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  • Topic: Discrete Fourier transform, Fast Fourier transform, Digital signal processing
  • Pages : 28 (7753 words )
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  • Published : March 23, 2011
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The high growth of the semiconductor industry over the past two decades has put Very Large Scale Integration in demand all over the world. Digital Signal Processing has played a great role in expanding VLSI device area. The recent rapid advancements in multimedia computing and high speed wired and wireless communications made DSP to grab increased attention. For an N-point transformation the direct computation of the Discrete Fourier Transform (DFT) requires N2 operations. Cooley and Turkey explained the concept of Fast Fourier Transform (FFT) which reduces the order of computation to Nlog2N. The FFT is not an approximation of the DFT, it's exactly equal to the DFT. FFT decomposes the set of data to be transformed into a series of smaller data sets to be transformed. The size of FFT decomposition is called "radix". Then, it decomposes those smaller sets into even smaller sets. At each stage of processing, the results of the previous stage are combined with twiddle factor multiplication. Finally, FFT is calculated for each small data set. Generally, FFT's can be decomposed using DFT's of even and odd points, which is called a Decimation-In-Time (DIT) FFT, or they can be decomposed using a first-half/second-half approach, which is called a "Decimation-In-Frequency" (DIF) FFT. A large number of FFT algorithms have been developed, but among all radix-4 are most widely used for practical applications due to their simple architecture, with constant butterfly geometry and the possibility of performing them ‘in place’. The algorithm for 16-point radix-4 FFT can be implemented with decimation either in time or frequency. In this work, the decimation in time (DIT) technique will be adopted in order to implement the 16-point radix-4 FFT.


1.1 Introduction
High performance VLSI-based FFT architectures are key to signal processing and telecommunication systems since they meet the hard real-time constraints at low silicon area and low power compared to CPU-based solutions. The fast Fourier transform (FFT) plays an important role in the design and implementation of discrete-time signal processing algorithms and systems. In recent years, motivated by the emerging applications in the modern digital communication systems and television terrestrial broadcasting systems, there has been tremendous growth in the design of high-performance dedicated FFT processors. Pipelined FFT processor is a class of real-time FFT architectures characterized by continuous processing of the input data which, for the reason of the transmission economy, usually arrives in the word sequential format. However, the FFT operation is very communication intensive which calls for spatially global interconnection. Therefore, much effort on the design of FFT processors focuses on how to efficiently map the FFT algorithm to the hardware to accommodate the serial input for computation. The FFT is a faster version of the Discrete Fourier Transform (DFT). The FFT utilizes some clever algorithms to do the same thing as the DTF, but in much less time. Ok, but what is the DFT? The DFT is extremely important in the area of frequency (spectrum) analysis because it takes a discrete signal in the time domain and transforms that signal into its discrete frequency domain representation. Without a discrete-time to discrete-frequency transform we would not be able to compute the Fourier transform with a microprocessor or DSP based system. The Discrete Fourier Transform (DFT) plays an important role in the analyses, design and implementation of the discrete-time signal- processing algorithms and systems It is used to convert the samples in time domain to frequency domain. The Fast Fourier Transform (FFT) is simply a fast (computationally efficient) way to...
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