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Masters Presentation at Griffith University Master of Computer and Information Engineering Magnus Nilsson 2000 - 2001

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Masters Presentation FFT, Realization and Implementation in FPGA Speaker Verification in JAVA Demonstration of FFT and JAVA application

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FFT, Realization and Implementation in FPGA Technical Function History of Fourier Transform Discrete Fourier Transform Fast Fourier Transform The Radix-2 Algorithm The Radix-4 Algorithm FPGA Complex FFT Bit Length and Implementation Results Conclusion

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Technical Function Background Ericsson Microwave System XILINX FPGA 1024-point FFT Task Study, Implement and evaluate FFT in FPGA Technical Function Collect data, execute a FFT and output the data. The implementation shall be optimized on execution time, area and cost.

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History of Fourier Transform Jean-Baptiste-Joseph Fourier Problem of flow of heat in solid bodies The analytical theory of heat, 1815 Universal problem solving technique Radar Speaker Verification Medical Science

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Discrete Fourier Transform N 2 complex multiplications (N)(N-1) complex additions ~ 2N 2 additions and multiplications

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Fast Fourier Transform Early 1960’s John W. Tukey and James W Cooley An algorithm for the machine calculation of complex Fourier series Runge and König Radix - 2 algorithm

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The Radix-2 Algorithm ~ 2N 2 additions and multiplications for DFT, Vs. N 2 /2 for FFT

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The Radix-4 Algorithm Base 4 i.e. N = 4 x More complex but less computation power utilized The Radix-4 algorithm consists of v steps (log(N)/log(4)) Each step involves N/4 number of butterflies 3*v*N/4 = (3N/8)log2N number of complex multiplications (3N/2)log2N complex additions Radix-2 Vs. Radix-4: 25% reduction of complex multiplications Complex additions will increase by 50%

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Radix-4 Dragonfly

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FPGA Field Programmable Gate Array For fast time to market hardware implementation Xilinx Virtex-E PCB with a Xilinx Virtex-E 1000

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Complex FFT Specification Minimum: 16 complex samples Maximum: 1024 complex samples Typical: 16 or 64 Number of bits for the input signal Minimum: 10 bits Maximum: 16 bits Typical: 12

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Construction configuration

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Bit Length Implementing in hardware Multiplications N bits x N bits = 2 N bits Minimize the phase and amplitude error Realizable Different types of bit lengths

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Implementation Ease, Eale, Modelsim and Symplify Virtex-E 2000 @ F c = 55 MHz, Computation phase = 640 ns my FFT Xilinx Virtex LogiCore block @ 110 MHz, Computation phase = 1.92 ms LogiCore = Serial My FFT = Parallel

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Result Tested using a Logical Analyser, Hewlett Pacard HP16555D (2.0 M Samples, 110/500 MHz) and a Pattern Generator

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Result

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Conclusion As the Radix-4 FFT algorithm utilizes less complex multipliers than the Radix-2 FFT algorithm, the Radix-4 algorithm is preferable for hardware implementation. A parallel programming approach seems to be the model when a real time system with high sampling rate is desired. To reach an acceptable level of phase error, it is desirable to use 16 bits precision on the input signal and the phase factor

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Speaker Verification in JAVA Technical Function JAVA Speaker Verification and Speaker Recognition VQ Speaker Verification Hardware Parallel Port Extension and access Results Conclusion

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Technical Function Background It would be interesting to develop a Speaker Verification system/software in JAVA, since the JAVA language is said to be platform independent and would be interesting as a research language. Task To study, implement and evaluate a VQ (Vector Quantization) Speaker Verification system in JAVA, using MFCC’s (Mel Frequency Cepstral Coefficients). Technical Function A graphical software implementation which shall record speech from a person through a microphone, verify the person as true speaker or false speaker.

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JAVA 1991 @ Sun Microsystems by James Gosling & Co Address the problem of building software for network consumer devices Survive transport across networks Operate on any client Safe to run Capability to work on a wide range of platforms and CPU's Virtual Machine Applet and Application Platform portability

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Speaker Verification and Speaker Recognition

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Accessing confidential information areas Access to remote computers Voice dialing Banking by telephone Telephone shopping Database access services Information services Voice mail PIN code for your ATM

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VQ Speaker Verification Speech Feature Extraction

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Mel Frequency Cepstral Coefficients

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Mel Frequency Wrapping

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Cepstral Coefficients Power of the triangular filter = summarized Log calculated Convert them to time domain using the Discrete Cosine Transform (DCT) Result is called the mel frequency cepstral coefficients (MFCC).

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Feature Matching Dynamic Time Warping (DTW) Hidden Markov Modeling (HMM) Gaussian Mixture Model (GMM) Vector Quantization (VQ) High Accuracy Interesting to implement

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LBG algorithm

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MFCC’s and Codebook

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Verification Threshold Cohort Speakers Ratio

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Graphical Implementation of application in JAVA

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Results

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Conclusion Since Java is said to be platform independent, some experiments has been conducted that has showed this is not always the case. As soon as you would like to access the hardware through Java you will face problems that will make your software to become platform dependent. It is interesting to note that all the algorithm developed for the speaker verification system is platform independent, except for those parts accessing the sound card of the users computer, and can easily be executed under both Microsoft Windows and Linux. Testing, simulation and verification of the speaker verification program show a total error rate of four percent.

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