# Fourier transform formula for squeeze casting

In the process of industrial production, physical quantities such as temperature, pressure and vibration are usually converted into electrical signals by sensors, and collected by data acquisition system. Due to the complexity of the field and the inherent properties of the measurement unit, it is inevitable that the actual measurement data will be doped with unnecessary noise interference. Usually, these interference signals are small amplitude and high frequency signals. In some cases, the existence of these interference signals will not affect the actual production. However, in other cases, due to the high accuracy requirements of the measurement data, these interference signals will cause serious distortion or error in the analysis. In this case, the interference signal must be clear Except.

In the process of squeeze casting experiment, due to the influence of the surrounding environment and the inherent properties of thermocouple and pressure sensor, there must be high-frequency noise components in the temperature and pressure data obtained by the experiment. Because the inverse algorithm requires high accuracy of data, these high-frequency noise signals are easy to cause calculation errors, so it is necessary to extract the high-frequency noise components from the original data obtained by the experiment The sound signal is removed. However, because the sampling frequency of the data acquisition instrument is 200Hz, these high-frequency noise components (usually 40-50hz) are inevitably included in the measurement data. In order to eliminate the influence of high frequency noise on the analysis of interface heat transfer coefficient, a low-pass filtering method based on fast Fourier transform is used to process the data.

Fourier transform is a mathematical function that can be used to represent different frequency components of continuous signal. It can transform continuous signal from time domain to frequency domain. The Fourier transform formula of function f (T) is as follows:

Inverse Fourier transform is to transform continuous signal from frequency domain to time domain. The formula of inverse Fourier transform is as follows

Fast Fourier transform (FFT) is an algorithm that can fast transform or inverse transform discrete data. The low-pass filtering method based on fast Fourier transform is to transform the data to frequency domain by using fast Fourier transform algorithm, then remove the high-frequency noise signal which is higher than the truncation frequency, and then convert the frequency domain data to time domain data by using inverse fast Fourier transform, so as to realize the data processing method of removing the high-frequency noise component in the data. Among them, the truncation frequency is the core parameter of the low-pass filtering method based on fast Fourier transform. Selecting an appropriate truncation frequency can remove the high-frequency noise components of the data without affecting the accuracy of the data. Therefore, how to select the truncation frequency is a very important problem.

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