Zunaib Ali Class No: 09

Answer the following questions with reference to Research Paper attached.

1. What is the application based on Fast Fourier Transform, describe it?

This paper describes the design of Fast Fourier Transform (FFT) for the Eureka-147 Digital Audio Broadcasting (DAB) system. Here, in this research paper several possible FFT implementations based on the single butterfly architecture are investigate, including an in-place memory structure, to minimize the hardware requirement.In the paper, a unified approach toward partitioning the whole memory into several banks is also described, so as to increase the equivalent memory bandwidth between the memory unit and the butterfly unit, which can be implemented in either radix-2 or high-radix arithmetic. Implementation results demonstrate the applicability of our work to the targeted channel demodulator and the advantages over previous solutions adopted for Digital Audio Broadcasting (DAB) system.

2. What is the problem based upon Fast Fourier Transform, describe it?

The Digital Audio Broadcasting (DAB) system, described in the European Eweka-147 standard, offers high-quality audio services, supports multimedia data to mobile reception and might replace the traditional radio system. Basically, two strategies are employed to implement the DAB receiver:

a. The DSP-based architecture andb. The Application-Specific Integrated Circuit (ASIC-based) implementation

The former has the characteristics of maximum flexibility, ease of use and simple programming, but it can only provide limited processing capability. On the contrary, the ASIC-based implementation has the potentials of supporting real-time symbol decoding and low-cost implementation.An overview of DAB system in which the ISO/MPEG coding is adopted for source coding and COFDM (Coded Orthogonal Frequency Division Multiplexing) for channel coding and modulation, is shown in figure. After convolutional coding, the data is interleaved in frequency for the fast information channel and in time as well as in frequency for the main service channel, and the OFDM modulation is then performed. OFDM stands for Orthogonal Frequency Division Multiplexing; it’s a technology that

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Zunaib Ali Class No: 09

provides the operator to beat the challenges of Non-Line-of-Sight (NLOS) transmission in the more efficient manner. In this paper, we focus on the design and implementation of the channel demodulator, which essentially performs a Fast Fourier Transform (FFT) because the two basic strategies discussed above have some limitations i.e. one provide limited processing capability and other type have Lack of adequate design tools & have not yet been subject to formal evaluation and comparative analysis. One major disadvantage of the other two methods is size of distributed ram is too much large. So to avoid all this FFT in implemented.

Figure 1: Digital Audio Broadcasting System

3. Why Fourier transform was necessary in that application, can the application be analyzed in the time domain?

Fourier series as well as Fourier transform is an extremely powerful mathematical tool that allows you to view your signals in a different domain, inside which several difficult problems become very simple to analyze. First and foremost, a Fourier transform of a signal tells you what frequencies are present in your signal and in what proportions.Specific to this example, Fourier transform is very important because in digital audio broadcasting the role of frequency is too much important, a miner difference in frequency spectrum can cause distortion and inter symbol interference between two frequency spectrums. Have we ever noticed that each of our phone's number buttons sounds different when we press during a call and that it sounds the same for every phone model? That's because they are each composed of two different sinusoids which can be used to uniquely identify the button. When we use our phone to punch in combinations to navigate a menu, the way that the other party knows what keys you pressed is by doing a Fourier transform of the input and looking at the frequencies present. In the same way like explained in mobile phone example the digital data is transmitted and received using different frequency bands.So in order to make Digital Audio Broadcasting possible, without interference and noise, we must have to make use of correct band of frequency allotted. To do so we have to

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study the frequency spectrum of signals to be transmitted as carrier waves, for this we have to use Fourier transforms to convert time-domain in to frequency-domain. So it is obvious that this application cannot be analyzed in time domain because we will not be able to tell that the signal consists of which frequency components. Hence make Fourier transform necessary for its analysis.

4. How Fourier transform actually proves useful for that application?

The electromagnetic spectrum shows that for broadcasting we have to use specific frequency bands or range of frequencies. So the digital data is transmitted and received using different frequency bands. Only transferring the function to frequency domain would have helped us to identify the correct band of frequencies. So FFT is useful in converting time-domain to frequency-domain & hence making Digital Audio Broadcasting possible, without interference and noise.

Figure 2: EM Spectrum.

5. Discuss any drawbacks encountered while using the Fourier transformation tool?

In general, two basic types of FFT architectures can be found in the literature: a. The pipelined architecture (each stage consisting of a butterfly unit) and b. The single butterfly architecture.

