n-1) The output "W(n)" is assumed to be as follows in accordance with the equation (1). Substituting the equation (5) for the equation (4), The left side "L" of the equation (6) is modified as follows. If it is assumed that B<<1, there will be cosβ≒1, and sin ≒ so that the equation (7) is as follows. In the equation (8), cos( ·cos n)≒1, and sin( ·. cos n)≒βIcosβn so that the eqution (8) is as follows. Comparing the equations (9) and (6), the function "f(n)" is as follows. The eqution (10) is simplified as follows. f(n)=2(cosA+BcosCn) where In accordance with the equations (11) and (12), the constants A, B, C and P are calculated from the amplitude of the frequency modulation wave, angular frequency of a carrier thereof, modulation index thereof, and angular frequency thereof. The constants thus calculated are substituted for the constants in the following equations (13) and (14) by which the impulse signal X(n) applied to the input terminal Ti is expressed. (a) n=0 X(0)=Psin(A+ BsinC CsinA ) (b) n≠0 X(n)=0 In accordance with the equation (11), further, the multiplying coefficient "f(n)" is calculated at the time nT (T is the period of sampling time). In operation , at the time nT of "0" (n=0), an impulse signal X(0) calculated in the equation (13) is applied to the input terminal Ti so that a frequency modulation wave W(0)=Psin(α+Isinβ) is produced at the ouput terminal To in accordance with the equation(5). At the time T, 2T, 3T ----- (n=1, 2, 3 -----), impulse signals X(1), X(2), X(3) ----- of "0" based on the equation (14) are sequentially applied to the input terminal Ti so that frequency modulation waves W(1)=sin(2α+Isin2β), W(2)=sin(3α+Isin3β), W(3)=sin(4α +Isin4β) ----- are sequentially produced at the output terminal To. Correspondingly, the multiplying coefficient "f(n)" is changed as follows. f(0)=2(cosA+B) f(1)=2(cosA+BcosC) f(2)=2(cosA+Bcos2C) f(3)=2(cosA+Bcos3C) The frequency modulation waves are supplied to the D/A converter 8 from which the converted analog signals are then supplied to the amplifier 9. The analog signals amplified in the amplifier 9 are supplied to the speaker 10 thereby producing sound. The FM modulator shown in Fig.2 can be included in a general purpose signal processor because the calculation, and generation of an impulse as described above can be easily performed therein. In addition, a recursive digital filter can be provided in a general purpose signal processor. Further, a large capacity of ROM is unnecessary to be included therein. Fig. 3 shows an FM modulator in a second embodiment according to the invention wherein a multiplying circuit 11 having a multiplying coefficient "S" is added to the FM modulator in the first embodiment. In operation, the output of the delaying circuit 3 is partly supplied to the multiplying circuit 11 producing a frequency modulation wave W(n). The freqnency modulation wave W(n) to be sampled at nT (=0, T, 2T -----) is calculated as follows. At the time nT of "0" (n=0), an impulse having an amplitude of "1" is applied to the input terminal Ti so that a following output is produced at the output terminal To. W(0)=0 The difference of the first and second embodiment is that the amplitude of the frequency modulation wave is calculated in the first embodiment by the amplitude of the impulse applied to the input terminal Ti, while it is calculated in the second embodiment by the multiplying coefficient of the multiplying circuit 11. Fig. 4 shows an FM modulator of a third embodiment according to the invention wherein a multiplying circuit 12 having a multiplying coefficient of "-f(n)/2" and adding circuit 13 for adding outputs of the first delaying circuit 3 and a multiplying circuit 12 are added to the FM modulator of the first embodiment. In operation, the output of the first delaying circuti 3 is partly supplied to the multiplying circuit 12, and then outputs of the first adding circuit 1 and multiplying circuit 12 are added in the adding circuit 13 to produce a frequeucy modulation signal W(n) at the output terminal To. Fig. 5 shows a recursive digital filter on which the FM modulator of the third embodiment is based wherein like parts are indicated by like reference numerals. A