Abstract
Canonic real-valued fast Fourier transform (RFFT) has been proposed to reduce the arithmetic complexity by eliminating redundancies. In a canonic N-point RFFT, the number of signal values at each stage is canonic with respect to the number of signal values, i.e., N. The major advantage of the canonic RFFTs is that these require the least number of butterfly operations and only real datapaths when mapped to architectures. In this paper, we consider the FFT computation whose inputs are not only real but also even/odd symmetric, which indeed lead to the well-known discrete cosine and sine transforms (DCTs and DSTs). Novel algorithms for generating the flow graphs of canonic RFFTs with even/odd symmetric inputs are proposed. It is shown that the proposed algorithms lead to canonic structures with N2+1 signal values at each stage for an N-point real even symmetric FFT (REFFT) or N2−1 signal values at each stage for an N-point RFFT real odd symmetric FFT (ROFFT). In order to remove butterfly operations, several twiddle factor transformations are proposed in this paper. We also discuss the design of canonic REFFT for any composite length. Performances of the canonic REFFT/ROFFT are also discussed. It is shown that the flow graph of canonic REFFT/ROFFT has less number of interconnections, less butterfly operations, and less twiddle factor operations, compared to prior works.
| Original language | English (US) |
|---|---|
| Article number | 45 |
| Journal | Eurasip Journal on Advances in Signal Processing |
| Volume | 2017 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 1 2017 |
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Keywords
- Canonic flow graph
- Discrete cosine transform (DCT)
- Discrete sine transform (DSTs)
- Even symmetric inputs
- Fast Fourier transform (FFT)
- Odd symmetric inputs
- Real-valued FFT (RFFT)
- Twiddle factor transformation
Cite this
Canonic FFT flow graphs for real-valued even/odd symmetric inputs. / Lao, Yingjie; Parhi, Keshab K.
In: Eurasip Journal on Advances in Signal Processing, Vol. 2017, No. 1, 45, 01.12.2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Canonic FFT flow graphs for real-valued even/odd symmetric inputs
AU - Lao, Yingjie
AU - Parhi, Keshab K
PY - 2017/12/1
Y1 - 2017/12/1
N2 - Canonic real-valued fast Fourier transform (RFFT) has been proposed to reduce the arithmetic complexity by eliminating redundancies. In a canonic N-point RFFT, the number of signal values at each stage is canonic with respect to the number of signal values, i.e., N. The major advantage of the canonic RFFTs is that these require the least number of butterfly operations and only real datapaths when mapped to architectures. In this paper, we consider the FFT computation whose inputs are not only real but also even/odd symmetric, which indeed lead to the well-known discrete cosine and sine transforms (DCTs and DSTs). Novel algorithms for generating the flow graphs of canonic RFFTs with even/odd symmetric inputs are proposed. It is shown that the proposed algorithms lead to canonic structures with N2+1 signal values at each stage for an N-point real even symmetric FFT (REFFT) or N2−1 signal values at each stage for an N-point RFFT real odd symmetric FFT (ROFFT). In order to remove butterfly operations, several twiddle factor transformations are proposed in this paper. We also discuss the design of canonic REFFT for any composite length. Performances of the canonic REFFT/ROFFT are also discussed. It is shown that the flow graph of canonic REFFT/ROFFT has less number of interconnections, less butterfly operations, and less twiddle factor operations, compared to prior works.
AB - Canonic real-valued fast Fourier transform (RFFT) has been proposed to reduce the arithmetic complexity by eliminating redundancies. In a canonic N-point RFFT, the number of signal values at each stage is canonic with respect to the number of signal values, i.e., N. The major advantage of the canonic RFFTs is that these require the least number of butterfly operations and only real datapaths when mapped to architectures. In this paper, we consider the FFT computation whose inputs are not only real but also even/odd symmetric, which indeed lead to the well-known discrete cosine and sine transforms (DCTs and DSTs). Novel algorithms for generating the flow graphs of canonic RFFTs with even/odd symmetric inputs are proposed. It is shown that the proposed algorithms lead to canonic structures with N2+1 signal values at each stage for an N-point real even symmetric FFT (REFFT) or N2−1 signal values at each stage for an N-point RFFT real odd symmetric FFT (ROFFT). In order to remove butterfly operations, several twiddle factor transformations are proposed in this paper. We also discuss the design of canonic REFFT for any composite length. Performances of the canonic REFFT/ROFFT are also discussed. It is shown that the flow graph of canonic REFFT/ROFFT has less number of interconnections, less butterfly operations, and less twiddle factor operations, compared to prior works.
KW - Canonic flow graph
KW - Discrete cosine transform (DCT)
KW - Discrete sine transform (DSTs)
KW - Even symmetric inputs
KW - Fast Fourier transform (FFT)
KW - Odd symmetric inputs
KW - Real-valued FFT (RFFT)
KW - Twiddle factor transformation
UR - http://www.scopus.com/inward/record.url?scp=85020500878&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85020500878&partnerID=8YFLogxK
U2 - 10.1186/s13634-017-0477-9
DO - 10.1186/s13634-017-0477-9
M3 - Article
VL - 2017
JO - Eurasip Journal on Advances in Signal Processing
JF - Eurasip Journal on Advances in Signal Processing
SN - 1687-6172
IS - 1
M1 - 45
ER -