JPH05165478A - Sound source device - Google Patents

Abstract

PURPOSE:To obtain an intermediate pitch between two musical sounds signals and to obtain intermediate timbre between both signals. CONSTITUTION:A waveform A is read from waveform memories 2 and 4 storing the plural kinds of waveforms in plural cycles by a two-phase counter 17, waveform number counters 26 and 30 and waveform number tables 10 and 12 while maintaining the formant of the waveform A at a pitch different from that of the waveform A. A waveform B differring the formant from that of the waveform A is read from waveform memories 6 and 8 by the two-phase counter 17, waveform number counters 34 and 38 and waveform number tables 14 and 16 at a pitch different from that of the waveform A by one octave while maintaining the formant of the waveform B at the different pitch as mentioned above. These two read waveforms are weighted by multipliers 98 and added by an adder 102.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sound source device used in, for example, a tone generator or a sound effect generator.

[0002]

2. Description of the Related Art Conventionally, as a sound source device, for example, an input waveform of a certain pitch is sampled at a predetermined sampling period, stored in a storage means, and read from this storage means at the same speed as at the time of sampling. It is known that a musical tone of the same pitch as the input waveform is generated.However, in the case of generating a musical tone of a pitch different from the input waveform in such a device, it is stored in the storage unit at a speed different from that at the time of sampling. It is being read out.

However, in this case, the read formant of the waveform is moved from the formant of the input waveform, resulting in an unnatural tone. A filter is used when the formant does not move, that is, a fixed formant tone is obtained. However, when a desired formant is obtained by the filter, the configuration and scale of the filter are complicated and large.

In addition to the above, there is also one that obtains a fixed formant tone, for example, as disclosed in Japanese Patent Laid-Open No. 62-65098. In this method, phonemes of the input musical tone signal are sequentially cut out and repeatedly generated in a cycle different from the pitch of the input musical tone signal. While maintaining the formant of the input musical tone signal, a pitch different from the input musical tone signal is maintained. Is the one that produces the musical sound of.

[0005]

However, in such a device, a so-called vocoder which merely reproduces the formant change of the input voice signal as it is, and which can control the formant of the voice signal such as a tone signal according to the control operation. Was not.

[0006]

In order to achieve the above object, the present invention provides a storage means for storing a plurality of types of waveforms of a plurality of cycles, and at least two types of waveforms as pitches of these original waveforms. Is a reading means for reading from the storage means so that the formants of the original waveforms are maintained at different pitches and the pitches are the same, and an adding means for weighting the read waveforms and adding the weighted waveforms. , Are provided.

[0007]

According to the present invention, at least two kinds of waveforms are read from the storage means by the reading means. At that time, the two types of waveforms are read with a pitch different from the pitch of each original waveform, and the formant of the original waveform is maintained, that is, with a fixed formant. Then, the waveforms of the same pitch read by these fixed formants are weighted and added.

[0008]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In this embodiment, the present invention is applied to a tone generator of a musical tone generating device, and has waveform memories 2, 4, 6 and 8 as shown in FIG. The waveform memory 2 stores a plurality of types of waveforms, for example, waveforms A, B, C, ... Sampled at predetermined sampling frequencies, respectively, for a plurality of cycles. Similarly, waveform waveforms A, B, C, etc. sampled at predetermined sampling frequencies are stored in the other waveform memories 4, 6, 8 for a plurality of cycles.

The reading of each sampled value from the waveform memories 2, 4, 6, 8 is performed by the waveform number table 10,
The adder 18, 20, 22, 24 adds the start address of the predetermined waveform number supplied from 12, 14, 16 and the phase 1 signal and the phase 2 signal, which are supplied from the two-phase counter 17 described later and are sequentially increased. It is performed according to the address signal obtained by Multipliers 68, 70, 72,
Since the operation of 74 will be described later, the read speed coefficients RA and R will be described below.
It is assumed that B is inputting 1.

The various waveforms stored in the waveform memories 2, 4, 6 and 8 are assigned waveform numbers for each cycle, as shown in FIGS. 8 (a) and 9 (a). Each waveform number table 10, 12, 14, 16 converts this waveform number into the start address of each cycle.

