The Discrete Fourier Transform and its Applications to Signal and Image Processing

2021 ◽  
pp. 31-103
Author(s):  
Akarshika Singhal ◽  
Anjana Goen ◽  
Tanu Trushna Mohapatrara

The Discrete Fourier Transform (DFT) can be implemented very fast using Fast Fourier Transform (FFT). It is one of the finest operation in the area of digital signal and image processing. FFT is a luxurious operation in terms of MAC. To achieve FFT calculation with a many points and with maximum number of samples the MACs requirement could not be matched by efficient hardware’s like DSP. A parallel and pipelined Fast Fourier Transform (FFT) processor for use in the Orthogonal Frequency division Multiplexer (OFDM) and WLAN, unlike being stored in the traditional ROM. The twiddle factors in our pipelined FFT processor can be accessed directly. In this paper, we present the implementation of fast algorithms for the DFT for evaluating their performance. The performance of this algorithm by implementing them on the Xillinx 9.2i Spartan 3E FPGAs  by developing our own FFT processor architecture.


Signal processing algorithms like Discrete Fourier Transform, Discrete Cosine Transform, and Fast Fourier Transform Transforms find various applications in the field of Image processing, Wireless communication, Robotics, and many others. It covers basically three operations viz. Multiply, Shift and Accumulate. Hence if the input data goes on rising as in cases where high resolution is required the amount of multiply operations also rises significantly. For example the number of complex multiply operations in case of Discrete Fourier Transform is N2 , where N is the number of points. Latency becomes an important issue which needs to be addressed in today’s era as we, humans, thrive for the fastest systems with maximum resolution. To reduce latency we need to either emphasize on reduction in amount of data to be processed or change the processing structure which can affect the overall time to output. Multiplierless techniques for this purpose has been always a research area as it helps in reduction of the later part. Coordinate rotation of digital computer (CORDIC) based techniques are well known for the Multiplierless implementation of the sinusoids. However it carries certain drawbacks viz. large number of iterations and accuracy. This paper provides Coefficient combined & shift and add implementation (CCSSI) based approach for the design of Multiplierless rotators for various transforms for multiple constant rotators as well. The approach improves the range of coefficients with respect to number of adders (the range taken is from 4 to 10 adders) and number of point (the range taken is from 1 to 64 points) compared to the existing approaches and is shown in the results. It also presents a novel tunable Multiplierless architecture.


Information ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 257
Author(s):  
Alessandro Massaro ◽  
Giovanni Dipierro ◽  
Emanuele Cannella ◽  
Angelo Maurizio Galiano

The present paper discusses a comparative application of image processing techniques, i.e., Discrete Fourier Transform, K-Means clustering and Artificial Neural Network, for the detection of defects in the industrial context of assembled tires. The used Artificial Neural Network technique is based on Long Short-Term Memory and Fully Connected neural networks. The investigations focus on the monitoring and quality control of defects, which may appear on the external surface of tires after being assembled. Those defects are caused from tires which are not properly assembled to their respective metallic wheel rim, generating deformations and scrapes which are not desired. The proposed image processing techniques are applied on raw high-resolution images, which are acquired by in-line imaging and optical instruments. All the described techniques, i.e., Discrete Fourier Transform, K-Means clustering and Long Short-Term Memory, were able to determine defected and acceptable external tire surfaces. The proposed research is taken in the context of an industrial project which focuses on the development of automated quality control and monitoring methodologies, within the field of Industry 4.0 facilities. The image processing techniques are thus meant to be adopted into production processes, giving a strong support to the in-line quality control phase.


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