IMPLEMENTATION OF SDC - SDF ARCHITECTURE FOR RADIX-4 FFT

International Journal of VLSI design & Communication Systems (VLSICS) Vol.7, No.4, August 2016
DOI : 10.5121/vlsic.2016.7403 29
IMPLEMENTATION OF SDC - SDF
ARCHITECTURE FOR RADIX-4 FFT
G. Deeshma Venkatakanakadurga1
and Dr.G.R.L.V.N. Srinivasaraju2
1
PG Scholar, Dept of ECE, SVECW, Bhimavaram, AP,India
2
Professor, Head of the Dept, Dept of ECE, SVECW, Bhimavaram, AP,India
ABSTRACT
Very large scale integration and Digital signal processing are the very crucial technologies from the last
few decades. DSP applications require high performance, low area and low power VLSI circuits. This
paper is discussing about FFT which is one of the vital component in the digital signal processing. In this
Paper, we propose a single path delay commutator–feedback (SDC-SDF) Architecture for Radix-4 FFT
and presented its simulation and synthesis results. The Radix-4 FFT architecture consists of log4 N-1 SDC
Stages and 1 SDF stage. Previously, the radix-2 SDC-SDF (Single path delay commutator-feedback) FFT
architecture was includes log2 N-1 SDC Stages and 1 SDF stage. The proposed Radix-4 SDC-SDF
architecture reduces the number of multiplications and additions as well as number of stages which
achieves reduced area and low power. The resultant architecture is simulated using Modelsim, design
verification and synthesis results are done using Xilinx ISE. The proposed architecture is compared with
Radix-2 SDC-SDF FFT and it can achieve less area as well as low power consumption.
KEYWORDS
Radix-2 FFT, Radix-4 FFT, Single path delay commutator – feedback (SDC-SDF), Bit reverser.
1. INTRODUCTION
The Fast Fourier Transform (FFT) is one of the vital components in the field of digital signal
processing. It is very helpful to calculate the discrete Fourier transform (DFT) accurately. DFT is
one of the important operations in the field of digital signal processing. The DFT, with a
transform length N equal to a power of 2, is usually implemented with the fast Fourier transform.
Hardware designers are always tried to develop good architectures for the computation of the
FFT to get high performance and real-time requirements of modern applications. Pipelined
hardware architectures provide high throughputs and low latencies suitable for real time, as well
as a low area and power consumption.
Fast Fourier Transform (FFT) is the vital component in orthogonal frequency division
multiplexing (OFDM) systems [1]. OFDM has been adopted in a wide range of applications from
wired- communication modems, such as digital subscriber lines , to wireless communication
modems, such as IEEE802.11 Wi-Fi, IEEE802.16 Wi-Max or 3GPP long term evolution(LTE),
to process baseband data.

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Previously, some of them worked in this area and they also implemented some FFT architectures.
They are Multi-path delay commutaor, single-path delay feedback and single-path delay
commutator. MDC architecture [3]-[6] is used typically to process multiple- input data streams
because of its high throughput rate. But it is not suited for single input data stream.MDC
architectures require more hardware utilization compared to combined SDC-SDF architecture.
The SDC-SDF (Single path delay commutator-feedback) architecture reduces the memory size
and it can utilize multipliers fully. However the utilization of adders is still very low. SDC
architecture is seldom used to process the single-input data stream, because it uses more memory
resources than SDF and has a more complicated control.
Radix-2 FFT architecture mainly performs two operations. They are addition and subtraction.
After completion of subtraction operation it indeed involves complex multiplication.
An FFT algorithm for radix’s other than radix-2 one of the most important is radix-4. The radix-4
FFT was only used when N is the power of 4. We can achieve less computational complexity by
using higher radix. The operation of radix-4 FFT is similar to the radix-2 FFT.
In radix-4 FFT, the sequence is divided into 4 sub sequences and each of which is again divided
into 4 sub sequences and so on. In radix-4 FFT, the butterfly is based on the four point DFT. So
radix-4 algorithm requires somewhat fewer multiplications than the radix-2 algorithm.
In this paper, we propose an efficient combined SDC-SDF (Single path delay commutator-
feedback) radix-4 FFT architecture, which contains log4 N-1 SDC Stages and 1 SDF stage, and 1
bit reverser. This architecture can produce the output sequence as the same order of input [19].
2. THE COMBINED SDC-SDF RADIX-2 FFT
The existing single path delay commutator-feedback (SDC-SDF) radix-2 FFT architecture
contains 1 pre-stage, log2N-1 SDC stages, 1 post-stage, 1 SDF stage, and 1 bit reverser as shown
in figure 1(a) [1]. The pre stage modifies the complex input data to a new sequence that is real
part and the corresponding imaginary part.
The SDC stages contain an SDC PE; it can achieve 100% arithmetic resource utilization through
both complex adders and complex multipliers. The SDC PE, shown in figure 1(b), contains a real
add/sub unit, a data commutator, and an optimum complex multiplier unit. In the stage t, the data
commutator modifies its input data to generate a new data sequence and the index difference to
get the new sequence is N/2t
, where t indicates the index of the SDC stage. The output of data
commutaor is input to the real add/sub unit. The real add/sub unit consists of one adder and one
subtracter.These two operations are performed for each input data.
Figure 1(b) is SDC PE for Radix-2 FFT consists of optimum complex multiplier unit. It contains
2 multiplexers, 2 multipliers, 1 real adder, and 1.5 word memory. The signal s operates the
operation of the real adder that is both addition and subtraction operations.