The waveform number a and the count value of the waveform number counter 26, which will be described later, are added to the waveform number table 10 by the adder 28, which is input as a waveform number. The information a and the count value of the waveform number counter 30 added by the adder 32 are input as a waveform number, and the waveform information b and the count value of the waveform number counter 34 are input to the waveform number table 14. The one added by the adder 36 is input as the waveform number, and the one added by the adder 40 with the waveform information b and the count value of the waveform number counter 38 is input as the waveform number into the waveform number table 16. It

The waveform number counter 26 generates sound generation start information, a sound generation start data selection signal, an initial value, and a pitch coefficient PA.
And a pulse value C1 from the two-phase counter 17 to generate a count value, and the waveform number counter 30 generates sound generation start information, a sound generation start data selection signal, an initial value, a pitch coefficient PA, and a pulse from the two-phase counter 17. A count value is generated based on the signal C2, and the waveform number counter 3
4 generates a count value based on the sound generation start information, the sound generation start data selection signal, the initial value, the pitch coefficient PB, and the pulse signal C1 from the two-phase counter 17, and the waveform number counter 38 generates the sound generation start information and sound. A count value is generated based on the start data selection signal, the initial value, the pitch coefficient PB, and the pulse signal C2 of the two-phase counter 17. However, in FIG. 1, the illustration of the initial value and the tone generation start data selection signal is omitted.

The two-phase counter 17 has a phase 1 signal, a phase 2 signal, and a pulse signal C based on the frequency information F generated by pressing a key on the keyboard, for example.
1 and C2 are generated, the details of which are shown in FIG. Two
The phase counter 17 has an accumulator 42, and this accumulator 42
Is for accumulating the frequency information F each time a sampling signal having the same frequency as that used for sampling the waveform stored in the waveform memories 2, 4, 6, 8 is inputted. The instrument 42 is configured to generate a carry-out signal for each cycle corresponding to the key depression frequency, as shown in (a), following the tone generation start data selection signal and tone generation start information of FIG. ing. This carry-out signal is input to the frequency divider 44 set by the tone generation start information and is frequency-divided into 1/2, and then the carry-out signals shown in FIGS.
As shown in, the Q signal and the inverted XQ signal are generated.

The Q signal is differentiated by the differentiating circuit 46, and is shown in FIG.
As shown in (d), it is a pulse signal C1. Also, X
The Q signal is differentiated by the differentiating circuit 48 to be a pulse signal C2 as shown in FIG. Pulse signal C1, C2
As is apparent from FIGS. 3D and 3E, both have a cycle of twice the key pressing frequency, and the phase of the pulse signal C2 deviates from the pulse signal C1 by one cycle of the key pressing frequency. Is what

The two-phase counter 17 has counters 50 and 52 whose count value is incremented by 1 each time a sampling signal is input. The counter 50 is reset each time the pulse signal C1 is generated. , Counter 52
Are reset each time the pulse signal C2 is generated.
The sampling signal input to the counter 52 is
In the AND circuit 47, the output signal of the RS flip-flop 41 is interrupted, the flip-flop 41 is reset by the sound generation start information, and is set by the pulse signal C2. Therefore, the counter 52 is from the sound generation start information to the first pulse signal C2. The counting operation will be stopped. Therefore, the count value of the counter 50 is the phase1 signal, and the count value of the counter 52 is the phase2 signal. As is clear from FIGS. 3 (f) and 3 (g), phas
The e1 signal and the phase2 signal are out of phase by one cycle of the key pressing frequency.

The waveform number counter 26, as shown in FIG. 4, has a multiplier 54 that multiplies the supplied pitch coefficient PA by M times. In this specification, the period of the pulse signals C1 and C2 is doubled with respect to the period of the pitch to be generated as described with reference to FIG.
Is 2. Note that M may be designed to have another value. This pitch coefficient PA is also generated by pressing the keyboard. The output of the multiplier 54 is supplied to one input of the adder 58. The output of the flip-flop 62 described later is supplied to the other input of the adder 58.