fixed cosine wave Y(n) to be sampled at the time nT is produced at the output terminal To as follows. Y(n)=cosAn The Z-conversion Y(z) of the equation (16) is expressed as follows. Y(z) = 1-cosA·Z -1 1-2cosA·Z -1 +Z -2 The recursive digital filter shown in Fig. 5 is obtained in accordance with the equations (16) and (17), and further comprises an adding circuit 13 for adding outputs of the first adding circuit 1 and multiplying circuit 7 in addition to the construction of the recursive digital filter shown in Fig. 1, provided that the multiplying coefficient of the multiplying circuit 7 is changed from "sinA" to "-cosA". In operation, at the time nT of "0" (n=0), a cosine wave Y(n) a sampled, the value of which is expressed by the equation (16), is produced at the output terminal To, when an impulse signal X(n), the amplitude of which is "1", is applied to the input terminal Ti, that is to say, Y(0)=1. In the FM modulator of the third embodiment in Fig. 4, the multiplying circuits 6 and 12 having multiplying coefficients "f(n)" and "-f(n)/2" respectively are provided in place of the multiplying circuit 6 and 7 in Fig. 5. In operation, at the time nT of "0" (n=0), a sample value W(0)≒1 is obtained in accordance with the equation (18), when an impulse signal X(0) of "1" is applied to the input terminal Ti. As clearly understood from the equation (18), the signal W(n) is a frequency modulation wave to be expressed by a cosine wave. As explained before, the amplitudes of the frequency modulation waves are calculated by the amplitude of the signal X(n) applied to the input terminal Ti in the first embodiment, and by the multiplying coefficient "s" of the multiplying circuit in the second embodiment. In the third embodiment, however, the amplitude of the frequency modulation wave is approximately equal to the amplitude of the impulse signal X(n) applied to the input terminal Ti.

Claims: An FM modulator comprising first adding means (1) for adding an input signal and a signal which is fed back, first delaying means (3) for delaying the output signal from said first adding means (1) by a predetermined time, first multiplying means (6) for multiplying the output signal from the first delaying means (3) by a multiplying coefficient, which varies in its value in regard to time, second delaying means (4) for further delaying the output signal of said first delaying means (3) by a predetermined time, second multiplying means (5) for multiplying the output signal of said second delaying means (4) by a multiplying coefficient, characterized in that a second adding means (2) is provided for adding the output signals of the first and second multiplying means to produce said signal which is fed back, that said input signal is an impulse signal, that said muliplying coefficient of said first multiplying means varying in regard to time is changed according to a cosine function and that said multiplying coefficient of said second multiplying means has a fixed value of "-1", whereby said first adding means (1) produces a frequency modulation signal. An FM modulator as claimed in claim 1, characterized by a third multiplying means (11) for multiplying the output signal of the first delaying means wherein the frequency modulation signal is produced by said third multiplying means, not by said first adding means. An FM modulator as claimed in claim 2, characterized in that said multiplying coefficient of said third multiplying means has a fixed value. An FM modulator as claimed in claim 2, characterized in that said multiplying coefficient of said third multiplying means varies in its value in regard to time. An FM modulator as claimed in claim 3 or 4, characterized by a third adding means (13) for adding the output signals of said first adding means (1) and said third multiplying means (12), wherein said frequeny modulation signal is produced by said third adding means, not by said third multiplying means (12).

Inventors: NAKAYAMA KENJI, YAZAWA AKIRA, NAKAYAMA, KENJI, YAZAWA, AKIRA, NAKAYAMA, KENJI C/O NEC CORPORATION, YAZAWA, AKIRA C/O NEC CORPORATION
Applicants: NIPPON ELECTRIC CO, NEC CORPORATION
Application year: 1987
Main classification: H03C3
IPC codes: H03C3, H03F3