Demodulator for frequency-shift keyed signals by using the Goertzel algorithm
View Patent ↗Exemplary embodiments relates to a demodulator for frequency-shift keyed signals by using the Goertzel algorithm according to the general recursive calculating rule, where c re = 2 * cos ( 2 * π * f g f s ) with the sampling frequency f s and the specified frequency f g . To reduce the mathematical complexity in feed-power-limited devices, it is proposed that the sampling frequency f s is an integral multiple of the frequency f g of a specified discrete spectral component.
1. A demodulator for frequency-shift keyed signals, comprising:
a first state memory configured to store a state signal; and
a processor configured to filter input signals and process the filtered signals using a Goertzel algorithm according to a general recursive calculating rule M=s[n] 2 +s[n−1] 2 +s[n]*s[n−1]*c re
where s[n]=x[n]+c re *s[n−1]−s[n−2],
M is the magnitude of a specified discrete spectral component,
x[n] are the samples of the input signal,
s[n] are state signals, and
c re is the feedback coefficient of the state signal s[n−1],
where
c
re
=
2
*
cos
(
2
*
π
*
f
g
f
s
)
with a sampling frequency f s and a specified frequency f g ,
wherein the sampling frequency f s is an integral multiple of the frequency f g of the specified discrete spectral component,
wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 4, the feedback coefficient c re equals zero such that the state signal of the first state memory is not fed back, and
wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 6, the feedback coefficient c re equals one such that the state signal of the first state memory is fed back.
2. A method for demodulating frequency-shift keyed signals, comprising:
filtering input signals in a processor;
processing, in the processor, the filtered signals using a Goertzel algorithm according to a general recursive calculating rule M=s[n] 2 +s[n−1] 2 +s[n]*s[n−1]*c re
where s[n]=x[n]+c re *s[n−1]−s[n−2],
M is a magnitude of a specified discrete spectral component,
x[n] are samples of the input signal,
s[n] are state signals, and
c re is a feedback coefficient of the state signal s[n−1],
where
c
re
=
2
*
cos
(
2
*
π
*
f
g
f
s
)
with a sampling frequency f s and a specified frequency f g ,
wherein the sampling frequency f s is an integral multiple of the frequency f g of the specified discrete spectral component, and
wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 4, the feedback coefficient c re zero such that a state signal of a first state memory is not fed back, and
wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 6, the feedback coefficient c re equals one such that the state signal of the first state memory is fed back.
3. A demodulator for frequency-shift keyed signals, comprising:
a high-pass filter configured to filter a line signal;
a processor configured to sample the filtered signal and process samples output from the filter with a Goertzel algorithm, comparing a result of the algorithm to a threshold to determine whether the filter output is to be feedback for further processing with the Goertzel algorithm,
wherein the processor is configured to execute the Goertzel algorithm according to a general recursive calculating rule M=s[n] 2 +s[n−1] 2 +s[n]*s[n−1]*c re
where s[n]=x[n]+c re *s[n−1]−s[n−2],
M is a magnitude of a specified discrete spectral component,
x[n] are samples of the input signal,
s[n] are state signals, and
c re is a feedback coefficient of the state signal s[n−1],
where
c
re
=
2
*
cos
(
2
*
π
*
f
g
f
s
)
with a sampling frequency f s and a specified frequency f g ,
wherein if the line signal is filtered at a sampling frequency having a magnitude that is four times a frequency of a specified symbol frequency of the line signal the filter output is not fed back, and
wherein if the line signal is filtered at a sampling frequency having a magnitude that is six times a frequency of a specified symbol frequency of the line signal the filter output is fed back.
4. The demodulator of claim 2 , wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 4, the feedback coefficient c re is zero such that a state signal of a first state memory is not fed back, and wherein if a ratio of the sampling frequency f s to the frequency f g of the specified discrete spectral component is 6, the feedback coefficient c re equals one such that the state signal of the first state memory is fed back.