The output of the adder 58 is supplied to the subtractor 64, and the subtractor 64 subtracts the value obtained by adding 1 to the final waveform number of the waveform to be read from the output of the adder 58. This subtracted value is the changeover switch 66.
Is supplied to one contact 66a of the
The output of the adder 58 is supplied as it is to the other contact 66b. The contact 66 c of the changeover switch 66 is connected to the contact 65 a of the changeover switch 65. The changeover switch 66 is changed over according to the output of the comparator 68. While the output of the adder 58 is smaller than the value obtained by adding 1 to the final waveform number, the comparator 68
The contact 66c of the changeover switch 66 is switched to the contact 66b side, and when the output of the adder 58 becomes equal to or more than the value obtained by adding 1 to the final waveform number, the contact 66c is switched to the contact 66a side. The other contact 65 of the changeover switch 65
In b, the initial value of the waveform number is input, and as shown in FIG.
When the sound generation start data selection signal shown in is at high level,
The contact 65c is connected to the contact 65b, and is otherwise connected to the contact 65a as shown. The contactor 65c is connected to the input side of the flip-flop 62. The flip-flop 62 is a two-phase counter 1
The input data is held each time the pulse signal C1 supplied from 7 and the tone generation start information are input.

Therefore, for example, assuming that the initial value is 0, the pitch coefficient PA is 1.5, and the final waveform number is 4, when the sounding start information is supplied, the contactor 65c of the changeover switch 65 contacts the contact 65b. Since it is connected, the initial value 0 is stored in the flip-flop 62. After that, since the contact 65c of the changeover switch 65 is connected to the contact 65a, the pitch coefficient R is added to the output of the flip-flop 62 in the adder 58 every time the pulse signal C1 is supplied.
The value 3 that is M times (twice) A is accumulated and stored in the flip-flop 62. Therefore, the flip-flop 6
The output of 2 changes from 0 to 3.

Then, when the output of the adder 58 becomes 6, which is larger than the value 5 obtained by adding 1 to the final waveform number 4, the comparator 68 causes the contact 66c of the changeover switch 66 to move. Switching to the contact 66a side, the output of the subtracter 64 at that time (1 obtained by subtracting the value 5 obtained by adding 1 to the final waveform number from the output 6 of the adder 58) is stored in the flip-flop 62. Hereinafter, the output of the flip-flop 62 changes to 1, 4, 2, 0, ... And it is the integer part that is output as the count value. The reason why the value of the waveform number counter 26 is changed is to change the formant of the waveform read from the waveform memory 2 in the same manner as the time. The other waveform number counters 34 are similarly constructed.

The waveform number counter 30 is constructed as shown in FIG. Although it is almost the same as that of FIG. 4, a pulse signal C2 is generated from the sound generation start information shown in FIG.
A configuration for outputting the waveform number count value corresponding to the delay part up to is added. The initial value is stored in the flip-flop 62 in the same manner as in FIG. 4 by the sound generation start data selection signal and the sound generation start information. At the same time, the RS flip-flop 59 is set, the contact 60c of the changeover switch 60 is connected to the contact 60b, and 1 is input to one input terminal of the multiplier 54. Therefore, the sound generation start data selection signal and sound generation start information are lost, and the first pulse signal C2
The value obtained by adding the pitch coefficient PA and the initial value stored in the flip-flop 62 is input to the flip-flop 62 before is input. Therefore, the first pulse signal C
At 2, the value is stored in the flip-flop 62. Then, thereafter, the value of M times the pitch coefficient PA is sequentially added to the flip-flop 62 as in FIG. The other waveform number counters 38 are similarly constructed. Therefore, similarly to the above, the initial value is 0 and the pitch coefficient PA is 1.5.
When the final waveform number is 4, the output value from the sound generation start information to the pulse signal C2 is 0, and the count values below are 1.5, 4.5, 2.5 ... For each pulse signal C2.
And changes. The output values from the tone generation start information to the pulse signal C2 are meaningless data and are not actually used. However, what is actually output is these integer parts 1, 4, 2, ...
Is. Further, if the waveform number counter 34 is supplied with an initial value of 0, a pitch coefficient PB (also generated by pressing the keyboard) 0.75, and a final waveform number 5, the waveform number counter 34 is supplied. The count value of 0, 1.5, 3.0, 4.5, 5.0 ...
・, And 0, 1, 3, 4, 0, ... Are actually output. Similarly, the waveform number counter 38 is supplied with the initial value of 0, the pitch coefficient of 0.75, and the final waveform number of 5, and the pitch coefficient of 0.75. Therefore, the count value output following the initial value of 0 is 0.75, 2.25, 3.
75, 5.25, 0.75 ... And 0, 2, 3, 5, 0 ... are actually output. In addition, the final waveform number, when reading the waveform from the waveform memory,
Make settings so that different types of waveforms are not read. Also, in the above description, when the final waveform number is exceeded,
Although it returned to the beginning of the waveform number, the pulse signals C1 and C2 to the flip-flop 62 were output by the comparator 68.
May be blocked so that the change in the waveform number is not repeated.

