Design of optimized radix-2 and radix-4 butterflies from FFT with decimation in time

Neuenfeld, Renato; Fonseca, Mateus Beck; Costa, Eduardo

doi:10.1109/lascas.2016.7451037

Cited by 19 publications

(5 citation statements)

References 7 publications

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“…In the present mobile application, it was chosen the frequency recognition through the Fast Fourier Transform Radix-2 algorithm, according to [8], making use of the native Java development kit, while for the execution of MIDI sounds, the model that was done in [7] was retaken.…”

Section: Related Workmentioning

confidence: 99%

“…The input and output of an FFT are expressed in complex numbers, in this case, for its implementation, two arrangements are accepted to store the real and imaginary components in them, when using the recording tools of mobile devices, all the bytes of audio information are obtained, which are used within the real components, while the imaginary components are always filled with zeros, the output of the algorithm is contained in two other arrays, one corresponding to each type of component, where the frequency spectra are stored, since only the actual samples are used for input, only the first half of the components need to be analyzed. Each component of the frequency spectrum is related to the previous component, since it is the sampling frequency divided by the number of samples of the FFT [8].…”

Section: B Fast Fourier Transform (Fft)mentioning

confidence: 99%

“…The FFT algorithm used to develop the mobile application is Radix-2, which means that it must work on a group of samples whose number is a power of two [8].…”

Section: B Fast Fourier Transform (Fft)mentioning

confidence: 99%

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Monophonic Guitar Synthesizer via Mobile App

Leyva¹,

Ledesma²,

Orozco³

et al. 2021

IJACSA

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In the guild of guitarists, it is common to work with guitar synthesizers because the emulation of a great variety of sounds that are produced by different musical instruments, starting from just playing the guitar, which means, a piece of music is played with a guitar, but other musical instruments are actually heard such as, a saxophone, a violin, a piano or percussions, depending on the instrument that has been selected. The problem that arises in this article is that synthesizers are expensive and due to their size, the transportation of the equipment is often impractical. As mentioned, the development of a mobile application that has the function of a monophonic synthesizer is proposed as a solution. In this way, the cost is greatly reduced, and additionally, the user is able to install the application on a mobile device with Android operating system and connect it to an electric or electro-acoustic guitar through an audio interface; obtaining as a result, a functional technological instrument by offering guitarists an alternative with respect to conventional synthesizers. The construction of this application used the Fast Fourier Transform Radix-2 as a signal recognition algorithm, which allowed obtaining the fundamental frequencies generated by the guitar, which were transformed into MIDI notation and later used in sound emulation.

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Section: Related Workmentioning

confidence: 99%

Section: B Fast Fourier Transform (Fft)mentioning

confidence: 99%

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Monophonic Guitar Synthesizer via Mobile App

Leyva¹,

Ledesma²,

Orozco³

et al. 2021

IJACSA

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“…Equation ( 14) can be simplified as (17). It is treated as a 4-point DFT and can be realized using one butterfly radix-4 DIT-FFT algorithm [30].…”

Section: B Mixed-radix Butterfly-based 1-d Sdft Structurementioning

confidence: 99%

A Non-Feedback-Loop and Low-Computation- Complexity Algorithm Design for a Novel 2-D Sliding DFT Computation

Juang

Lai

2019

IEEE Access

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This paper presents a forward-path, novel, two-dimensional (2-D) sliding discrete Fourier transform (SDFT) algorithm based on the column-row 2-D DFT concept and the shifted window property. After applying a descending dimension method (DDM), a mixed-radix and butterfly-based structure can be further employed to effectively implement the proposed algorithm. Conceptually, it has many advantages, including greater stability, more accuracy, and less computational complexity because there are no extra feedback loops in the calculation. The evaluation results are based on the following conditions: (1) the window size (N ) to 16 × 16; (2) the test pattern is an SVC grayscale video, and the formats are CIF and 4CIF with 30fps; (3) one multiplication involves four real multiplications and two real additions. The proposed 2-D SDFT method clearly reduced the number of multiplications by 43.8% and only increased the number of additions by 33%, compared with the state-of-the-art Park's method. Additionally, for the first 100 frames of the CIF and 4CIF sequences, the proposed method saves 10.8% and 10.9% of the processing time, respectively, on average. Overall, the proposed DDM-based 2-D SDFT algorithm can be applied to calculate not only 1-D but also 2-D SDFT spectrum, and are especially appropriate for hybrid applications. INDEX TERMSSliding discrete Fourier transform (SDFT), two-dimension SDFT (2-D SDFT), column-row 2-D DFT, descending dimension method (DDM), DDM-based 2-D SDFT.

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“…These can be defined as follows, radix-2 algorithm consists of log 2 N stages, and each stage consists of N/2 stage blocks, and each block consists of 2 stage−1 butterflies. As in signal processing (digital), most of the required arithmetic computations are additions and multiplications, radix-2 offers N/2 × log 2 N complex multiplications and N × log 2 N complex additions [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%