High-frequency digital filtering system based on fast Fourier transform

Abstract

The invention discloses a high-frequency digital filtering system based on fast Fourier transform, which is characterized in that an analog signal is acquired and converted into a digital signal, a preprocessing module is used for denoising the digital signal, and window processing is carried out on the digital signal through a window function; the Fourier transform module converts a time domain signal into a frequency domain signal through fast Fourier transform and then performs frequency domain separation, the digital filtering module filters the signal through multiplication operation and transmits the filtered signal to the inverse Fourier transform module, the inverse Fourier transform module converts processed frequency domain data back to the time domain signal, and the inverse Fourier transform module transmits the time domain signal to the digital filtering module. The post-processing module carries out window removal processing on the time domain signal and then converts a digital signal into an analog signal to be output, high-frequency digital filtering is carried out through Fourier fast transform, spectrum characteristics of a complex signal are accurately processed, the filtering quality of the high-frequency signal is guaranteed, and the subsequent signal processing effect is improved.

Description

Technical Field

[0001] The invention relates to the technical field of digital filtering, in particular to a high-frequency digital filtering system based on Fourier fast transform. Background Art

[0002] Digital filtering is an important technology in digital signal processing. It is usually used to extract useful information from signals, remove noise or interference, reduce noise, and enhance signals in specific frequency bands. At the same time, it operates on digital signals to change the frequency components of signals and processes the input signals according to certain set standards, thereby enhancing or suppressing specific parts of the signals. In electronic equipment, digital filtering is often used in audio, video, communications, and biomedical signals.

[0003] At present, with the increasing complexity of signal properties, ordinary signal filtering methods are not accurate enough in processing the spectral characteristics of complex signals, and cannot guarantee the filtering quality of high-frequency signals, which reduces the effect of subsequent signal processing. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions: a high-frequency digital filtering system based on Fourier fast transform, comprising:

[0006] Acquisition module, pre-processing module, Fourier transform module, digital filtering module, inverse Fourier transform module, post-processing module and output module;

[0007] The signal acquisition module is responsible for collecting the analog signal Mnxh and converting it into a digital signal Szxh through an algorithm formula, and transmitting the converted digital signal to the preprocessing module;

[0008] The preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, obtains a denoised digital signal Qzsz, and performs window processing on the signal through a window function to reduce spectrum leakage, and transmits the processed signal to the Fourier transform module;

[0009] The Fourier transform module converts the time domain signal into the frequency domain signal through fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation, identifies and extracts the high-frequency signal to be retained and the low-frequency signal to be filtered out, and uniformly transmits the processed signals to the digital filtering module;

[0010] The digital filtering module applies a filter in the frequency domain, implements signal filtering through a multiplication operation, and transmits the filtered signal to the inverse Fourier transform module;

[0011] The inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through an algorithm formula and transmits it to the post-processing module;

[0012] The post-processing module performs window removal processing on the time domain signal, converts the digital signal into an analog signal output, and generates a signal filtering result report and sends it to the output module;

[0013] The output module displays the signal filtering result report on the visual interface.

[0014] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the signal acquisition module is responsible for collecting the analog signal Mnxh and converting it into a digital signal Szxh through an algorithm formula. The conversion formula includes:

[0015] Sample the continuous analog signal Mnxh(n) in the time domain to obtain discrete signal values:

[0016] Mnxh[n]=Mnxh(nT)

[0017] Where n=0,1,2,... represents the number of sampling times, and T represents the sampling time;

[0018] Quantize the sampled analog signal value Mnxh[n] into a digital signal:

[0019] Mbxh[n]=Q(Mnxh[n])

[0020] Wherein, Mbxh[n] represents the quantized signal, and Q(Mnxh[n]) represents the quantized function;

[0021] Convert the quantized value into binary digital form to obtain the final digital signal Szxh[n], which is expressed as:

[0022] Szxh[n]=Encode(Mbxh[n])

[0023] Wherein, Encode represents a coding conversion function.

[0024] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, and obtains a denoised digital signal Qzsz. The denoising formula is:

[0025] Qzsz[n]=H(f)*Szxh[n]

[0026] Wherein, Qzsz[n] represents the denoised signal, n=0,1,2,... represents the number of signals, and H(f) represents the frequency response of the high-pass filter.

