Circuit for generating periodic function

Details Circuit for generating periodic function Circuit for generating periodic function

2000-01-21

2003-02-11

Malzahn, David H. (Department: 2124)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

C708S276000

Reexamination Certificate

active

06519619

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a circuit for generating a periodic function, and more particularly to a circuit for digitally generating a periodic function in a signal processing circuit which is required to generate a periodic function, such as an image signal processing circuit and an aural signal processing circuit.
2. Description of the Related Art
Digital ROM table conversion is well known in the art as a method of generating a periodic function such as a sine wave. When a sine wave is to be generated, a sine wave function is stored in a function ROM in the range of a period, and addresses of the function ROM is periodically controlled. As a result, there can be generated a sine wave having a desired frequency.
For instance, Japanese Patent Publication No. 60-37486 has suggests a sine wave generator which stores a sine wave function in the range of a phase associated with one-fourth of a period. Values of the sine wave function in the rest of a phase are obtained by adding an external circuit.
Japanese Patent Publication No. 7-43620 suggests a circuit for generating a periodic function to make an improvement in the above-mentioned sine wave generator. The suggested circuit is designed to be able to generate a sine wave function in a period only by storing a sine wave function in a function ROM in a degree associated with one-fourth of a period, ensuring that a capacity of the function ROM is made four times smaller.
The circuit suggested in Japanese Patent Publication No. 7-43620 is illustrated in FIG.
1
.
As illustrated in
FIG. 1
, the circuit is comprised of an address counter
1
and a function ROM
2
. The address counter
1
is comprised of a first register
3
, an adder
4
, an accumulator
5
, a control circuit
14
for inverting a bit, and a second register
7
.
FIG. 2
is a table showing an operation of the circuit.
FIG. 3A
is a graph showing a relation between addresses of the function ROM
2
and amplitudes to be stored in the function ROM
2
, found when a sine wave function is to be stored in the function ROM
2
, and
FIG. 3B
shows waveforms of outputs transmitted from the function ROM
2
in the case that a numeral of
2
is stored in the first register
3
.
The adder
4
adds a value stored in the first register
3
to a value stored in the accumulator
5
, and transmits the sum to the accumulator
5
. The accumulator
5
latches the received sum at a sampling period.
The control circuit
14
receives a first bit output transmitted from the adder
4
. Herein, the first bit output is a bit output other than a second uppermost bit among bit outputs transmitted from the adder
4
. The control circuit
14
inverts the received first bit output or allows the received first bit output to pass therethrough without inverted, in accordance with a second uppermost bit transmitted from the adder
4
. An output transmitted from the control circuit
14
is latched by the second register
7
at a sampling period.
The function ROM
2
stores therein a periodic function value associated with one-fourth of a period thereof. The periodic function value stored in the function ROM
2
can be read out by providing a value stored in the second register
7
which value has been operated by the address counter
1
, to the function ROM
2
as an address.
A combination of an output transmitted from the function ROM
2
and a uppermost bit transmitted from the accumulator
5
as an encoded bit constitutes an output of the periodic function. Thus, it is possible to generate a periodic function by a period by virtue of a capacity of a function ROM, associated with one-fourth of a period of the function ROM.
A function transmitted from the function ROM
2
in the above-mentioned circuit would have a frequency F as defined below, under the following conditions.
Sampling frequency: fs
Address of the function ROM
2
: p bits
Value stored in the first register: n
The frequency F is defined as follows.
F=n×fs
/2
(p+2)
  (
A
)
Thus, it would be possible to set the output frequency F to be equal to the sampling frequency fs multiplied by n/2
(p+2)
, by varying the value n. In other words, the equation (A) indicates that even if an actual address of the function ROM
2
has p bits when a periodic function is to be generated, reading out the function ROM
2
is equivalent to reading out a function ROM having an address of (p+2) bits, and that a periodic function is generated by a period by virtue of a capacity of the function ROM
2
, associated with one-fourth of a period of the function ROM
2
.
Hereinbelow is analyzed storage of an amplitude of a periodic function into the function ROM
2
in the conventional circuit. In a first example, a sine wave function is selected as a periodic function. It is assumed that a minimum address in the function ROM
2
is defined as sin 0°, a maximum address in the function ROM
2
is defined as sin 90°, other addresses are defined as addresses obtained by equally dicretizing addresses ranging from the minimum address to the maximum, to thereby store a sine wave function having a quantized amplitude, into the function ROM
2
.
Assuming that an address of the function ROM
2
has p bits, and that an address value of the function ROM
2
is equal to m defined as 0≦m≦2
P
−1 where m is a positive integer, a sine wave function S associated with one-fourth of a period, to be stored in the function ROM
2
is defined as follows.
S
=sin(90°×(
m
/(2
P
−1)))
If an amplitude is quantized in q bits, a maximum amplitude is defined as (2
q
−1). Hence, a value V to be stored in the function ROM
2
is defined as follows.
V
=(2
q
−1)×sin(90°×(
m
/(2
P
−1)))
For instance, assuming that p is equal to two (p=2) and q is equal to five (q=5), since m is equal to 0, 1, 2 or 3, values of a sine wave function to be stored in the function ROM
2
are calculated as follows.
m
=0:31×sin 0°=0
m
=1:31×sin 30°≈16
m
=2:31×sin 60°≈27
m
=3:31×sin 90°=31
These calculation results are shown in FIG.
4
A.
In the conventional circuit illustrated in
FIG. 1
, the control circuit
14
inverts an address to be input into the function ROM
2
, or allows the address to pass therethrough without inverting. Hence, when a value of 1 is stored in the first register
3
(n=1), as shown in
FIG. 4B
, each of the maximum address (m=3) and the minimum address (m=0) in the function ROM
2
is successively twice read out. This causes a problem that a resultant periodic function includes distortion in a frequency plane.
Then, a second example is explained hereinbelow. The second example has an object to prevent the above-mentioned distortion in a frequency plane. Considering a turning point in addresses including a maximum address and a minimum address appearing subsequently to the maximum address in the function ROM
2
, it is assumed that values of a sine wave function are to be stored into the function ROM
2
at a phase angle having an offset relative to a sampling clock by a half period of the sampling clock. Thus, zero cross points in a resultant sine wave are located at a center between sampling clocks between second and third quadrants and also between fourth and first quadrants. As a result, the above-mentioned distortion in a frequency plane would not be generated.
Assuming that an address of the function ROM
2
has p bits, and that an address value of the function ROM
2
is equal to m defined as 0≦m≦2
P
−1 where m is a positive integer, since an offset phase angle associated with a half period of a sampling clock is defined as (90°/2
P
)/2, a sine wave function S associated with one-fourth of a period, to be stored in the function ROM
2
is defined as follows.
S
=sin(90°×((2
m
+1)/2
P+1
))
If an amplitude is quantized in q bits, a maximum amplitude is defined as (2
q
−1). Hence, a value V to

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