The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability

In the simulation analysis of SLM combined with FRFT, the effectiveness of FRFT is first analysed. Choose the order of FRFT p = 0.001 and the number of twiddle factors D = 4 for SLM. The simulation results are shown in Figure 2.

Fig. 2

It can be seen from Figure 2 that the PAPR of FRFT is further reduced based on FFT. When the threshold PAPR0 is around 6.6 dB, the probability that the PAPR under FRFT is higher than this threshold is <10⁻⁴, while the FFT result is >10⁻¹. It can be seen that the probability of high PAPR is reduced by about 104, the highest PAPR under FRFT is about 6.6 dB, and the PAPR under FFT can reach 9 dB. For the sake of comparison, the time domain signals with a time of 0–6.243 8 μs and a power of −10 dBm–6 dBm are uniformly selected. The simulation results are shown in Figure 3 [5].

Fig. 3

It can be seen from Figure 3 that the highest peak power of the original signal is around −6.05 dBm; after processing by the SLM algorithm, the highest peak power is around −6.27 dBm; and after processing by the FRFT-based SLM algorithm, the highest peak power is only −6.40 dBm. Moreover, the signal processed by the SLM algorithm based on FRFT has the least glitches and the smoothest signal. Therefore, by combining the FRFT algorithm, the PAPR suppression capability of SLM is further improved. In an actual system, one can consider sacrificing part of the PAPR suppression performance to improve the impact of the introduction of the SLM algorithm on the system. Since the introduction of the SLM algorithm will bring high complexity to the system, as the rotation factor increases, the complexity also doubles. The simulation results of the influence of the combination of FRFT and SLM algorithm on the complexity of the SLM algorithm are shown in Figure 4 [6].

Fig. 4

It can be seen from Figure 4 that the PAPR suppression ability when the number of twiddle factors D = 2 in the FRFT-based SLM algorithm lies between the suppression ability of D = 8 and D = 16 in the single SLM algorithm, and is equal to the suppression ability of D = 16. Closer. Therefore, using the SLM algorithm with D = 2 under FRFT to replace the SLM algorithm with D = 16 under FFT has similar PAPR suppression performance, but the introduction of the SLM algorithm reduces the complexity of the system by 8 times.

Limiting algorithms mainly achieve the purpose of suppressing PAPR through signal distortion. Here we consider the simplest peak clipping and limiting. First, the effectiveness of the combined algorithm is analysed. The limiting threshold in the limiting algorithm is 6.6, and the obtained CCDF curve is shown in Figure 5.

Fig. 5

Due to the suppression characteristics of the limiting algorithm, the curve trends of the two processing signals are very similar. Compared with the SLM algorithm, the PAPR suppression effect of the limiting algorithm is more prominent. It can be seen from Figure 5 that the signal processed by FRFT is more sensitive to amplitude limiting. The probability that the PAPR of the signal processed by FRFT is >5.8 dB is 10⁻⁴, and the probability that the PAPR of the signal processed by FFT is >5.8 dB at this time Up to 0.8. The optical path simulation analysis of the combined algorithm is also performed, and the observation window is the same as the FRFT combined SLM algorithm. The simulation results are shown in Figure 6.

Fig. 6

It can be seen from Figure 6 that the peak power of the original signal is −6.02 dBm; the peak power of the signal processed by the limiter is −6.30 dBm; the peak power of the signal processed by the FRFT-based limiter algorithm is −6.40 dBm. The FRFT combined with the limiting algorithm has the best glitch smoothness. Since the selected limit thresholds are the same, theoretically the highest PAPR values that can be reached by the two FT signals are the same. However, after 249,984 bit information is transmitted through the optical path, the peak value of the signal processed by FRFT is lower than the peak value of the signal processed by FFT. It can be seen that the combination of FRFT and limiting algorithm is more effective. The limiting algorithm will have an impact on the system's bit error rate performance. The two FTs combined with the limiting algorithm are simulated and analysed for the system's bit error rate performance after optical transmission. The simulation results are shown in Figure 7 [7].

Fig. 7

It can be seen from Figure 7 that the bit error rate performance of FRFT and FFT are equivalent, which conforms to the theoretical analysis. However, due to the introduction of the limiting algorithm, the bit error rate performance is significantly reduced. When the optical signal-to-noise ratio is 8 dB, the bit error rate increases from 10⁻⁴ to 10⁻³.

