Fast Fourier Transform (FFT)

"This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform.
In terms of multiplicative complexity, both algorithms are more efficient, in general, than the well known Goertzel Algorithm."

The master thesis studies the applicability of Black-Scholes-Model extensions to pricing options on stock indices. Polish options on the WIG20 stock index traded on the GPW the provide for the object of the study. The thesis analyses the characteristics of the Polish derivative market and applies stochastic theory to pricing Polish options. The traditional Black-Scholes-Merton model is extended to accommodate various stochastic approaches including Martingale Pricing methods, Fourier Transforms, and Monte-Carlo simulation. The approaches are implemented by means of the Python computer language. The results produced by different pricing methods are compared to the results of the standard Black-Scholes-Merton.

[the download only contains excerpts, but you are welcome to contact me for more info]

In this paper, a similarity measure for images based on values from their respective Fourier Transforms is proposed for image registration. The approach uses image content to generate signatures and is not based on image annotation and therefore does not require human assistance. It uses both, the real and complex components of the FFT to compute the final rank for measuring similarity. Any robust approach must accurately represent all objects in an image and depending on the size of the image data set, diverse techniques may need to be followed. This paper discusses implementation of a similarity rating scheme through the Open CV library and introduces a metric for comparison, carried out by considering Intersection bounds of a covariance matrix of two compared images with normalized values of the Magnitude and Phase spectrum. Sample results on a test collection are given along with data using existing methods of image histogram comparison. Results have shown that this method is particularly advantageous in images with varying degrees of lighting.

One of the greatest environmental issues we face today is the accumulation of non-degradable plastics. Plastic debris are discarded every year, everywhere polluting the nature. Polyhydroxybutyrate (PHB) is produced by joining of poly ß-hydroxybutyrate monomers by ester bonds. Bioplastics have numerous applications in different fields of life they are used in clothing industrial products, fluid containers, surgical materials. PHB is completely biodegradable and highly hydrophobic thermoplastic polyester. The aim of this study is to yield high and efficient PHB accumulation bacteria has been selected by quantification and extraction method. The culture medium and growth parameters for all the isolates were optimized for maximum production. The highest PHB production was observed with groundnut oil cake with 27% respectively and orange peel 23% respectively. The optimum PHB production condition were observed in 48h and 72h at 30°C. Authentication of PHB extract by Fourier transform-infrared (FTIR) by identifying its functional units as C-H, CH2, C=O, and CO. The yield of PHB can further optimized by production parameters as substrates. Keywords: Polyhydroxybutyrate (PHB), agro-industrial waste, fourier-transform infrared spectroscopy (FTIR).

La evolución humana u hominización es el proceso de evolución biológica de la especie humana desde sus ancestros hasta el estado actual. El estudio de dicho proceso requiere un análisis interdisciplinar en el que se aúnen conocimientos procedentes de ciencias como lagenética, la antropología física, la paleontología, la estratigrafía, la geocronología, la arqueología y la lingüística.

Presenting novel designs for a Ripple Carry Adder, a Subtractor, and a Pipelined Array Multiplier using the Five-input Majority Gate (MAJ5) in Quantum-dor Cellular Automata (QCA). These designs are then used to implement the Fast Fourier Transform (FFT) Algorithm. The FFT implementation was previously introduced in 2012. However, it suffered from inefficiencies in terms of both area and speed, which are essential features for the aforementioned algorithm. The new designs are designed, optimized, and simulated using QCADesigner. It is shown that they indeed achieve higher levels of compactness and speed, due largely to the utilization of MAJ5, in addition to a new wire-crossing scheme suggested by another group. These building blocks are then used to optimize the FFT QCA implementation.

Neste trabalho é introduzido um novo algoritmo, desenvolvido no ambiente Matlab, para realizar uma estimação dos coeficientes de uma série trigonométrica de Fourier, baseado no método dos mínimos quadrados seqüencial. São apresentadas  simulações e resultados obtidos usando dados experimentais.

