Abstract
This paper presents a low-complexity algorithm and architecture to compute power spectral density (PSD) using the Welch method. The Welch algorithm provides a good estimate of the spectral power at the cost of high computational complexity. We propose a new modified approach to reduce the computational complexity of the Welch PSD computation for a 50% overlap. In the proposed approach, an N/2-point FFT is computed, where N is the length of the window and is merged with the FFT of the previous N/2-point to generate an N-point FFT of the overlapped segment. This requires replacing the windowing operation as a convolution in the frequency domain. Fortunately, the frequency-domain filtering requires a symmetric 3-tap or 5-tap FIR filter for raised cosine windows. The proposed method needs to compute (L+1) N/2-point FFTs instead of L N-point FFTs, where L is the number of overlapping segments. In the proposed novel merged FFT approach, the even samples are computed exactly, while the odd samples require a shift by a half-sample delay and are estimated using a bidirectional fractional-delay filter. The complexity reduction comes at the cost of slight performance loss due to the approximation used for the implementation of the fractional-delay filter. The performance loss is about 8% using fractional-delay filter with 2 multipliers. A novel architecture is presented based on the proposed algorithm. The proposed architecture not only consumes 33% less energy compared to the original method but also reduces the latency by about 44% for 8 overlapping segments. Further a low-complexity architecture is presented to compute a special case of the short-time Fourier transform based on the proposed PSD computation algorithm.
| Original language | English (US) |
|---|---|
| Article number | 6525419 |
| Pages (from-to) | 172-182 |
| Number of pages | 11 |
| Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
| Volume | 61 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2014 |
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Keywords
- FFT
- Welch method
- fractional-delay filter
- frequency-domain convolution
- low-complexity
- low-power
- power spectral density
- windowing
Cite this
Low-complexity welch power spectral density computation. / Parhi, Keshab K; Ayinala, Manohar.
In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 61, No. 1, 6525419, 01.01.2014, p. 172-182.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Low-complexity welch power spectral density computation
AU - Parhi, Keshab K
AU - Ayinala, Manohar
PY - 2014/1/1
Y1 - 2014/1/1
N2 - This paper presents a low-complexity algorithm and architecture to compute power spectral density (PSD) using the Welch method. The Welch algorithm provides a good estimate of the spectral power at the cost of high computational complexity. We propose a new modified approach to reduce the computational complexity of the Welch PSD computation for a 50% overlap. In the proposed approach, an N/2-point FFT is computed, where N is the length of the window and is merged with the FFT of the previous N/2-point to generate an N-point FFT of the overlapped segment. This requires replacing the windowing operation as a convolution in the frequency domain. Fortunately, the frequency-domain filtering requires a symmetric 3-tap or 5-tap FIR filter for raised cosine windows. The proposed method needs to compute (L+1) N/2-point FFTs instead of L N-point FFTs, where L is the number of overlapping segments. In the proposed novel merged FFT approach, the even samples are computed exactly, while the odd samples require a shift by a half-sample delay and are estimated using a bidirectional fractional-delay filter. The complexity reduction comes at the cost of slight performance loss due to the approximation used for the implementation of the fractional-delay filter. The performance loss is about 8% using fractional-delay filter with 2 multipliers. A novel architecture is presented based on the proposed algorithm. The proposed architecture not only consumes 33% less energy compared to the original method but also reduces the latency by about 44% for 8 overlapping segments. Further a low-complexity architecture is presented to compute a special case of the short-time Fourier transform based on the proposed PSD computation algorithm.
AB - This paper presents a low-complexity algorithm and architecture to compute power spectral density (PSD) using the Welch method. The Welch algorithm provides a good estimate of the spectral power at the cost of high computational complexity. We propose a new modified approach to reduce the computational complexity of the Welch PSD computation for a 50% overlap. In the proposed approach, an N/2-point FFT is computed, where N is the length of the window and is merged with the FFT of the previous N/2-point to generate an N-point FFT of the overlapped segment. This requires replacing the windowing operation as a convolution in the frequency domain. Fortunately, the frequency-domain filtering requires a symmetric 3-tap or 5-tap FIR filter for raised cosine windows. The proposed method needs to compute (L+1) N/2-point FFTs instead of L N-point FFTs, where L is the number of overlapping segments. In the proposed novel merged FFT approach, the even samples are computed exactly, while the odd samples require a shift by a half-sample delay and are estimated using a bidirectional fractional-delay filter. The complexity reduction comes at the cost of slight performance loss due to the approximation used for the implementation of the fractional-delay filter. The performance loss is about 8% using fractional-delay filter with 2 multipliers. A novel architecture is presented based on the proposed algorithm. The proposed architecture not only consumes 33% less energy compared to the original method but also reduces the latency by about 44% for 8 overlapping segments. Further a low-complexity architecture is presented to compute a special case of the short-time Fourier transform based on the proposed PSD computation algorithm.
KW - FFT
KW - Welch method
KW - fractional-delay filter
KW - frequency-domain convolution
KW - low-complexity
KW - low-power
KW - power spectral density
KW - windowing
UR - http://www.scopus.com/inward/record.url?scp=84892594837&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84892594837&partnerID=8YFLogxK
U2 - 10.1109/TCSI.2013.2264711
DO - 10.1109/TCSI.2013.2264711
M3 - Article
AN - SCOPUS:84892594837
VL - 61
SP - 172
EP - 182
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
SN - 1549-8328
IS - 1
M1 - 6525419
ER -