KeywordsChebyshev polynomial, symmetrical Zolotarev polynomial of the first kind, spectrum of Zolotarev polynomial, power expansion, trigonometric functions, forward and backward recursion, binomial coefficients

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The Discrete Zolotarev Transform (DZT) brings an improvement in the field of spectral analysis of nonstationary signals. However, the transformation algorithm called Approximated Discrete Zolotarev Transform (ADZT) suffers from high computational complexity. The Short Time ADZT (STADZT) requires high segment length, 512 samples, and more, while high segment overlap to prevent information loss, 75% at least. The STADZT requirements along with the ADZT algorithm computational complexity result in a rather high computational load.The algorithm computational complexity, behavior, and quantization error impacts are analyzed. We present a solution which deals with high computational load employing co-design methods targeting Field Programmable Gate Array (FPGA). The system is able to compute one-shot DZT spectrum 2 048 samples long in ≈ 22 ms. Real-time STADZT spectrum of a mono audio signal of 16 kHz sampling frequency can be computed with overlap of 91%.

This paper discusses the usage of symmetrical Zolotarev polynomials (ZPS)s in spectral analysis. Evaluation of Discrete Zolotarev transform (DZT) coefficients is briefly discussed. However, the DZT coefficients evaluation is problematic. An alternative novel method embedding ZPSs is proposed. The novel method, so-called DZT zoom, improves the spectrum's time resolution for non-stationary signals compared to narrowband spectrogram. Results are comparable to the approximated DZT (ADZT). The DZT zoom distinguishing property is the focus on a particular frequency band of the spectrum.