Rotating machines are an integral part of large electrical power machinery in most of the industries. Any degradation or outages in the rotating electric machinery can result in significant losses in productivity. It is critical to monitor the equipment for any degradation’s so that it can serve as an early warning for adequate maintenance activities and repair. Prior research and field studies have indicated that the rotating machines have a particular type of signal structure during the initial start-up transient. This signal structure can be modelled by an exponentially damped sinusoidal signal during initial start-up. The major focus of this project is to take advantage of this a prior knowledge of signal structure to study the effect of degradation in two main signal parameters: frequency components of transient signal and the associated exponential damping factor.
In this work, a data acquisition system is first used to sample the transient signal. This signal is analysed on an embedded TMS320 based DSP core platform. Both FFT and MPM estimators have been implemented to study various signals captured by the data-acquisition system. For measuring the frequency of operation, both FFT and MPM were employed whereas the damping coefficient is calculated using MPM method. Initial implementation and validation was conducted in MATLAB and Simulink. Once validated, the code was ported on to TMS320 platform. The results show good agreement with expected results for both simulated and real-time data. The real-time data from AC water pumps which have rotating motors built-in were collected and analysed.
It is found that the frequency estimation performance of the MPM matches that of the FFT for synthetic and real time data. The evaluation of the condition of machines based on the damping coefficient using MPM matched with the actual condition of the machine.

Induction motors are widely used in transportation, mining, petrochemical, manufacturing and in almost every other field dealing with electrical power. These motors are simple, efficient, highly robust and rugged thus offering a very high degree of reliability. But like any other machine, they are vulnerable to faults, which if left unmonitored, might lead to catastrophic failure of the machine in the long run. On-line
condition monitoring of the induction motors has been widely used in the detection of faults. This paper delves into the various faults and study of conventional and innovative techniques for induction motor faults with an identification of future research areas.

Ce TP a pour objectif de prendre en main le logiciel MATLAB. Les notions traitées sont la manipulation de variables aléatoires et de vecteurs, l’utilisation de fonctions, la représentation graphique, la génération de nombres aléatoires, le calcul d’écart-type de la variance, le calcul de la variance et la corrélation et la génération des signaux aléatoires en utilisant des systèmes linéaires invariants dans le temps. En ce qui concerne la 2 ème  partie, on étudie les propriétés du filtrage adaptatif (filtre de Wiener) en utilisant l’algorithme LMS.

Banyak referensi mengenai metode Fast Fourier Transform, akan tetapi masih jarang yang berbahasa Indonesia dan runtut. Paper ini dibuat dengan tujuan agar mempermudah dalam mempelajari Fast Fourier Transform DIT (Decimation In Time). Asalkan pembaca mau membaca dengan pelan-pelan dan runtut, insyaAllah metode FFT DIT ini dapat mudah dipahami dan diimplementasikan secara manual.

Définition : sauter en hauteur, c'est se projeter dans l'espace en vue de franchir un obstacle vertical. Logique interne : traits caractéristiques-appel un pied-performance chiffrée = mesure hauteur obstacle-nombre d'essai limité, chaque essai à effectuer dans un temps limité-piste d'élan limitée Problèmes fondamentaux :-trouver compromis entre vitesse horizontale et verticale-créer et conserver vitesse (et donc énergie) = continuité entre course et impulsion-organiser un placement du corps et des segments permettant cette continuité-perceptifs (dos à la barre)-affectifs (course en courbe inhabituelle et chute sur le dos dans l'espace arrière) Enjeux de formation : transformation de ressources-cognitifs et affectifs : réussir épreuve comportant un certain risque, estime de soi gestion des essais (impasses…) informationnelles : anticipation coïncidence (point d'appel, marques…) analyse trajectoire position du corps dans l'espace-biomécaniques : coordination = enchaînement des phases dissociation = rôle jambe d'appui / jambe libre, rôles des bras… équilibration = dans la course et au dessus de la barre-énergétiques : gestion du concours (nombre d'essai) gainage, souplesse… Analyse technique et biomécanique : Le saut en hauteur est un saut à dominante verticale. 1) la course d'élan : L'élan s'effectue sur une trajectoire composée d'une partie rectiligne perpendiculaire au plan de la barre suivie d'une deuxième partie curviligne. Il s'agit dans un premier temps de créer de la vitesse, l'emmagasiner grâce à une course haute et dynamique pour ensuite pouvoir l'utiliser la plus efficacement possible lors de l'impulsion.