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Figure 1(a). The combined SDC-SDF architecture for Radix-2 FFT
Figure 1(b). The SDC PE for Radix-2 FFT
The post stage changes back the new sequence to the complex format. The last stage is the single
path delay feedback stage, which is similar to the radix-2 butterfly, requires a complex adder and
a complex subtracter. By using the modified addressing method, the bit reverser requires only
N/2 data buffer and we get the data in normal order.
3. PROPOSED SYSTEM
The main advantage of proposed SDC-SDF (Single path delay commutator-feedback) Radix-4
FFT architecture is we are applying inputs through single path and we are getting outputs through
single path. The proposed single path delay commutator processing engine can require less
number of complex multipliers and adders compared to the existing SDC-SDF (Single path delay
commutator-feedback) Radix-2 FFT architecture.
The proposed SDC-SDF (Single path delay commutator-feedback) Radix-4 FFT architecture
requires 1 Pre-stage, log4N – 1 SDC stages, 1 Post-stage, 1 SDF stage and 1 bit reverser as shown
in figure 2(a).
This architecture is based on Radix-4 Butterfly operation. That is 4 Operations are performed at
the same time. The pre-stage changes the complex input data into real part followed by the
imaginary part. For example initially the data in the form of 0_r,0_i,1_r,1_i etc., we get the
output of pre stage as 0_r,1_r,2_r,3_r in the 1st
cycle and 0_i,1_i,2_i,3_i in the 2nd
cycle. Like
that the pre-stage modifies the Complex input data into real part and the following imaginary
part.
Next, the output of pre-stage is input to the SDC stages. Single path data commutator stages are
depends on N value. The proposed architecture consists of log4 N – 1 or ½ log2N – 1 SDC stages.
Single path delay commutator processing engine consists of data commutator, Radix-4 butterfly
and complex multipliers 1 and 2 as shown in figure 2(b). Data commutaor shuffles real input data
to new data sequence, whose index difference is 3N/4, N/2, N/4. After generating the new data
sequence, before going to the butterfly4, they were multiplied by complex multipliers1. Here k
value varies from 0 to 3.

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The operation of data commutator was performed in 4 cycles. In the first cycle k=0, second cycle
k=1, third cycle k=2 and finally fourth cycle k=3. Depending on the k value the output of data
commutators were multiplied by complex multipliers1.
Next block is radix-4 butterfly. In this it get the data from complex multipliers1. The main
advantage of Radix-4 butterfly is they perform 4 operations at the same time. Internally radix-4
butterfly consists of adders/subtractors. It gets the 4 inputs and performs the addition/subtraction
between these 4 sequences and finally generates the 4 outputs. The output of butterfly4 is
multiplied by complex multipliers 2. This multiplication also depends on k value. Finally we get
the 4 outputs as real output, complex output1, complex output2 and complex output3.
Figure 2(a). Proposed Architecture for combined SDC-SDF Radix-4 FFT
Figure 2(b). The single path delay commutator processing engine for Radix-4 FFT
The process can be continued by applying to the other couples (inputs) to the SDC1 and so on. If
we perform the above process towards log4N – 1 single path delay commutaor stages to
Completion. Finally, we can complete the maximum part of the radix-4 FFT operation.
The output of SDC stages is input to the post stage. This stage was exactly opposite to the pre-
stage. The post-stage shuffles the new sequence to complex input data. Next stage is SDF stage.
It gets the input from post-stage. Single path data feedback consists of radix4 butterfly and thrice
N/4 delay elements. The advantage of single path delay feedback stage to changes the data
sequence, and then the delay memory is reduced to N/4 for the bit reverser. This combined SDC-
SDF (Single path delay commutator-feedback) architecture produces the output in normal order
as same as the order of input.
4. RESULTS AND COMPARISON
The design of combined SDC-SDF (Single path delay commutator-feedback) architecture for
Radix-4 FFT has been made by using Verilog Hardware Description Language (Verilog HDL).

