FFT Genlik Spektrumu Tahmini için Sinir Ağı Mimarilerinin Karşılaştırmalı Analizi

Abstract

Bu makale, Hızlı Fourier Dönüşümünün (FFT) büyüklük spektrumunu tahmin etmek için çeşitli sinir ağı (NN) mimarilerinin karşılaştırmalı bir analizini sunmaktadır. Frekans bileşenlerinin büyüklüğünü tahmin etmek için ileri beslemeli sinir ağı (FNN), tekrarlayan sinir ağı (RNN), geçitli yineleyen birim (GRU), uzun-kısa süreli bellek (LSTM), çift yönlü LSTM (BiLSTM) ve tek boyutlu evrişimli sinir ağı (1D-CNN) modelleri kullanılmıştır. Her modelin performansı ortalama kare hata (MSE), ortalama mutlak hata (MAE) ve R-kare (R2) metrikleri kullanılarak değerlendirilmiştir. Deneysel sonuçlar, LSTM modelinin 0.7742 R-kare değeri ve 0.1375 MAE değeri ile diğerlerinden daha iyi performans elde ettiğini göstermektedir. Buna karşılık, FNN modelinin Fourier-dönüşümlü veriler üzerinde sınırlı bir tahmin yeteneği sergilediği, bunun da verilerde bulunan zamansal bağımlılıkları ve karmaşık örüntüleri modelleme kapasitesinin yetersiz olmasından kaynaklandığı düşünülmektedir.

Keywords

• FFT
• LSTM
• Büyüklük Spektrumu Tahmini
• Sinir Ağı Mimarileri
• Zaman Serisi Tahmini

Comparative Analysis of Neural Network Architectures for FFT Magnitude Spectrum Estimation

Abstract

This paper presents a comparative analysis of various neural network (NN) architectures for predicting the magnitude spectrum of the Fast Fourier Transform (FFT). To estimate the magnitude of the frequency components, feedforward neural network (FNN), recurrent neural network (RNN), gated recurrent unit (GRU), long short-term memory (LSTM), bidirectional LSTM (BiLSTM), and one-dimensional convolutional neural network (1D-CNN) architectures were employed. The performance of each model is evaluated using mean squared error (MSE), mean absolute error (MAE), and R-square (R2) metrics. Experimental results show that the LSTM model outperforms the others, achieving an R-square value of 0.7742 and a MAE value of 0.1375. In contrast, the FNN model exhibits limited predictive capability on the Fourier-transformed data, which may be attributed to its insufficient capacity to model the temporal dependencies, and complex patterns present in the data.

Keywords

• FFT
• LSTM
• Magnitude Spectrum Estimation
• Neural Network Architectures
• Time Series Prediction

References

1. Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90), 297–301.
2. Rabiner, L. R., & Schafer, R. W. (1978). Digital processing of speech signals Prentice Hall. New Jersey, 121-123.
3. Acharya, U. R., Sree, S. V., Swapna, G., Martis, R. J., & Suri, J. S. (2013). Automated EEG analysis of epilepsy: a review. Knowledge-Based Systems, 45, 147-165.
4. Kanasewich, E. R. (1981). Time sequence analysis in geophysics (3rd ed.). The University of Alberta Press.
5. Skolnik, M. I. (1980). Introduction to radar systems (Vol. 3, pp. 81-92). New York: McGraw-hill.
6. Proakis, J. G. (2007). Digital signal processing: principles, algorithms, and applications, 4/E. Pearson Education India.
7. Goldsmith, A. (2005). Wireless communications. Cambridge University Press.
8. Subha, D. P., Joseph, P. K., Acharya U, R., & Lim, C. M. (2010). EEG signal analysis: a survey. Journal of medical systems, 34(2), 195-212.