O objetivo da pesquisa foi realizar um estudo sobre a Transformada de Fourier, visando o entendimento em sua forma contínua e discreta, para a compreensão do algoritmo que efetua a Transformada Rápida de Fourier (FFT), direcionado para calcular a dinâmica de sistemas magnéticos nanoestruturados. No período do projeto foi feito um levantamento bibliográfico sobre o algoritmo da transformada rápida de Fourier aplicado a sistemas magnéticos. Buscamos os conteúdos didáticos mais relevantes sobre o assunto para elaboração do trabalho e propositalmente compreensão dos algoritmos, também foi realizado o estudo da linguagem de programação Fortran e de ferramentas computacionais, como: compiladores (para implementação dos algoritmos) e programas de plotagem gráfica (para gerar os gráficos dos dados produzidos pelos sistemas). Após o domínio da sub-rotina que calcula a tal transformada sobre as
imagens de uma função, foram implementados os sistemas ou programas para fazer as simulações com a mesma, dando
início a etapa de coleta de dados e geração de resultados. Foram realizadas simulações em sistemas magnéticos ferromagnéticos e antiferromagnéticos. Identificamos os picos de ressonância gerados pela FFT com o auxílio de um programa de plotagem gráfica. Resultados conhecidos da literatura foram reproduzidos satisfatoriamente. Os resultados mostram que a Transformada de Fourier, através do algoritmo FFT é um método viável para o estudo de dinâmicas em sistemas físicos de ordem nanométrica, sendo com isso, favorável para nossas simulações.

ABSTRAK Fast Fourier Transform (FFT) adalah suatu algoritma untuk menghitung transformasi Fourier diskrit (Discrete Fourier Transform, DFT) dengan cepat dan efisien. Transformasi Fourier cepat diterapkan dalam beragam bidang, mulai dari pengolahan sinyal digital, memecahkan persamaan diferensial parsial, dan untuk algoritma untuk mengalikan bilangan bulat besar. Ada pun kelas dasar dari algoritma FFT yaitu decimation in time (DIT) dan decimation in frequency (DIF). Garis besar dari kata fast diartikan karena formulasi FFT jauh lebih cepat dibandingkan dengan metode perhitungan algoritma Fourier Transform sebelumnya. Pada penelitian tugas akhir ini telah dibuat suatu aplikasi sistem pengolahan suara untuk menampilkan output frequency FFT, gelombang sinyal suara dan sederetan nilai waktu pada file data suara berbentuk .wav. Tool yang digunakan untuk membuat aplikasi sistem pengolahan suara yaitu Matlab 2013a. Metode yang digunakan pada aplikasi ini metode waterfall.

Voice recognition is becoming more and more important in everyday life of people. In real world there are many ways of implementing those algorithms but as we learn Fourier Transform why not to try. So our team’s main goal is to implement simple algorithm based on Fourier Transform to recognize “YES” or “NO” words.For signals, this is typically done via the cross-correlation function (of two signals) which is very similar to convolution. As such, it can be mathematically done via the FFT, which is specifically designed to be efficient. Once you take the correlation function, you can decide what threshold you want to be a "match".
In mathematics, the discrete Fourier transform (DFT) is a specific kind of Fourier transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function (which is often a function in the time domain). But the DFT requires an input function that is discrete and whose non-zero values have a limited (finite) duration. Such inputs are often created by sampling a continuous function, like a person's voice. And unlike the discrete-time Fourier transform (DTFT), it only evaluates enough frequency components to reconstruct the finite segment that was analyzed. Its inverse transform cannot reproduce the entire time domain, unless the input happens to be periodic (forever).
Therefore it is often said that the DFT is a transform for Fourier analysis of finite-domain discrete-time functions. The sinusoidal basis functions of the decomposition have the same properties.
Since FFT algorithms are so commonly employed to compute the DFT, the two terms are often used interchangeably in colloquial settings, although there is a clear distinction: "DFT" refers to a mathematical transformation, regardless of how it is computed, while "FFT" refers to any one of several efficient algorithms for the DFT.

Serealia memiliki komponen gizi berupa karbohidrat yang tinggi. Hal tersebut kemudian dilakukan berbagai pengolahan dengan pendekatan adanya karbohidrat tinggi pada bahan pangan tersebut. Tidak hanya itu, kandungan gizi lainnya juga turut terdapat pada bahan pangan tersebut, kemudian ikut dalam mengambil bagian untuk menentukan produk akhir dari proses pengolahan tersebut, sehingga kemudian menghasilkan produk pangan serealia yang beragam dan kemudian mampu mendiversifikasi pangan dari komoditas ini serta mampu cara/teknis pengolahannya agar dapat menghasilkan nilai jual komoditas tersebut. Tanaman padi (Oryza sativa L.) merupakan tanaman yang berasal dari kawasan Asia, di mana kultivarnya telah tumbuh di dunia hingga mencapai 2000 varietas. Tanaman ini cenderung tumbuh di kawasan yang beriklim tropis bersifat tinggidan lemah, dengan daun-daun yang melengkung ke bawah dan masa dormansinya lama (Haryadi, 2006). Banyak kultivar tanaman ini yang dikenal karena kualitas hasil panennya yang sangat digemari oleh masyarakat seperti varietas Rojolele, varietas IR 64 (varietas kembangan dari Kementrian Pertanian), varietas Cianjur, dan masih banyak varietas lainnya yang dapat dijumpai di kalangan masyarakat.