The waveform number counter 26 has a pulse signal C.
Since the counting operation is performed by 1 and the counting operation is performed by the pulse signal C2 in the waveform number counter 30, there is a time lag in the counting value between the waveform number counters 26 and 30, which corresponds to one cycle of the key pressing frequency.
Similarly, the waveform number counters 34 and 38 also have a time lag corresponding to one cycle of the key pressing frequency.

The count values of the waveform number counters 26, 30, 34, 38 thus generated are added to the waveform information a, b in this embodiment by the adders 28, 32, 36, 40, respectively. The added value is supplied to the waveform number tables 10, 12, 14 and 16, and the leading value of the address for the waveform memory is given. The waveform information a and b are also generated by pressing the keyboard, the waveform information a is for the waveform memories 2 and 4, and the waveform information b is for the waveform memories 6 and 8.
Waveform number 0, if waveform A is stored in waveform numbers 0 to 6, waveform B is waveform number 7
If stored from 1 to 13, 7 is represented. The waveform A
For example, the pitches of B and B are different by one octave, and the formants thereof are also different.

The above-mentioned pitch coefficient PA represents how many times the cycle of the waveform A is read when the waveform A is read out as the pitch of the depressed key on the keyboard. Then, since it is read at a period of 3/2 of the waveform A, it is set to 1.5. Similarly, when the waveform B is read as the pitch of the key pressed on the keyboard, the period is the waveform B. It is expressed as a multiple of the cycle of, and is 0.75 because it is read at the cycle of 3/4 of the waveform B in this embodiment.

Therefore, when the waveform memories 2, 4, 6, and 8 store the waveforms A of the waveform numbers 0 to 6 as shown in FIG. 8A, the sound generation start information and the pulse signal C1 are the waveform numbers. When supplied to the counter 26, the start address of the waveform number 0 is first supplied from the waveform number table 10 to the adder 18, and the adder 18 receives the sampling signal from the two-phase counter 17 over two cycles of the key pressing frequency. Since the phase1 signal whose value increases in the same cycle as the above is supplied and the signal of the adder 18 is supplied to the waveform memory 2 as the address signal, the waveforms of waveform numbers 0 to 2 are supplied as shown in FIG. 8B. A is read out. Next, when the pulse signal C1 is generated, the waveform counter 26
Since the value of is 3 and the waveform information A is 0, 3 is supplied to the waveform number table 10, and the adder 18
Is given the start address of waveform number 3, and then p
Waveform numbers 3 to 5 as the hase1 signal increases
Waveform A is read out.

Similarly, when the pulse signal C2 generated after being delayed by one cycle of the key pressing frequency from the pulse signal C1 and the sound generation start information are supplied to the waveform number counter 30, the count value of the waveform number counter 30 is as described above. Since the waveform information A is 0 and the waveform information A is 0, the start address of the waveform number 1 is supplied from the waveform number table 12 to the adder 20, and as shown in FIG. The waveform A having waveform numbers 1 to 3 is read out. Next, when the pulse signal C2 is generated, the waveforms A having the waveform numbers 4 to 6 are read out in the same manner.

When the waveform B is stored in the waveform numbers 7 to 13 of the waveform memories 2, 4, 6, and 8 as shown in FIG. 9A, 7 is added as the waveform information b to the adder 3
6 and the tone generation start information and the pulse signal C1 are supplied to the waveform number counter 34, the count value becomes 0 as described above, and the waveform number table 14
Supplies the start address of the waveform number 7 to the adder 22, and the phase1 signal is also supplied to the adder 22, so that the next pulse signal C1 is generated.
From the waveform memory 6, half cycles of the waveform number 7 and the waveform 8 are read out as shown in FIG. 9B. Then, when the pulse signal C1 is generated next time, the waveform number counter 34
Since the count value of is 1, the waveform number counter 1
4 supplies the start address of the waveform number 8 to the adder 22, and thereafter one cycle of the waveform number 8 and the half cycle of the waveform number 9 are similarly read out.

