Low-complexity welch power spectral density computation

Keshab K. Parhi, Manohar Ayinala

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


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 languageEnglish (US)
Article number6525419
Pages (from-to)172-182
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number1
StatePublished - Jan 2014


  • FFT
  • Welch method
  • fractional-delay filter
  • frequency-domain convolution
  • low-complexity
  • low-power
  • power spectral density
  • windowing


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