[0027] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the formula for window processing of the denoised signal by the preprocessing module through the window function is:

[0028] Qzsz[n]=Mnxh[n]*w[n]

[0029] Wherein, w[n] represents the window function, and Qzsz[n]=Mnxh[n]*w[n] represents window processing of the denoised signal.

[0030] As a preferred solution of the high-frequency digital filtering system based on fast Fourier transform described in the present invention, the formula for converting the time domain signal into the frequency domain signal by the fast Fourier transform module is as follows:

[0031]

[0032] Where X[k] represents the frequency domain signal, k represents the index frequency, Syxh[n] represents the value of the time domain signal at n sampling points, n represents the time index, and N represents the total number of sampling points of the signal; Represents a complex exponential function, frequency dependent in Fourier transform, representing a complex number of rotation.

[0033] As a preferred solution of the high-frequency digital filtering system based on fast Fourier transform described in the present invention, the Fourier transform module converts the time domain signal into a frequency domain signal through fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation. The frequency domain separation formula is:

[0034] Fl[k]=Flsignal[k]+Fl noise [k]

[0035] Among them, Fl[k] represents the signal after frequency domain separation, Flsignal[k] represents the frequency domain of the signal, and Fl noise [k] represents the frequency domain of the noise.

[0036] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the digital filtering module applies a filter in the frequency domain and implements signal filtering through multiplication operation. The filtering formula is:

[0037] Lb[k]=Ht[k]*Fl[k]

[0038] Wherein, Lb[k] represents the frequency domain of the filtered signal, and Ht[k]*Fl[k] represents the filter Ht[k] applied in the frequency domain to filter the signal Fl[k] separated in the frequency domain.

[0039] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through an algorithm formula, and the conversion formula is:

[0040]

[0041] Where Zh[k] represents the converted time domain signal, k represents the index frequency, Lb[k] represents the frequency domain of the filtered signal, n represents the time index, and N represents the total number of sampling points of the signal; represents the complex exponential function, which represents a rotation of a complex number.

[0042] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the post-processing module performs window removal processing on the time domain signal, and the processing formula is:

[0043]

[0044] Wherein, Qc[k] represents the signal after window removal, Zh[k] represents the converted time domain signal, and w[n] represents the window function.

[0045] As a preferred solution of the high-frequency digital filtering system based on Fourier fast transform described in the present invention, the post-processing module performs window removal processing on the time domain signal, and then converts the digital signal into an analog signal output, and the conversion formula is:

[0046]

[0047] Where S(t) represents the converted analog signal, N represents the total number of sampling points of the signal, Qc[k] represents the signal after removing the window, n represents the time index, T represents the sampling period, and δ(t) represents the pulse signal converted from the discrete signal to the time domain.

[0048] A computer device comprises: a memory and a processor; the memory stores a computer program, wherein: the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0049] A computer-readable storage medium stores a computer program, wherein: when the computer program is executed by a processor, the steps of any one of the methods of the present invention are implemented.

[0050] Beneficial effects of the present invention: In the high-frequency digital filtering system based on fast Fourier transform provided by the present invention, the signal acquisition module acquires the analog signal Mnxh and converts it into a digital signal Szxh through an algorithm formula. The preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, obtains a denoised digital signal Qzsz, and performs window processing on the signal through a window function, and transmits the processed signal to the Fourier transform module. The Fourier transform module converts the time domain signal into a frequency domain signal through fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation, identifies and extracts the high-frequency signal to be retained and the low-frequency signal to be filtered out, and unifies the processed signals. The signal is transmitted to the digital filtering module, which applies a filter in the frequency domain, realizes signal filtering through multiplication operation, and transmits the filtered signal to the inverse Fourier transform module. The inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through the algorithm formula and transmits it to the post-processing module. The post-processing module performs windowing on the time domain signal, converts the digital signal into an analog signal output, and generates a signal filtering result report. The output module displays the signal filtering result report on the visual interface, and uses Fourier fast transform to perform high-frequency digital filtering and accurately process the spectral characteristics of complex signals, thereby ensuring the filtering quality of high-frequency signals and improving the effect of subsequent signal processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0052] Figure 1 An overall flow chart of a high-frequency digital filtering system based on Fourier fast transform is provided for the first embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0054] Example 1, reference Figure 1 , as an embodiment of the present invention, provides a high-frequency digital filtering system based on Fourier fast transform, comprising:

[0055] With the increasing complexity of signal properties, the common signal filtering method is not accurate enough in processing the spectral characteristics of complex signals, and cannot guarantee the filtering quality of high-frequency signals, which reduces the effect of subsequent signal processing. Therefore, a high-frequency digital filtering system based on Fourier fast transform is proposed. Please refer to Figure 1 ,The system includes a signal acquisition module, a preprocessing module, a Fourier transform module, a digital filtering module, an inverse Fourier transform module, a post-processing module and an output module;

[0056] The signal acquisition module is responsible for collecting the analog signal Mnxh and converting it into a digital signal Szxh through an algorithm formula, and transmitting the converted digital signal to the preprocessing module;

[0057] The conversion formula is as follows:

[0058] Sample the continuous analog signal Mnxh(n) in the time domain to obtain discrete signal values:

[0059] Mnxh[n]=Mnxh(nT)

[0060] Where n=0,1,2,... represents the number of sampling times, and T represents the sampling time;

[0061] The sampled analog signal value Mnxh[n] is quantized into a digital signal, and the formula is as follows:

[0062] Mbxh[n]=Q(Mnxh[n])

[0063] Wherein, Mbxh[n] represents the quantized signal, and Q(Mnxh[n]) represents the quantized function;

[0064] Convert the quantized value into binary digital form to obtain the final digital signal Szxh[n], which is expressed as follows:

[0065] Szxh[n]=Encode(Mbxh[n])

[0066] Among them, Encode represents the encoding conversion function, which converts analog signals into digital signals so that the signals can be processed in computers or digital processors, providing flexibility and accuracy. Digital signals can be more easily applied to various digital signal processing algorithms to improve signal quality.

[0067] The preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, obtains the denoised digital signal Qzsz, and performs window processing on the signal through a window function to reduce spectrum leakage, where:

[0068] The denoising formula is as follows:

[0069] Qzsz[n]=H(f)*Szxh[n]

[0070] Through preliminary denoising, high-frequency noise can be removed, the effective components of the signal can be enhanced, and the interference with subsequent processing can be reduced. In the formula, Qzsz[n] represents the denoised signal, n=0,1,2,... represents the number of signals, and H(f) represents the frequency response of the high-pass filter;

[0071] The window processing formula is as follows:

[0072] Qzsz[n]=Mnxh[n]*w[n]

[0073] The window function helps smooth the signal edge, reduce the leakage effect in the frequency domain conversion, and improve the accuracy of the frequency domain analysis. In the formula, w[n] represents the window function, Qzsz[n]=Mnxh[n]*w[n] represents the window processing of the denoised signal. The window processing effectively shapes the signal spectrum and improves the signal separation capability of the subsequent Fourier transform.

[0074] The Fourier transform module converts the time domain signal into the frequency domain signal through the fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation, identifying and extracting the high-frequency signal to be retained and the low-frequency signal to be filtered out, where:

[0075] The signal conversion formula is as follows:

[0076]

[0077] The FFT algorithm efficiently converts time domain signals into frequency domain signals, allowing real-time applications and fast analysis. In the formula, X[k] represents the frequency domain signal, k represents the index frequency, Syxh[n] represents the value of the time domain signal at n sampling points, n represents the time index, and N represents the total number of sampling points of the signal. Represents the complex exponential function, which is related to the frequency in Fourier transform and represents a rotated complex number. Frequency domain filtering and signal analysis can be easily performed through Fourier transform;

[0078] The frequency domain separation formula is as follows:

[0079] Fl[k]=Flsignal[k]+Fl noise [k]

