Goertzel Algorithm Demodulator for FSK Signals
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Solution Overview
Problem
Existing demodulators for frequency-shift keyed signals, particularly those using the Goertzel algorithm, face high computing complexity, power consumption, and time requirements, making them unsuitable for real-time capable peripheral devices with limited power, such as those in explosion-protected automation technology.
Innovation Solution
A demodulator implementing the Goertzel algorithm with a reduced number of mathematical steps by optimizing the sampling frequency ratio to the symbol frequency, allowing for lower power consumption and efficient implementation in power-limited devices, using the recursive calculating rule M=s[n]2+s[n−1]2+s[n]*s[n−1]*cre, where cre=2*cos(2*π*fgfs), and sampling frequency fs being an integral multiple of the frequency fg, thereby reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Goertzel algorithm is used for FSK demodulation, then frequency detection capability is improved, but computing complexity increases
Solution Approach 1:
The patent changes the sampling frequency parameter to be an integral multiple of the symbol frequency (fs = k * fg where k is an integer). This parameter change causes the feedback coefficient cre to become a simple integer (0, ±1), eliminating the need for complex multiplications and reducing computing complexity while maintaining frequency detection capability
Solution Approach 2:
The patent creates an asymmetric relationship between sampling frequency and symbol frequency, where the sampling frequency is deliberately set as an integral multiple of the symbol frequency rather than using equal or arbitrary frequencies. This asymmetric configuration simplifies the mathematical operations in the Goertzel algorithm
2Measurement precision
If the Goertzel algorithm is used for FSK demodulation, then frequency detection capability is improved, but power consumption increases
Solution Approach 1:
By changing the sampling frequency to an integral multiple of symbol frequency, the patent reduces the number of mathematical operations (eliminating multiplications by non-integer coefficients), which directly reduces power consumption in the processor while maintaining accurate frequency detection
Solution Approach 2:
The patent extracts and eliminates the most power-consuming operations from the Goertzel algorithm by setting cre to integer values, thereby removing the need for complex multiplications and reducing overall power consumption
3Measurement precision
If the Goertzel algorithm is used for FSK demodulation, then frequency detection capability is improved, but processing time increases
Solution Approach 1:
The patent reduces processing time by changing the sampling frequency parameter to an integral multiple of symbol frequency, which simplifies the recursive calculations in the Goertzel algorithm and enables faster computation of spectral components
Data Source
AI summary
Exemplary embodiments relates to a demodulator for frequency-shift keyed signals by using the Goertzel algorithm according to the general recursive calculating rule, wherecre=2*cos(2*π*fgfs)with the sampling frequency fs and the specified frequency fg. To reduce the mathematical complexity in feed-power-limited devices, it is proposed that the sampling frequency fs is an integral multiple of the frequency fg of a specified discrete spectral component.