Ce TP a pour objectif de corriger le son afin d’obtenir une bonne qualité d’un enregis-
trement (du son), ainsi qu’appliquer les relations et les lois vu en traitement de signal.
Il a pour but de :
1. Etude théorique du son et caractérisation du bruit
2. Caractérisation et filtrage du bruit
3. Génération et filtrage de l’écho

The Colorado River flows more than 2400 kilometers, from its source in the Rocky Mountains in the United States through deserts and canyons, to the wetlands of a delta into the Gulf of California in Mexico. Detection of variations over the long term for a series of hydrological variables is an important and critical issue, which is subject to increasing interest because of the current topic of climate change. This study covers a 70 year time period from 1940 to 2010, using a Fast Fourier Transform (FFT) analysis of 118 daily precipitation sites located throughout the Colorado River basin. Tests for homogeneity and independence are applied to the data series; also a regression analysis is used just in specific cases. The data series of the stations is characterized as a function of frequency domain in order to identify a return rate of hydro-meteorological variables within the basin, verifying the existence of dominant periodic cycles in the data series. Different magnitudes in the precipitation periodicity are also examined. It is concluded that the precipitation of the Colorado River basin behaves in dominant periodic cycles of approximately 10.7 or 12.8 years. Nevertheless, there are three small areas in the basin which react in a different way: the mountains of Arizona showed a dominant period of 8 years; the higher elevations in the state of Colorado, 6.4 years; and the peaks of Wyoming, 4.6 years. These identified areas are the highest peaks where precipitation is more frequent. Besides, the moving average adjusts over a constant 13 year period for the data series of the stations. This suggests that precipitation in the basin completes a cycle every 13 years, verifying the FFT results. The FFT analysis may also be applied for frequency detection of other hydro-climatic variables such as temperature, humidity, streamflow and evapotranspiration.

Este trabalho avalia o desempenho comparativo das transformadas rápidas de Fourier e de Hartley, servindo-se do  algoritmo Cooley-Tukey radix-2 implementado no microcontrolador ESP8266. No desempenho comparativo considerou-se o tempo de execução do algoritmo para comprimentos diferentes dos dados de entrada. Os resultados obtidos apresentam um ganho na velocidade de processamento da ordem de 34% com o emprego da transformada rápida de Hartley em relação à de Fourier. Foi desenvolvido também um protótipo de analisador de vibrações mecânicas empregando a transformada rápida de Hartley e o acelerômetro MPU6050.

Growth in technology has led to unprecedented demand for high speed architectures for complex signal processing applications. In 4G wireless communication systems, bandwidth is a precious commodity, and service providers are continuously met with the challenge of accommodating more users with in a limited allocated bandwidth. To increase data rate of wireless medium with higher performance, OFDM (orthogonal frequency division multiplexing) is used. Recently DWT (Discrete wavelet transforms) is adopted in place of FFT (Fast Fourier transform) for frequency translation. Modulation schemes such as 16-QAM, 32-QAM, 64-QAM and 128-QAM (Quadrature amplitude modulation) have been used in the developed OFDM system for both DWT and FFT based model. In this paper we propose a DWT-IDWT based OFDM transmitter and receiver that achieve better performance in terms SNR and BER for AWGN channel. It proves all the wavelet families better over the IFFT-FFT implementation. The OFDM model is developed using Simulink, various test cases have been considered to verify its performance. The DWT-OFDM using Lifting Scheme architecture is implemented on FPGA optimizing hardware, speed & cost. The wavelet filter used for this is Daubechies (9, 7) with N=2. The RTL code is written in Verilog-HDL and simulated in Modelsim. The design is then synthesized in Xilinx and implemented on Virtex5 FPGA board and the results were validated using ChipScope.

