AC induction noise canceler

1. A method for removing noise from a detection circuit output signal in an alarm system using a software filter, the method comprising:

converting the detection circuit output signal into a digital signal, wherein the digital signal includes a series of sampled values;

entering a most recent of the sampled values into a circular index containing a number of previously sampled values;

multiplying each of the values in the circular index by a predetermined filter coefficient; and

summing products of each of the multiplied circular index values and filter coefficients to output a filtered digital signal value;

wherein the multiplying and summing steps are performed in accordance with the equation:

y

⁡

[

n

]

=

∑

i

=

0

N

⁢

b

i

⁢

x

⁡

[

n

-

i

]

where y[n] is the filtered digital signal value, x[n] is the most recent of the sampled values, b i are the predetermined filter coefficients, and N is a length of the filter.

2. The method in accordance with claim 1 , wherein the filter coefficients are calculated according to the formula:

b

i

=

{

sin

⁡

[

(

i

-

τ

)

⁢

Ω

c

]

(

i

-

τ

)

⁢

π

,

for

⁢

⁢

i

≠

τ

Ω

c

/

π

,

for

⁢

⁢

i

=

τ

}

i

=

0

,

1

,

…

⁢

,

2

⁢

M

where b i are the filter coefficients, τ is a number of taps of the software filter, M is equal to τ if the filter coefficients are symmetric, and Ω c =(ω stop +ω pass )/(2×f s ), where ω stop is a stopband lower frequency of the software filter, ω pass is a passband upper frequency of the software filter, and f s is a sampling frequency of the sampled values.

3. The method in accordance with claim 2 , wherein ω stop is in a range of 40 Hz to 60 Hz.

4. The method in accordance with claim 1 , wherein the noise is line frequency noise.

5. The method in accordance with claim 1 , wherein the noise is AC induction noise.

6. An alarm system comprising: at least one detection circuit;

an ADC operatively connected to the at least one detection circuit and configured to convert a detection circuit output signal in the at least one detection circuit into a digital signal;

a software filter operatively connected to the ADC and configured to receive the converted digital signal and to filter noise associated with a predetermined frequency range from the digital signal; and

a CPU operatively connected to the software filter and configured to receive the filtered signal and to identify an operational state of the at least one detection circuit based on the filtered signal;

wherein the software filter is configured to:

receive a serious of sampled values from the ADC;

enter a most recent of the sampled values into a circular index containing a number of previously sampled values;

multiply the values in the circular index by predetermined filter coefficients; and

sum products of each of the multiplied circular index values and filter coefficients to arrive at a filtered digital signal value;

wherein the multiplying and summing are performed in accordance with the equation:

y

⁡

[

n

]

=

∑

i

=

0

N

⁢

b

i

⁢

x

⁡

[

n

-

i

]

 where y[n] is the filtered digital signal value, x[n] is the most recent of the sampled values, b i are the predetermined filter coefficients, and N is a length of the filter.

7. The alarm system in accordance with claim 6 , wherein the detection circuit comprises at least one sensor located in a zone of a monitored structure.

8. The alarm system in accordance with claim 6 , wherein the noise is line frequency noise.

9. The alarm system in accordance with claim 6 , wherein the noise is AC induction noise.

10. The method in accordance with claim 6 , wherein the predetermined frequency range is 40 Hz to 60 Hz.

11. The alarm system in accordance with claim 6 , wherein the ADC is configured to convert the detection circuit output signal into a stream of integers at a predefined sampling rate.

12. The alarm system in accordance with claim 11 , wherein the filter coefficients are calculated according to the formula:

b

i

=

{

sin

⁡

[

(

i

-

τ

)

⁢

Ω

c

]

(

i

-

τ

)

⁢

π

,

for

⁢

⁢

i

≠

τ

Ω

c

/

π

,

for

⁢

⁢

i

=

τ

}

i

=

0

,

1

,

…

⁢

,

2

⁢

M

where b i are the filter coefficients, τ is a number of taps of the software filter, M is equal to τ if the filter coefficients are symmetric, and Ω c =(ω stop +ω pass )/(2×f s ), where ω stop is a stopband lower frequency of the software filter, ω pass is a passband upper frequency of the software filter, and f s is a sampling frequency of the sampled values.

13. The alarm system in accordance with claim 12 , wherein ω stop is in a range of 40 Hz to 60 Hz.

14. The alarm system in accordance with claim 6 , wherein the CPU is configured to initiate one or more actions based on the identified operational state of the at least one detection circuit.