Development of a digital signal processing model using a frequency synthesizer and synthesis of quadrature conversion circuits

. An important issue of improving the quality of the functioning of measuring systems is the improvement of the conversion methods and the algorithmization of the processes for eliminating various noises and interferences that arise in the tasks of analog-to-digital information conversion.The article analyzes the algorithms for assessing the accuracy of digital signal processing (DSP) in a complex of issues due to the development of digital and digital-analog element base, as well as the development of methods and algorithms for processing and generating signals.

. Functional diagram of a quadrature transformation module with perturbation compensation. Csignal switching devices; QM -quadrature mixer; С1 -frequency synthesis devices for the receiving device; С2 -frequency synthesis device for test signal.
Assuming if in a quadrature transformation, there are no unbalances in the results of the transformation. then the real values of the common -mode and quadrature components of the signals at the outputs of the CS can be determined [11,12]: If we accept the signal in (4) as a reference, and then the discrete Fourier transforms of this signal will also turn out to be a reference: The above expressions do not take into account quantization noise, and the selected frequency band must be wide enough to analyze real signals. Further, comparing the natural decomposition coefficients previously obtained by formulas (3) and (5), we obtain the actual real deviation parameters [13,16,17], a*, b*, ∆φ*(i), ∆k*(i) at the i-th frequency point: Then, accordingly, the amplitude spectra of the common-mode and quadrature components in the common-mode channel of the complex area of the test and reference signal can be taken away, as shown in Fig.2 a, b and similar spectra for the test, as well as the reference signals, respectively, are shown in Fig.3 a, b [14,15,21] Fig.2 (a) Spectra for the test signal in the common-mode region; b) the spectra of the reference signal in the common-mode part of the harmonic.
It is recommended to always take into account the influence of quantization noise. In particular, the presence of quantization noise of the specified test signals at the input of the considered quadrature mixer may somewhat limit the accuracy of the evaluation of expressions (6)(7)(8)(9). Since the algorithm for setting the reference signal is modeled taking into account the expected disturbances, it can be assumed that it does not contain distortions. We assume that if the output of the CS signal spectra is in an ideal form [18,22,23,25]: It is possible to imagine a deviation compensation algorithm for a test signal: In the future, according to the specified algorithm, the switch K is switched to the real specified signal under study, i.e., according to the results of the obtained deviation parameters (10. and 11), the results of the study are corrected. To develop a system implementing digital filtering algorithms, various circuit solutions were used: digital control devices, operational amplifiers with a different set of frequency characteristics and signal conversion coefficients. In particular, the Nyquist digital quadrature transformation method was widely used in practical research on the dynamic expansion of the ranges of analog modules [19,20,26].
The quadrature components of the signal in a certain frequency spectrum will be carried out, respectively, at the difference and total frequency limits. To remove the total frequency components, low-pass filters (LPF) are used. In the final result we have: The structural foundations of the LPF are filters with a finite impulse response (FIR). Then the amplitude characteristics of the input signal is found by the formula: Thus, when the common-mode and quadrature components are known, it will be possible to determine the initial phase of a given input signal:

Conclusion
Thus, it can be concluded that the conversion of an analog signal into a discrete form with quantization is one of the most common types of tasks in automated information processing. At the same time, the choice of sampling frequency in them is determined by the range of the signal spectrum. If, for example, the spectrum of the signal suitable for conversion is limited by the frequency fmax , to restore the signal without loss of information content, the sampling rate should be 2 times higher. In other words, if the highest frequency harmonic of the input analog signal has a period T, then for this harmonic period it should correspond to two sampling counts.