— Electrical machines are devices that change either mechanical or electrical energy to the other and also can alternate the voltage levels of an alternating current. The need for electrical machines cannot be overemphasized since they are used in various applications in the world today. Its design is to meet the specifications as stated by the user and this design has to be an economical one. The design therefore revolves around designing the machine to meet the stipulated performance required, the cost available and the lasting life of the machine. This work aims to eliminate the tediousness involved in the manual hand calculations of designing the machines by making use of a graphical user interface and using iterations in situations where the data would have been assumed.

This paper briefly discusses various types of inverters
and the output waveforms of square wave inverter and SPWM
inverter. FFT analysis is performed on the outputs obtained for
SPWM inverter. The variation in THD by varying the
Modulating Index and Carrier Frequency is also included.

This paper aims at development and performance analysis of a speaker dependent speech recognition system using MATLAB®. The issues that were considered are 1) Can Matlab, be effectively used to complete the aforementioned task, 2) Accuracy of the Gaussian Mixture Model used for parametric modelling, 3) Performance analysis of the system, 4) Performance of the Gaussian Mixture Model as a parametric modelling technique as compared to other modelling technique and 5) Can a Matlab® based Speech recognition system be ported to a real world environment for recording and performing complex voice commands. The aforementioned system is designed to recognize isolated utterances of digits 0-9. The system is developed such that it can easily be extended to multisyllabic words as well.

El habla es un tipo de señal complicada producto del resultado de una serie de transformaciones ocurridos en diferentes niveles: semántica, lingüı́stica y acústica. Entonces estas transformaciones conducen a diferencias en las caracterı́sticas de un individuo ampliamente estudiadas por la Biometrı́a. La identificación de locutor (indentificar quiénes la persona que emitió la voz) en sistesis, es un análisis detallado de las caracterı́sticas únicas del habla de cada individuo basado en untuaciones. En este contexto este proyecto se centro en la identificación de locutor mediante palabras aisladas usando Modelos Ocultos de Markov ó Hidden Markov Model (HMM) adicionalmente se restimaron los parametros en los modulos de extraccion de caracteristicas y el tamaño de los codebooks para aumentar la eficacia de identificar un locutor que se describe en tres pasos: Extracción de carácteristicas, modelado e identificación, escribiendose para cada paso la teorı́a y la implementación del código fuente en Java para algunos casos. Iniciando el procesamiento de voz para obtener las caracterı́sticas más importantes de un individuo se utilizó Coeficientes Cepstrales en las Frecuencias Mel ó Mel Frequency Cepstral
Cofficients(MFCC), debido a que en la actualidad otorgan los mejores resultados en el análisis Cepstral según el estado de arte,posteriormente; se hiso uso de la cuantificación vectorial ó Vector quantization (VQ)  grupando los datos (vectores caracterı́sticos) por medio del algoritmo de clasificación K-means, que mejora sustancialmente el tiempo de procesamiento. Para el modelamiento de los datos se hiso uso de los  HMM, asumiendo el modelo estadı́stico como un proceso de Markov, los HMM fueron entrenados para generar la secuencia de observaciones (sı́mbolos de observación), para luego encontrar la secuencia de estados con mayor probabilidad determinados por el algoritmo de Viterbi. Adicionalmente se restimaron los parametros de los modulos de pre procesamiento, extracción de caracteristicas y el cuantificador vectorial basado en codebooks, para sugerir el tamaño de codebook mas adecuado para aumentar la taza de identificación de locutor. Finalmente, nuestros resultados experimentales muestran a detalle los parámetros con los que se obtienen mejores resultados teniendo un 90 % de aceptación para un grupo reducido y cerrado de 5 personas en condiciones reales (con ruido de fondo) con una tendencia de decrecimiento a medida que aumenta el número de población y una mayor efectividad en condiciones ideales (ambiente cerrado y sin ruido de fondo).

É objectivo deste artigo mostrar quais são as capacidades
e limitações do uso da plataforma de desenvolvimento
Arduino, num caso concreto, o cálculo da FFT (Fast Fourier
Transform) para diferentes frequências do sinal de entrada.
Para tal vão ser efectuadas algumas medições de carácter
prático utilizando o modelo Arduino Duemilinove.
Como segundo objectivo, e não menos importante,
espera-se fazer uma comparação entre os microcontroladores
utilizados nos modelos Arduino Mega com ATmega1280,
Arduino Duemilinove com ATmega168 e Arduino Duemilinove
com ATmega328. Tentando assim dar uma perspectiva
das suas capacidades e limitações neste campo.