[0080] Frequency domain separation helps to identify and separate different frequency components, making the analysis of high-frequency and low-frequency signals more accurate. In the formula, Fl[k] represents the signal after frequency domain separation, Flsignal[k] represents the frequency domain of the signal, and Fl noise [k] represents the frequency domain of the noise;

[0081] The digital filter module applies filters in the frequency domain and implements signal filtering through multiplication operations. The signal filtering formula is as follows:

[0082] Lb[k]=Ht[k]*Fl[k]

[0083] Filtering in the frequency domain by multiplication is more efficient than filtering directly in the time domain. In the formula, Lb[k] represents the frequency domain of the filtered signal, and Ht[k]*Fl[k] represents the filter Ht[k] applied in the frequency domain to filter the signal Fl[k] separated in the frequency domain. The filter characteristics can be precisely set to selectively enhance or weaken specific frequency components.

[0084] The inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through an algorithm formula. The conversion formula is as follows:

[0085]

[0086] Through the inverse Fourier transform, the processed frequency domain data can be converted back to the time domain for further analysis or output. In the formula, Zh[k] represents the converted time domain signal, k represents the index frequency, Lb[k] represents the frequency domain of the filtered signal, n represents the time index, and N represents the total number of sampling points of the signal. It represents the complex exponential function, which is related to the frequency in Fourier transform and represents a rotated complex number. After frequency domain processing, it ensures that important time domain signal information is preserved to avoid information loss;

[0087] The post-processing module performs windowing on the time domain signal, converts the digital signal into an analog signal output, and generates a signal filtering result report to be sent to the output module, where:

[0088] The window processing formula is as follows:

[0089]

[0090] The window removal process helps to restore the original characteristics of the signal, reduce the influence of the window function on the signal, and make the signal smoother and more natural. In the formula, Qc[k] represents the signal without the window, Zh[k] represents the converted time domain signal, and w[n] represents the window function.

[0091] The formula for converting digital signal to analog signal output is as follows:

[0092]

[0093] Converting digital signals into analog signals allows the signals to be used in actual devices, such as audio, sensor outputs, and other devices, making it easier to interact with the real world. In the formula, S(t) represents the converted analog signal, N represents the total number of sampling points of the signal, Qc[k] represents the signal after the window is removed, n represents the time index, T represents the sampling period, and δ(t) represents the discrete signal converted into a pulse signal in the time domain.

[0094] The output module reports the signal filtering results on a visual interface.

[0095] By using Fourier fast transform for high-frequency digital filtering, the spectral characteristics of complex signals can be accurately processed, the filtering quality of high-frequency signals is guaranteed, and the effect of subsequent signal processing is improved.

[0096] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0097] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0098] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0099] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0100] Embodiment 2 is an embodiment of the present invention, which provides a high-frequency digital filtering system based on Fourier fast transform. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0101] A set of high-frequency signal simulators (named SignalX-2000) was used to generate analog signals to simulate high-frequency interference in real environments. The experimental data included the collected analog signals, pre-processed noise reduction signals, fast Fourier transform frequency domain signals, digital filtering signals, inverse Fourier transform time domain signals, and the final output analog signals.

[0102] The test steps are as follows:

[0103] Signal acquisition: First, the analog signal of the target frequency range (frequency range is 5kHz to 20kHz) is generated by SignalX-2000, and the sampling frequency is set to 50kHz to ensure that the high-frequency signal characteristics can be fully collected. The sampled data is quantized and encoded to form a discrete digital signal and stored in the system memory.

[0104] Preprocessing noise reduction: After signal acquisition, the preprocessing module performs noise reduction on the signal. The low-frequency noise component is removed by adjusting the frequency response of the high-pass filter. Then, the signal is processed by applying a window function (using a Kaiser window) to reduce the spectrum leakage effect and optimize the frequency response characteristics, so that the high-frequency characteristics in the signal are enhanced. The noise-reduced data is transmitted to the Fourier transform module.

[0105] Fast Fourier Transform and Frequency Domain Separation: The Fourier Transform module uses Fast Fourier Transform (FFT) to convert time domain signals into frequency domain signals. In the frequency domain, the system uses a high-precision algorithm to separate the frequency domain signals, filter out high-frequency signals in the range of 5kHz to 20kHz, and filter out excess low-frequency components. This process significantly improves the system's ability to identify high-frequency signals, making subsequent filtering operations more targeted.

