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Introduction. SYSC5603 (ELG6163) Digital Signal Processing Microprocessors, Software and Applications Miodrag Bolic. Objective. FFT Introduction Some FFT algorithms FFT on PDSP FFT floating to fixed-point conversion Hardware implementation of FFT. FFT for TMS320x67 with 2 buffers.

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Introduction

Introduction

SYSC5603 (ELG6163) Digital Signal Processing Microprocessors, Software and Applications

Miodrag Bolic


Objective
Objective

  • FFT Introduction

  • Some FFT algorithms

  • FFT on PDSP

  • FFT floating to fixed-point conversion

  • Hardware implementation of FFT


Fft for tms320x67 with 2 buffers
FFT for TMS320x67 with 2 buffers

Buffer (ping)

Destination address 1

count

Source

address

Serial

EDMA

Port

FFT

Buffer (pong)

Processing

Destination address 2

event (internal timer 1 is selected)

count

Switch address at the completion of a

transfer


Fft fixed point xilinx
FFT Fixed point - Xilinx

  • Performing the calculations with no scaling and carrying computation

    • The growth of the fractional bits created from the multiplication are truncated after the multiplication.

    • The width of the output will be the (input width + number of stages + 1).

    • For example, a 1024-pt transform with an input of 16 bits consisting of 1 integer bit and 15 fractional bits, will have an output of 27 bits with 12 integer bits and 15 fractional bits.

  • Scaling at each stage using a fixed-scaling schedule

  • Scaling automatically using block-floating point

[Xilinx05]


Block floating point
Block-floating point

  • The computation is fixed-point

  • After every addition there is an overflow test

  • If the overflow is detected the array is divided by ½

  • The number of division is counted to determine the scale factor

  • SNR depends on how many overflows occurs


Butterfly computation for decimation in time
Butterfly computation for Decimation in Time

  • Linear noise model

[Oppenheim98]






Pipelined fft architecture
Pipelined FFT architecture

• Radix-2 multipath delay commutator (R2MDC)

• Radix-2 single-path delay feedback (R2SDC)

• Radix-4 multipath delay commutator (R4MDC)

• Radix-4 single-path delay commutator (R4SDC)

• Radix-4 single-path delay feedback (R4SDF)

• Radix-22 single-path delay commutator (R22SDC)

[Li03]


Radix 2 multipath delay commutator
Radix-2 multipath delay commutator

  • The total number of delay elements is 4 + 2 + 2 + 1 + 1 = 10 for the 8-point FFT.

  • The utilization of the butterfly and the multiplier is 50%

[Li03]


Radix 2 single path delay feedback
Radix-2 single-path delay feedback

  • The total number of delay elements is N – 1=N/2 + N/4 +... + 1

[Li03]


Fft processor
FFT processor

  • Datapath

    • memories,

    • butterflies and

    • complex multipliers.

  • Control unit

[Li03]


Requirements
Requirements

  • Requirement

    • Transform length is 1024

    • Transform time is less than 40 ms (continuously)

    • Continuous I/O

    • 25.6 Msamples/sec. throughput

    • Complex 24 bits I/O data

  • Steps in designing

    • Architecture selection

    • Partitioning

    • Scheduling

    • Word length selection

    • RTL model generation

    • Validation of models

[Li03]


Resource analysis
Resource analysis

  • Computation time for the 1024-point FFT

  • The number of butterfly operations for Radix2

  • Assume 1 clock cycle per Butterfly

  • The minimum number of Butterflies is

  • This is optimal with the assumption that ALL data are available to ALL stages, which is impossible for continuous data streams. Each butterfly has to be idle for 50% in order to reorder the incoming data.

[Li03]


Resource analysis1
Resource analysis

  • The solution: the number of butterflies is 10

  • The number of complex multipliers is 9

  • Memory length for Radix-2 single-path delay feedback is N-1

[Li03]


Ram based commutator
RAM Based Commutator

  • A dual-port memory is required since the read and write operation must be performed in one clock cycle.

[Li03]






References
References

[Altera05] Altera, FFT MegaCore Function User Guide, DSP Literature, 2005.

[Li03] W Li, Studies on implementation of low power FFT processors, Thesis, Linköpings University, 2003

[Oppenheim98] A. V. Oppenheim, R. W. Schafer, Discrete-time signal processing, 2nd edition, Prentice Hall, 1998.

[Xlinx05] Xilinx, “Fast Fourier Transform v3.2”,DS260 August 31, 2005


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