This document presents the implementation of the FFT algorithm in a general purpose microprocessor on the Arduino Mega 2560 board. A program was made that allowed capturing two different analog signals through ADC and calculating the FFT in both channels. The results from the calculations were sent by serial communication to a PC where they were plotted in real time

This unique study investigates the frequency spectrum of certain Rosicrucian vowel chants using PRAAT (Boersma 2001, 341-345) software and analysis. Certain Rosicrucian vowel sound intonations, which are shared by other traditions, were pre-recorded in a recording studio and analyzed. Given that many physiological, emotional, and psychic effects are experienced by both the intoner and the listener when these vowel sounds are produced, the frequency characteristics of such sounds may lead to correlations that reveal the cause of their health-producing effects. Studies of intensity vs. time and spectral characteristics related to the pitch and formant of the sound were also considered. It is anticipated that the results will provide a deeper understanding of the relationships between frequencies and their possible " resonant " effects on tissues. Sommaire Cette étude unique étudie le spectre de fréquence de certains chants de voyelles rosicruciens en utilisant le logiciel PRAAT (Boersma 2001, 341-345) et l'analyse. Certaines intonations de voyelles Rosicruciennes partagées par d'autres traditions ont été préenregistrées dans un studio d'enregistrement et analysées. Étant donné que de nombreux effets physiologiques, émotionnels et psychiques sont ressentis par le chanteur et l'auditeur lorsque ces sons vocaliques sont produits, les caractéristiques de fréquence de ces sons peuvent conduire à des corrélations qui révèlent la cause de leurs effets bénéfiques sur la santé. Des études de l'intensité en fonction du temps et des caractéristiques spectrales liées à la hauteur et au formant du son ont également considérées. On s'attend à ce que les résultats fournissent une compréhension plus profonde des relations entre les fréquences et de leurs possibles effets « résonnants » sur les tissus. Análisis Fourier de la entonación de ciertos sonidos vocales místicos utilizando el sistema PRAAT

Explorations of a new mapping strategy for spectral spatial- isation demonstrate a concise and flexible control of both spatiomorphology and spectromorphology. With the crea- tion of customized software by the author for audio-rate histograms, spectral processing function smoothing, spec- tral centroid width modulation, audio-rate distance-based amplitude panning, audio-rate ambisonic equivalent pan- ning, a growing library of audio trajectory functions, and an assortment of spectral transformation functions, this article aims to explain the rationale of this process.

In this paper, we propose a simulation-before-test (SBT) fault diagnosis methodology based on the use of a fault dictionary approach. This technique allows the detection and localization of the most likely defects of open-circuit type occurring in Complementary Metal-Oxide-Semiconductor (CMOS) analog integrated circuits (ICs) interconnects. The fault dictionary is built by simulating the most likely defects causing the faults to be detected at the layout level. Then, for each injected fault, the spectre's frequency responses and the power consumption obtained by simulation are stored in a table which constitutes the fault dictionary. In fact, each line in the fault dictionary constitutes a fault signature used to identify and locate a considered defect. When testing, the circuit under test is excited with the same stimulus, and the responses obtained are compared to the stored ones. To prove the efficiency of the proposed technique, a full custom CMOS operational amplifier is implemented in 0.25 µm technology and the most likely faults of opencircuit type are deliberately injected and simulated at the layout level.

An implementation of a spectrum snalyzer with Arduino using Goertzel Algorithm.

[PT] Implementação de um analisador de espectro de frequência em uma matriz de led com o Arduino Pro Mini usando um amplificador operacional e um microfone. O  algoritmo usando foi o de DFT de Goertzel.

The article introduces the theoretical foundations of the modern method of storing, transmitting and processing signals: digital processing. It’s a way to use relatively small number of values instead of continuous real signal.  For example, when transmitting information in telephony, speech is concentrated in the bandwidth up to 4 kHz. But we need doubled frequency 8 kHz sampling in digital form. This is a fundamental requirement. The reason is that the sampled signal is not just a set of quantities, but a set of short scaled pulses of large value. Resulting spectrum has multiple copies of original one infinitely duplicated on sampling frequency steps. If these copies do not overlap significant (due to the limited original useful spectrum) we could restore initial signal with filtering just one of them. That’s why doubled sampling frequency is needed. If the number of samples used is finite (as in the real cases), then we can use only an equal number of samples of the spectrum (or ...