Similarly, when the pulse signal C2 and the tone generation start information are supplied to the waveform number counter 38, the count value of the waveform number counter 38 becomes 0, and this and the waveform information b are supplied to the adder 40, The waveform number table 16 supplies the start address of the waveform number 0 to the adder 24. Since the phase 2 signal is also supplied to the adder 40, one cycle of the waveform number 7 and a half cycle of the waveform number 8 are read out as shown in FIG. 9D. When the pulse signal C2 is generated next time, the count value of the waveform number counter 38 becomes 2. Therefore, the waveform number table 16 supplies the leading address of the waveform number 9 to the waveform memory 8, and the waveform number 9 changes according to the change of the phase2 signal. 1 cycle and half cycle of waveform number 10 are read out.

8 (b) and 8 (d) obtained as described above.
The waveform obtained by adding the waveforms of is read at the same cycle as the cycle in which a part of the waveform A is cut out and sampled, and is repeated at the pitch of the pitch at which the read waveform is generated. It is possible to obtain a waveform different from the original pitch of the waveform A, which is the pitch of the repeating cycle, while maintaining the formant of the waveform A. Similarly, as for the waveform B, the waveform obtained by adding the waveforms of (b) and (d) of FIG. 9 retains the formant of the original waveform B and maintains the original pitch of the original waveform B at the pitch of the repeating cycle. Can obtain different waveforms.

In this embodiment, the adders 18, 2
0, 22, 24 supplied to the phase1 signal, pha
The se2 signal is multiplied by the read speed coefficients RA and RB by the multipliers 68, 70, 72 and 74, and then the respective adders 1
It is supplied to 8, 20, 22, and 24. Read speed coefficient R
A and RB are used when it is desired to change the read formant of the waveform, and are set to 1 when it is not necessary to change.

According to the above, the formant does not move, but a waveform discontinuity is generated by cutting out a part of the waveform. For example, FIGS. 9B and 9D.

In order to eliminate such waveform discontinuity,
The waveforms read from the waveform memories 2, 4, 6, and 8 are multiplied by the window function from the cosine waveform generation circuit 76. The cosine waveform generation circuit 76 is (1/2) (1 + c
osX) has cosine tables 78 and 80 that store the curves generated when X changes from −π to π as window function signals. Frequency information F and proportional constant K1 are added to the phase1 and phase2 signals. When the results of multiplication by the multipliers 82 and 84 are supplied to the cosine tables 78 and 80 as address signals,
The read signal is the window function signal cos1 signal, sos
There are two signals.

When the phase 1 signal and the phase 2 signal are simply supplied to the cosine tables 78 and 80 as address signals, the final value of the address changes according to the pitch. That is, the phase1 signal and the phase2 signal are
Since the value increases by 1 every sampling period, if the frequency information F is changed and the pitch is changed, ph
The number of increment operations for obtaining the phase1 and phase2 signals changes, and as a result, phase1 and ph
The peak value of the as2 signal changes in inverse proportion to the frequency, and the final value of the address supplied to the cosine tables 78 and 80 changes according to the pitch. In order to prevent such a situation and make the final value of the address always the same, the frequency information F
And the proportional constant K1.

The window function cos1 generated in this way
Is multiplied by the waveform read from the waveform memory 2 in the multiplier 86, and a waveform as shown in FIG. 8C is obtained. Similarly, the window function cos2 is multiplied by the waveform read from the waveform memory 4 in the multiplier 90, and the result is shown in FIG.
A waveform as shown in is obtained.

Further, the window function cos1 is multiplied by the waveform read from the waveform memory 6 in the multiplier 88 to obtain a waveform as shown in FIG. 9 (c). Similarly, the window function c
Os2 is multiplied by the waveform read from the waveform memory 8 in the multiplier 92 to obtain a waveform as shown in FIG. 9 (e).

The two waveforms thus read out from the waveform memories 2 and 4 and multiplied by the window function are added by the adder 94, similarly read out from the waveform memories 6 and 8 and multiplied by the window function. The two generated waveforms are added by the adder 96.