9. Prasad, R. (2004). OFDM for wireless communications systems (Vol. 2). Artech House.
10. Oppenheim, A. V., & Schafer, R. W. (2010). Discrete-time signal processing (3rd ed.). Pearson.
11. Arsalan, M., Santra, A., & Issakov, V. (2023). Power-efficient gesture sensing for edge devices: mimicking fourier transforms with spiking neural networks. Applied Intelligence, 53(12), 15147-15162.
12. Goodfellow, I., Bengio, Y., Courville, A., & Bengio, Y. (2016). Deep learning (Vol. 1, No. 2). Cambridge: MIT press.
13. Elman, J. L. (1990). Finding structure in time. Cognitive Science, 14(2), 179–211.
14. Lipton, Z. C., Berkowitz, J., & Elkan, C. (2015). A critical review of recurrent neural networks for sequence learning. arXiv preprint arXiv:1506.00019.
15. Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078.
16. Hochreiter, S., Jürgen S. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.
17. Singh, K., & Malhotra, J. (2022). Two-layer LSTM network-based prediction of epileptic seizures using EEG spectral features. Complex & Intelligent Systems, 8(3), 2405-2418.
18. Yang, Z., Zhang, Y., Qian, K., & Wu, C. (2023). {SLNet}: A spectrogram learning neural network for deep wireless sensing. In 20th USENIX Symposium on Networked Systems Design and Implementation (NSDI 23) (pp. 1221-1236).
19. Santamaria-Vazquez, E., Martinez-Cagigal, V., Vaquerizo-Villar, F., & Hornero, R. (2020). EEG-inception: a novel deep convolutional neural network for assistive ERP-based brain-computer interfaces. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 28(12), 2773-2782.
20. Sherstinsky, A. (2020). Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network. Physica D: Nonlinear Phenomena, 404, 132306.
21. Oleiwi, Z. C., AlShemmary, E. N., & Al-Augby, S. (2024). Developing hybrid CNN-GRU arrhythmia prediction models using fast Fourier transform on imbalanced ECG datasets. Mathematical Modelling and Engineering Problems, 11, 413–429.
22. Liu, C., Cheng, S., Ding, W., & Arcucci, R. (2023). Spectral cross-domain neural network with soft-adaptive threshold spectral enhancement. IEEE Transactions on Neural Networks and Learning Systems, 36(1), 692–703.
23. Eleyan, A., & Alboghbaish, E. (2024). Electrocardiogram signals classification using deep-learning-based incorporated convolutional neural network and long short-term memory framework. Computers, 13(2), 55.
24. Yemets, K., Izonin, I., & Dronyuk, I. (2025). Enhancing the FFT LSTM time series forecasting model via a novel FFT based feature extraction–extension scheme. Knowledge, 9(2), 35.
25. Zouaidia, K., Ghanemi, S., & Rais, M. S. (2021). Hourly wind speed forecasting using FFT-encoder-decoder-LSTM in south west of Algeria (Adrar). International Journal of Informatics and Applied Mathematics, 4(1), 72-83.
26. Cen, S., Kim, D. O., & Lim, C. G. (2023). A fused CNN‐LSTM model using FFT with application to real‐time power quality disturbances recognition. Energy Science & Engineering, 11(7), 2267-2280.
27. Westhausen, N. L., & Meyer, B. T. (2020). Dual-signal transformation LSTM network for real-time noise suppression. arXiv preprint arXiv:2005.07551.
28. Jain, G., Sharma, M., & Agarwal, B. (2019). Optimizing semantic LSTM for spam detection. International Journal of Information Technology, 11, 239–250.
29. Berghian-Grosan, C., Isik, S., Porav, A. S., Dag, I., Ay, K. O., & Vithoulkas, G. (2024). Ultra-high dilutions analysis: Exploring the effects of potentization by electron microscopy, Raman spectroscopy and deep learning. Journal of Molecular Liquids, 401, 124537.
30. Yazar, I., Anagun, Y., & Isik, S. (2025). Predicting compressor mass flow rate using various machine learning approaches. International Journal of Turbo & Jet-Engines, 42(1), 15–21.
31. Tieleman, T., & Hinton, G. (2012). Lecture 6.5—RMSProp. In Neural Networks for Machine Learning. Coursera.