[0106] Digital filtering: In the digital filtering module, a bandpass filter designed with polynomials is used to further fine-tune the high-frequency signal, retain the spectrum characteristics within the target frequency band, and filter out unnecessary interference components. The filter performs convolution operations in the frequency domain. After convolution processing, the data has high accuracy, reduced noise interference, and is easy to process later.

[0107] Inverse Fourier transform: The frequency domain signal after digital filtering is returned to the time domain through the inverse Fourier transform (IFFT). The IFFT process performs an inverse transform based on the previous high-frequency signal selection results, so that the restored signal has clear high-frequency characteristics in the time domain, ensuring the restoration effect of the target signal.

[0108] Post-processing and output: Finally, the system performs windowing on the signal after the inverse Fourier transform to further reduce the impact of frequency leakage and complete signal restoration. After being processed by the digital-to-analog converter, the analog signal is finally output. The output results are displayed in real time on the system visualization interface, and a detailed signal filtering report is generated. By comparing the filtering results in the existing technology, this system has significant advantages in high-frequency filtering effects.

[0109] Table 1 Experimental data table

[0110]

[0111] It can be seen from the table data that the system shows a significant weakening effect on low-frequency noise in the noise reduction process, with an average noise reduction amplitude of about -18dB, which is nearly 33% higher than the average noise reduction effect (-12dB) of the existing technology. In the process of high-frequency signal acquisition, the spectrum leakage problem is effectively reduced through the optimization application of the window function, which greatly improves the recognition rate of high-frequency components. Especially in signal samples 3 and 4 under the sampling frequency of 50kHz, the frequency domain separation accuracy after noise reduction processing reaches 96%, which is significantly improved compared with the 90% accuracy of the traditional system. Through fast Fourier transform and high-precision frequency domain separation algorithm, the system can achieve an average frequency domain separation accuracy of 96% in different frequency samples, especially in high-frequency signal sample 6 (30-45kHz), the separation accuracy reaches 97%. This is significantly different from the traditional method. Traditional filtering systems usually find it difficult to achieve a separation accuracy of more than 95% under similar conditions. Therefore, this system has outstanding innovation in frequency domain signal processing. Through high-precision frequency domain separation, it ensures accurate filtering and efficient retention of high-frequency signal components. The table data shows that the signal accuracy after inverse Fourier transformation is significantly better than the existing technology, with an average accuracy of about 95%. In high-frequency samples 6 and 7, the recovery accuracy reached 98% and 96% respectively, fully demonstrating the advantages of this system in inverse transformation recovery. Compared with the time domain recovery accuracy of traditional systems, which is generally around 90%, this system has significantly improved the fidelity of high-frequency signals during the recovery process. This effect is mainly due to the optimization of frequency domain separation and digital filtering modules in the system design, which effectively reduces low-frequency noise interference while maintaining the original characteristics of high-frequency signals.

[0112] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A high-frequency digital filtering system based on Fourier fast transform, characterized in that: include: Acquisition module, pre-processing module, Fourier transform module, digital filtering module, inverse Fourier transform module, post-processing module and output module; The signal acquisition module is responsible for collecting the analog signal Mnxh and converting it into a digital signal Szxh through an algorithm formula, and transmitting the converted digital signal to the preprocessing module; The preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, obtains a denoised digital signal Qzsz, and performs window processing on the signal through a window function to reduce spectrum leakage, and transmits the processed signal to the Fourier transform module; The Fourier transform module converts the time domain signal into the frequency domain signal through fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation, identifies and extracts the high-frequency signal to be retained and the low-frequency signal to be filtered out, and uniformly transmits the processed signals to the digital filtering module; The digital filtering module applies a filter in the frequency domain, implements signal filtering through a multiplication operation, and transmits the filtered signal to the inverse Fourier transform module; The inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through an algorithm formula and transmits it to the post-processing module; The post-processing module performs window removal processing on the time domain signal, converts the digital signal into an analog signal output, and generates a signal filtering result report and sends it to the output module; The output module displays the signal filtering result report on the visual interface.