By increasing the limit threshold of the limit algorithm in the case of FRFT, the influence of the introduction of the limit algorithm on the bit error rate is improved. After many adjustments, when the limiting threshold is increased to 7.4, the FRFT combined with the limiting algorithm and the CCDF curve of the limiting algorithm when the threshold is 6.6 are basically the same, that is, the PAPR suppression performance of the two cases is basically the same. The results are as follows Figure 8. At this time, the bit error rate transmitted through the optical path is shown in Figure 9.

Fig. 8

Fig. 9

It can be seen from Figure 9 that after increasing the limiting threshold, the bit error rate performance of the signal processed by FRFT has been significantly improved. And as the optical signal-to-noise ratio increases, the improvement effect becomes more obvious. After the optical signal-to-noise ratio reaches 10 dB, the bit error rate of the signal processed by FRFT has been.

my country's financial repression has a clear state-owned bias. Financial institutions such as state-owned banks have long been in a monopoly position, and their capital rationing tends to favour state-owned economic departments and large enterprises. At the same time, the interest on loans received by state-owned economic departments is far below market levels. The World Bank's survey shows all the production scores of enterprises. The samples are divided according to whether they have a foreign capital component, whether a foreign capital component is >25%, and whether they have a state-owned component. Or equal to 25% are classified as non-foreign-funded enterprises, and the above sub-samples are grouped and regressed. The results are shown in Table 1. The explanatory variable is the proportion of informal financial financing. From the regression results, whether it is a foreign-funded enterprise or a foreign-funded enterprise, the company's informal financial financing ratio will not be affected by financial repression, and financial repression will not increase the enterprise's informal financial financing ratio. This may be due to the foreign capital component. The information asymmetry in the credit market is reduced. Formal financial institutions will think that enterprises with foreign-funded components have better credit qualifications. Therefore, they tend to lend to enterprises with foreign-funded components. This can alleviate the credit constraints of enterprises and avoid them. Will affect the proportion of informal financial financing of enterprises. The proportion of informal financial financing of companies that do not have foreign-invested components in the above sample is significantly affected by financial repression. At the same time, enterprises with state-owned components are not affected by financial repression in terms of informal financial financing. That is to say, a network of state-owned relationships can effectively alleviate the financing constraints of enterprises, and enterprises with state-owned components have closer relations with the government. It is easier to obtain the resources or credit needed for development from the government, so it has no significant impact on the proportion of informal finance, while financial repression has a significant positive effect on the proportion of informal finance for non-state-owned enterprises. The above results verify Hypothesis 1, that financial repression has significant characteristics of ‘discrimination on ownership’ [8].

As far as the size of the enterprise is concerned, we guess that because small-scale enterprises have higher operating risks and fewer mortgageable assets, they are often discriminated against by financial institutions in the credit market, and the resources needed for development are more dependent on informal financial financing. The impact of financial repression is more serious; but when the degree of financial repression is high, the cost of formal financial financing rises and large enterprises will also prefer to choose informal financial financing. According to the grouping standard of the World Bank questionnaire, the number of employees in small companies is 5–19, the number of employees in medium-sized companies is 20–99, and the number of employees in large companies is 100 or more. The samples are divided according to this standard and the regression is performed. Analysis. We first use formal financial financing and informal financial financing as the explained variables to perform sub-sample regression. The regression results show that financial repression has significantly reduced the proportion of formal financial financing and increased the proportion of informal financial financing. There is no significant difference in different scales. We believe that this may be due to excessive financial repression, which has exceeded the critical value affecting state-owned enterprises and large enterprises. This is basically in line with our conjecture. Immediately after sub-sample regression with sub-indices of informal financial financing, it can be seen from Table 2 that the regression results basically verify Hypothesis 2 [9]. In the sub-sample regression of enterprises of different sizes, the coefficients of financial repression are all positive, but the significance is different. In the case of deepening financial repression, companies will increase informal financial financing, while large companies will significantly increase commercial credit financing but have no significant impact on informal private lending and financing, and small companies will significantly increase informal private lending but have no significant impact on commercial credit financing. There was no significant impact. Medium-sized enterprises increased their commercial credit financing and informal private lending. This may be because large companies have more resources to establish relatively good business relationships with other companies, and therefore commercial credit financing will increase; while small companies cannot establish good business relationships with other companies due to differences in scale, so they only can rely on social networking and other informal private lendings. The regression results also confirm the large-scale discrimination of financial repression against commercial credit and informal private lending, as shown in Table 2 [10].