33
The simulation results has been evaluated by using Modelsim 6.3c and synthesis Performances
are estimated by using Xilinx 14.1
Figure 3(a). Simulation Waveform of Radix-4 SDC-SDF FFT
In Figure 3(a).complex input consists of real part and imaginary part. Here, in_real is the real part
and in_imag is the imaginary part. Here, we are applying 16 inputs (complex) of 32 bit range
through single path, clk, control as well as twiddle of 3 bit. Signal s of 4 bit represents number of
inputs.
Figure 3(b). Simulation Waveform continue1 of Radix-4 SDC-SDF FFT
In Figure 3(b).complex output consists of real part and imaginary part. Here, out_real is the real
part and out_imag is the imaginary part. After receiving 16 inputs (complex data), we are getting
outputs (out_real and out_imag) through single path of 32 bit range.
Fig. 4(a) RTL Schematic of Radix-4 SDC-SDF FFT

34
In Fig.4 RTL Schematic shows input and output signals.clk, in_real of 32 bit, in_imag of 32 bit,
control of 5 bit, twiddle of 3 bit and s are inputs. Out_real of 32 bit and out_imag of 32 bit are
outputs.
Fig. 4(b): RTL Schematic detailed view of Radix-4 SDC-SDF FFT
In Fig. 4(b) RTL Schematic detailed view of SDC-SDF (Single path delay commutator -
feedback) Radix-4 FFT shows 5 blocks. They are 1 Pre-stage, 1 SDC Stage, 1 Post-stage, 1 SDF
stage and 1 Bit-Reverser. The design was verified through this RTL Schematic view.
Table1: Design Summary of Single path delay comutator-feedback Radix-4 FFT
S.No. PARAMETERS VALUE
1. No. of slice registers (in %) 2
2. Number of slice LUTs (in %) 61
3. Number of DSP 48E 1s (in %) 9
4. Min. Clock period 39.473 ns
5. Frequency 25.334 MHz
6. On-chip logic 0.007
7. Dynamic Power 0.047 W
8. Quiescent Power 0.073 W
9. Total Power 0.120 W

35
Single path delay commutaor–feedback Radix-4 FFT is compared with SDC-SDF (Single path
delay commutaor–feedback) Radix-2 FFT in various parameters like dynamic power, quiescent
power, number of slice registers, number of slice LUTs, and number of DSP 48E 1s. The
implementation results give the same outputs, but in power consumption and area is less
compared with SDC-SDF Radix-2 FFT.
Table2: Comparison between Single path delay comutator-feedback Radix-4 FFT and Radix-2 FFT
S.No. Parameters SDC-SDF Radix-2 FFT SDC-SDF Radix-4 FFT
1. No. Of slice registers (in %) 3 2
2. Number of slice LUTs (in %) 72 61
3. Number of DSP 48E 1s (in %) 25 9
4. Dynamic Power 0.048 W 0.047 W
5. Quiescent Power 0.073 W 0.073 W
6. Total Power 0.122 W 0.120 W
Fig.5 Comparison of Number of slice LUTs of SDC-SDF of Radix-4 and Radix-2 FFT
From Fig.5 we understood the Number of slice LUTs of single path delay commutator-feedback
(SDC-SDF) Radix-4 FFT is less compared with SDC-SDF Radix-2 FFT. It says that output of
SDC-SDF Radix-4 FFT is obtained as fast as compared to SDC-SDF Radix-2 FFT.

36
Fig.6 Comparison of Number of DSP 48E 1s of SDC-SDF of Radix-4 and Radix-2 FFT
From Fig.6 we understood the Number of DSP 48E 1s of single path delay commutator-feedback
(SDC-SDF) Radix-4 FFT is less compared with SDC-SDF Radix-2 FFT. It says that output of
SDC-SDF (single path delay commutator-feedback) Radix-4 FFT is obtained as fast as compared
to SDC-SDF Radix-2 FFT.
Fig.7 Comparison of Dynamic Power of SDC-SDF of Radix-4 and Radix-2 FFT
From Fig.7 we understood the Dynamic Power of single path delay commutator-feedback Radix-
4 FFT is low compared with SDC-SDF Radix-2 FFT. It says that the SDC-SDF Radix-4 FFT is
architecture performance is increased.
Fig.8 Comparison of Total Power of SDC-SDF of Radix-4 and Radix-2 FFT

37
From Fig.8 we understood the Dynamic Power of single path delay commutator-feedback (SDC-
SDF) Radix-4 FFT is low compared with SDC-SDF Radix-2 FFT. It says that the SDC-SDF
Radix-4 FFT is architecture performance is increased.
5. CONCLUSION
The proposed SDC-SDF (Single path delay commutator-feedback) radix-4 FFT architecture
produces the output data in the same order as input. The proposed architecture reduces number of
complex multiplications as well as number of stages compared with the radix-2 FFT architecture.
The Single path delay commutator-feedback Radix-4 FFT architecture is simulated using
Modelsim and design verification, area and power reports were done using Xilinx ISE 14.1.
Finally, the proposed architecture can achieves reduced area and low power consumption.
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