2. The high-frequency digital filtering system based on Fourier fast transform according to claim 1, characterized in that: The signal acquisition module is responsible for collecting the analog signal Mnxh and converting it into a digital signal Szxh through an algorithm formula. The conversion formula includes: Sample the continuous analog signal Mnxh(n) in the time domain to obtain discrete signal values: Mnxh[n]=Mnxh(nT) Where n=0,1,2,... represents the number of sampling times, and T represents the sampling time; Quantize the sampled analog signal value Mnxh[n] into a digital signal: Mbxh[n]=Q(Mnxh[n]) Wherein, Mbxh[n] represents the quantized signal, and Q(Mnxh[n]) represents the quantized function; Convert the quantized value into binary digital form to obtain the final digital signal Szxh[n], which is expressed as: Szxh[n]=Encode(Mbxh[n]) Wherein, Encode represents a coding conversion function.

3. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 2, characterized in that: The preprocessing module performs preliminary noise reduction on the transmitted digital signal Szxh, removes low-frequency noise, and obtains a denoised digital signal Qzsz. The denoising formula is: Qzsz[n]=H(f)*Szxh[n] Wherein, Qzsz[n] represents the denoised signal, n=0, 1, 2, ... represents the number of signals, and H(f) represents the frequency response of the high-pass filter.

4. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 3, characterized in that: The formula for the preprocessing module to perform window processing on the denoised signal through the window function is: Qzsz[n]=Mnxh[n]*w[n] Wherein, w[n] represents the window function, and Qzsz[n]=Mnxh[n]*w[n] represents window processing of the denoised signal.

5. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 4, characterized in that: The formula for converting the time domain signal into the frequency domain signal by the Fourier transform module through the fast Fourier transform is as follows: Where X[k] represents the frequency domain signal, k represents the index frequency, Syxh[n] represents the value of the time domain signal at n sampling points, n represents the time index, and N represents the total number of sampling points of the signal; Represents a complex exponential function, frequency dependent in Fourier transform, representing a complex number of rotation.

6. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 5, characterized in that: The Fourier transform module converts the time domain signal into the frequency domain signal through fast Fourier transform, and then applies the algorithm formula to perform frequency domain separation. The frequency domain separation formula is: Fl[k]=Flsignal[k]+Fl noise [k] Among them, Fl[k] represents the signal after frequency domain separation, Flsignal[k] represents the frequency domain of the signal, and Fl noise [k] represents the frequency domain of the noise.

7. A high-frequency digital filtering system based on Fourier fast transform as claimed in claim 6, characterized in that: The digital filtering module applies a filter in the frequency domain and implements signal filtering through multiplication operations. The filtering formula is: Lb[k]=Ht[k]*Fl[k] Wherein, Lb[k] represents the frequency domain of the filtered signal, and Ht[k]*Fl[k] represents the filter Ht[k] applied in the frequency domain to filter the signal Fl[k] separated in the frequency domain.

8. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 7, characterized in that: The inverse Fourier transform module converts the processed frequency domain data back to the time domain signal through an algorithm formula, and the conversion formula is: Where Zh[k] represents the converted time domain signal, k represents the index frequency, Lb[k] represents the frequency domain of the filtered signal, n represents the time index, and N represents the total number of sampling points of the signal; represents the complex exponential function, which represents a rotation of a complex number.

9. The high-frequency digital filtering system based on Fourier fast transform as claimed in claim 8, characterized in that: The post-processing module performs window removal processing on the time domain signal, and the processing formula is: Wherein, Qc[k] represents the signal after window removal, Zh[k] represents the converted time domain signal, and w[n] represents the window function.

10. The high-frequency digital filtering system based on Fourier fast transform according to claim 9, characterized in that: The post-processing module performs windowing on the time domain signal and then converts the digital signal into an analog signal for output. The conversion formula is: Where S(t) represents the converted analog signal, N represents the total number of sampling points of the signal, Qc[k] represents the signal after removing the window, n represents the time index, T represents the sampling period, and δ(t) represents the pulse signal converted from the discrete signal to the time domain.

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