Fault diagnosis of the rotary machines is investigated through different kinds of signals. However, the literature shows that the vibration signal analysis is the most commonly used and effective approach. This research investigates the engine faults, including the misfire and valve clearance faults, using the vibration data captured by four sensors placed in different locations of the automobile engine and under different experimental circumstances. The application of the Fast Fourier Transform (FFT) is proposed as a feature extraction methodology which leads to the extraction of 16 features. In addition, four features are extracted using the acquired signals eigenvalues. The statistical approach is proposed to select features for classification of the engine's state. The Artificial Neural Networks (ANN), Support Vector Machines (SVM), and k Nearest Neighbor (kNN) classification algorithms are employed to predict if the motor works healthily based on the selected features and, if not, what kind of faults is in the engine. The performance of ANN, SVM, and kNN in fault diagnosis is analyzed considering different scenarios, features, and based on multiple performance metrics. Comparing the results with the similar efforts in the literature proves the validity of the proposed methods and highlights their superiorities.

— The Radix-2 decimation-in-time Fast Fourier Transform is the simplest and most common form of the Cooley–Tukey algorithm. The FFT is one of the most widely used digital signal processing algorithms. It is used to compute the Discrete Fourier Transform and its inverse. It is widely used in noise reduction, global motion estimation and orthogonal-frequency-division-multiplexing systems such as wireless LAN, digital video broadcasting, digital audio broadcasting. It is described as the most important numerical algorithm of our lifetime. The number of applications for this transform continues to grow. The Decimation-In-Time radix-2 FFT using butterflies has designed. The butterfly operation is faster. The outputs of the shorter transforms are reused to compute many outputs, thus the total computational cost becomes less. The 32 bit input FFT is synthesized using Verilog. The simulation results and the implementation details such as design summary, RTL schematic and others can be noticed. The design is developed using hardware description language VHDL / Verilog on Xilinx 14.2 xc3s500E. Keywords-Fast Fourier Transform (FFT); Decimation in Time (DIT); Radix-2 I. INTRODUCTION The Discrete Fourier transform (DFT) is obtained by decomposing a sequence of values into components of different frequencies. The Fast Fourier transforms (FFTs) are the efficient algorithms to compute the DFT. The FFT algorithms are based on the principle of decomposing the computation of DFT into sequences of smaller DFTs [1]. This operation is useful in many fields but computing it directly from the definition is often too slow to be practical. The FFT is used in various applications where the frequency-domain representation of a signal has to be analyzed. In the communications area, the FFT has gained attention because of its use in orthogonal frequency division multiplexing (OFDM) systems. For OFDM receivers, a FFT processing block is required [2]. Several communication systems require medium resolution (9–12 bits) analog-to-digital converters with bandwidths in the tens of MHz range [3]. The applications that use the FFT impose challenging specifications for its processing, such as small silicon area, high throughput, short processing time and reduced power consumption. For these applications, pipeline FFT architectures are accurate [4]. FFT has applications in mixed radix system, one of the popular numerical systems in which FFT numerical base or radix varies from one position to another position [5]. FFT is the most popular digital spectrum analysis technique [6]. The DFT is one of the fundamental operations in digital signal processing. The original computation of DFT with sample input requires complex multiplications. Cooley and Tukey first introduced the concept of FFT to demonstrate a significant computational reduction from to by making efficient use of symmetry and periodicity properties of the twiddle factors. These properties are: Symmetry property: / = (1) Periodicity property: = (2) The related algorithms for the computation of the DFT are generally known as the FFTs. DFT and FFT are very popular signal processing tools [7]. An FFT computes the DFT and produces exactly the same result as evaluating the DFT definition. Computing the DFT of N points in the naive way using the definition takes O(N2) arithmetical operations while a FFT can compute the same DFT in only O(N log N) operations. FFT module can be designed for the receiver and can be used for the transmitter IFFT with external conjugation either in hardware or software [8]. The discrete Hartley transform (DHT) is widely used in signal and image processing applications. The advantage of the DHT over the DFT is that it can be used to avoid complex operations when the input sequence is real. The forward and inverse DHTs differ from each other in their form only in the scaling factor [9]. The decimation in-time (DIT) and the decimation in-frequency (DIF) algorithms are the typical forms of the FFT algorithm.