Overflow analysis in the fixed-point implementation of the first-order Goertzel algorithm for complex-valued input sequences

Medina-Melendrez, Modesto; Arias-Estrad, Miguel; Castro, Albertina

doi:10.1109/mwscas.2009.5236016

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…As the GF is an IIR Filter type, the arithmetic growth within the internal registers must be controlled. Several works [31][32][33] suggest different scaling considerations in order to minimise or avoid the overflow situations in the calculation process. We apply the scaling process at the input of the iterative section to 𝑤 1 and 𝑤 2 , and not to the input signal, because this has a negative impact on the SNR, when they are reintroduced into the Goertzel algorithm mapping module (see figure 8) by an arithmetic shift (saving FPGA resources), and is configurable by software.…”

Section: Arithmetic Treatmentmentioning

confidence: 99%

An implementation of a channelizer based on a Goertzel Filter Bank for the read-out of cryogenic sensors

et al. 2023

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In this work we present an application of the Goertzel Filter for the channelization of multi-tonal signals, typically used for the read-out of cryogenic sensors which are multiplexed in the frequency domain (FDM), by means of Microwave Superconducting Quantum Interference Device (SQUID) Multiplexer (μMUX). We demonstrate how implementing a bank of many of these filters, can be used to perform a channelization of the multi-tonal input signal to retrieve the data added by the sensors. We show how this approach can be implemented in a resource-efficient manner in a Field Programmable Gate Array (FPGA) within the state-of-the-art, which allows great scalability for reading thousands of sensors; as is required by Radio Telescopes in Cosmic Microwave Background Radiation (CMB) surveys using cryogenic bolometers, particles detection like Neutrino mass estimation using cryogenic calorimeters or Quantum Computing.

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Section: Arithmetic Treatmentmentioning

confidence: 99%

An implementation of a channelizer based on a Goertzel Filter Bank for the read-out of cryogenic sensors

et al. 2023

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“…According to [41], the first order Goertzel algorithm performs better than the second order in fixed-point implementation due to the presence of two recursions in the second order, in which both methods have the same number of iterations N. To increase the SQNR for real-valued input sequences, [42] proposed to apply a scaling factor O(1/N) on the input data for the first order and a scaling factor O(1/N 2 ) for the second order. With regard a complex-valued input sequence, [41] proposed a scaling factor π/4N to the input sequence x (n) for the first order filter. Applying a scaling factor on the recursive filter will assure its stability by avoiding overflow.…”

Section: B Accuracy -Sqnr Evaluationsmentioning

confidence: 99%

“…The fixed-point results of the radix-2 FFT have been added as reference. We have not applied a scaling factor at each stage of the FFT process as it was proposed in [40] [41]. We only applied the adjustment of scaling factor at the input sequence in the same manner for Goertzel and the proposed filters.…”

Section: First Order Second Ordermentioning

confidence: 99%

The JM-Filter to Detect Specific Frequency in Monitored Signal

Jaber

Massicotte

2021

IEEE Trans. Signal Process.

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The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing inside a Digital Signal Processor (DSP). It has been widely known and argued in relevant literature that the Fast Fourier Transform (FFT) is useless in detecting specific frequencies in a monitored signal of length N because most of the computed results are ignored. In this paper, we present an efficient FFT-based method to detect specific frequencies in a monitored signal, which will then be compared to the most frequently used method which is the recursive Goertzel algorithm that detects and analyses one selectable frequency component from a discrete signal. The proposed JM-Filter algorithm presents a reduction of iterations compared to the first and second order Goertzel algorithm by a factor of r, where r represents the radix of the JM-Filter. The obtained results are significant in terms of computational reduction and accuracy in fixed-point implementation. Gains of 15 dB and 19 dB in signal to quantization noise ratio (SQNR) were respectively observed for the proposed first and second order radix-8 JM-Filter in comparison to Goertzel algorithm.

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“…In low-cost systems without a FPU, fixed-point arithmetic can be used as a high-speed alternative to floating-point software emulation, as long as the problems of overflow and underflow are avoided (due to the restricted range of values that can be represented) [11]. In general, fixed-point will suffer from reduced accuracy due to the inability to represent the same range of values as a floating-point representation of the same bit-width.…”

Section: Introductionmentioning

confidence: 99%

An Evaluation of the Goertzel Algorithm for Low-Power, Embedded Systems

Brown¹,

Timoney²,

Lysaght³

2014

25th IET Irish Signals &Amp; Systems Conference 2014 and 2014 China-Ireland International Conference on Information and Communi

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-The Goertzel Algorithm provides an efficient mechanism for tone detection in signal processing. However, on Wireless Sensor Network nodes, there is often not sufficient processing power to implement this using floating-point arithmetic, so fixed-point implementations are used. In this paper we compare the quality of the results for a typical audio application with different resolutions of fixed-point support using MATLAB. We also provide performance figures based on implementing this on a representative sensor node platform. Our results show that, for this application-space, 16-bit fixed-point arithmetic provides the best tradeoff of accuracy against performance. No previous work has addressed this specific aspect of implementating the Goertzel algorithm.

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Overflow analysis in the fixed-point implementation of the first-order Goertzel algorithm for complex-valued input sequences

Cited by 5 publications

References 6 publications

An implementation of a channelizer based on a Goertzel Filter Bank for the read-out of cryogenic sensors

An implementation of a channelizer based on a Goertzel Filter Bank for the read-out of cryogenic sensors

The JM-Filter to Detect Specific Frequency in Monitored Signal

An Evaluation of the Goertzel Algorithm for Low-Power, Embedded Systems

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