In order to eliminate the discontinuity, the output of the adder 94 is read out from the waveform memories 2 and 4 with a pitch corresponding to the key-pressing frequency shifted by one cycle of the key-pressing frequency. It is a product of the window functions cos1 and cos2, and the formant is the same as that of the waveform A. The output of the adder 96 is read out from the waveform memories 6 and 8 with a pitch corresponding to the key pressing frequency shifted from the waveform memories 6 and 8 by one cycle of the key pressing frequency. It is obtained by multiplying the window functions cos1 and cos2 in order to eliminate continuity, and the formant is the same as that of the waveform B. Thus, the outputs of the adders 94 and 96 have the same pitch and the same formant as the original waveform.

The output of the adder 94 is multiplied by the weighting factor W1 in the multiplier 98, and similarly, the output of the adder 96 is multiplied by the weighting factor 2 in the multiplier 100. These multipliers 98,
The outputs of 100 are added in the adder 102 and output. Here, the weighting factor W1 is a value proportional to the pitch (key pressing frequency) at the time of the pitch of the waveform A, 0 at the pitch of the waveform B, and at the intermediate pitch. The weight coefficient W2 is 0 when the pitch of the waveform A is set, and the weight B is set to the waveform B.
Is set to 1 for the pitch of, and a value proportional to the pitch at that time for the middle pitch. Therefore, it is possible to obtain a tone-free musical tone that is amplitude-modulated when different waveform pitches are added, and a natural crossfade can be realized.

In the above embodiment, the present invention is applied to the tone generator of the musical sound generator, but the present invention can be applied to the tone generator of the sound effect generator. Further, in the above embodiment, the count values of the waveform number counters 26, 30, 34, 38 are changed similarly to the temporal change of the waveform formant. However, there is almost no temporal change of the waveform formant. When the pitch is not changed, the pitch coefficients PA, PB supplied to the waveform number counters 26, 30, 34, 38 can be fixed, and the configuration of the waveform number counters 26, 30, 34, 38 can be simplified. can do. In addition, the waveform number counters 26, 30,
The count values of 34 and 38 may be changed according to an operator such as a pedal. Also, in the above example,
Although the cosine waveform is used as the window function, other known window functions may be used. Further, in the above embodiment, the weighting factors W1 and W2 have been shown to change linearly according to the pitch at that time, but those that change curvedly may be used. In the above embodiment, the waveform memory 2,
Although 4, 6, and 8 are provided, if the time-division reading is performed, only one waveform memory needs to be provided.

[0039]

As described above, according to the present invention, the formants of the respective original waveforms are maintained so that at least two types of waveforms have the same pitch with a pitch different from the pitch of these original waveforms. Then, the waveforms read out from the storage means are weighted, and the waveforms thus read are weighted before being added. Therefore, the amplitude modulation feeling that occurs when the waveforms with different pitches are added does not occur, and two types are obtained. It is possible to obtain an intermediate tone color of the waveform.

[Brief description of drawings]

FIG. 1 is a block diagram of an embodiment of a sound source device according to the present invention.

FIG. 2 is a block diagram of a two-phase counter used in the embodiment.

3 is a waveform diagram of the two-phase counter of FIG.

FIG. 4 is a waveform number counter 26 used in the embodiment.
It is a block diagram of.

FIG. 5 is a waveform number counter 30 used in the embodiment.
It is a block diagram of.

FIG. 6 is a block diagram of a cosine waveform generation circuit used in the same embodiment.

7 is a waveform diagram of the cosine waveform generation circuit of FIG.

FIG. 8 is a diagram showing a processing state of waveforms read from the waveform memories 2 and 4 of the same embodiment.

FIG. 9 is a diagram showing a processing state of a waveform read from the waveform memories 6 and 8 of the same embodiment.

[Explanation of symbols]

 2 4 6 8 Waveform memory 10 12 14 16 Waveform number table 26 30 34 38 Waveform number counter 98 100 Multiplier

Claims (1)

[Claims] 1. A storage means for storing a plurality of types of waveforms having a plurality of periods, and at least two types of waveforms having the same pitch while maintaining the formant of each original waveform at a pitch different from the pitch of these original waveforms. A sound source device comprising: a reading means for reading from the storage means so as to be high; and an adding means for weighting the read waveforms and then adding the weighted waveforms.