The main concern is the trade-off between hardware overhead and speed requirement.Although the pipelined version can provide a higher throughput rate than the conventional single butterfly implementation, we are still interested in the single butterfly architecture because of the specifications of the channel demodulator as well as the hardware considerations on the implementation of a DAB receiver. For the single butterfly implementation, a basic problem arises is how to efficiently arrange memory read/write accesses for the purposes of increasing its throughput rate. The commonly used solutions include:

a. Use the high-radix implementation to reduce the total number of memory accesses at the expense of increasing the arithmetic complexity, i.e., the hardware requirement of a high-radix butterfly unit.

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b. Partitioning the memory into several banks to allow concurrent accesses of multiple data at the price of using a more complicated addressing scheme, which might correspond to a higher routing area.

Other problem, for a butterfly unit without employing pipelining, the critical path is the summation of the memory read operation, arithmetic operation, and memory write operation. To increase the overall operational frequency, we divide the operations of the butterfly unit into three different steps, each corresponding to a mentioned operation as shown in Fig.3 Due to the in-place computation, we have to schedule the tasks assigned to the pipelined butterfly unit such that no control hazard occurs during memory accesses. A control hazard results from the conflict when the butterfly unit intends to access more than two data in the same memory bank.

Figure 3: Radix-2 DIT Pipeline Butterfly Unit

6. Can you implement same application using any other transformation tool?

Based on the specifications of the channel demodulator of the DAB receiver, we show that the single butterfly architecture FFT is suited for the DAB systems. Similarly, any transformation tool that would have helped will be the one which helps in transformation from time domain to frequency domain could be used. The continuous Fourier transform could never been used here because simply we are dealing here with discrete frequencies not analogue frequencies, so it will be safer to say that only DFT can be used here, although Laplace transform also provides a way for transformation to frequency domain but even that could not be used here because it is also for continuous values.

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b. Partitioning the memory into several banks to allow concurrent accesses of multiple data at the price of using a more complicated addressing scheme, which might correspond to a higher routing area.

Other problem, for a butterfly unit without employing pipelining, the critical path is the summation of the memory read operation, arithmetic operation, and memory write operation. To increase the overall operational frequency, we divide the operations of the butterfly unit into three different steps, each corresponding to a mentioned operation as shown in Fig.3 Due to the in-place computation, we have to schedule the tasks assigned to the pipelined butterfly unit such that no control hazard occurs during memory accesses. A control hazard results from the conflict when the butterfly unit intends to access more than two data in the same memory bank.

Figure 3: Radix-2 DIT Pipeline Butterfly Unit

6. Can you implement same application using any other transformation tool?

Based on the specifications of the channel demodulator of the DAB receiver, we show that the single butterfly architecture FFT is suited for the DAB systems. Similarly, any transformation tool that would have helped will be the one which helps in transformation from time domain to frequency domain could be used. The continuous Fourier transform could never been used here because simply we are dealing here with discrete frequencies not analogue frequencies, so it will be safer to say that only DFT can be used here, although Laplace transform also provides a way for transformation to frequency domain but even that could not be used here because it is also for continuous values.

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Zunaib Ali Class No: 09

b. Partitioning the memory into several banks to allow concurrent accesses of multiple data at the price of using a more complicated addressing scheme, which might correspond to a higher routing area.

Other problem, for a butterfly unit without employing pipelining, the critical path is the summation of the memory read operation, arithmetic operation, and memory write operation. To increase the overall operational frequency, we divide the operations of the butterfly unit into three different steps, each corresponding to a mentioned operation as shown in Fig.3 Due to the in-place computation, we have to schedule the tasks assigned to the pipelined butterfly unit such that no control hazard occurs during memory accesses. A control hazard results from the conflict when the butterfly unit intends to access more than two data in the same memory bank.

Figure 3: Radix-2 DIT Pipeline Butterfly Unit

6. Can you implement same application using any other transformation tool?

Based on the specifications of the channel demodulator of the DAB receiver, we show that the single butterfly architecture FFT is suited for the DAB systems. Similarly, any transformation tool that would have helped will be the one which helps in transformation from time domain to frequency domain could be used. The continuous Fourier transform could never been used here because simply we are dealing here with discrete frequencies not analogue frequencies, so it will be safer to say that only DFT can be used here, although Laplace transform also provides a way for transformation to frequency domain but even that could not be used here because it is also for continuous values.

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