Algorithm 2 Welch’s Method

Require:  $x\left[n\right]|n\in \{0,1,\cdots ,N-1\}$ Require:  $0\le l_{seg}\le N|\in \mathbb{N}$ Require:  $0\le l_{over}\le N|\in \mathbb{N}$    $----Splitthesignalx\left[n\right]intoKsegments.$    $----X\left[K\right]matrixforallsegments(K\times \left(l_{seg}\right))$    $X\left[K\right]\leftarrow \left[\right]\left[\right]$    $K\leftarrow N/l_{seg}$    $X\left[K\right]=split(x\left[n\right],l_{seg},l_{over})\{\forall k\in [1,\cdots ,K]\}$    $----Convolveeachsegment{x}_k\left[t\right]withw\left[n\right]$    $----ComputetheFFTof{x}_k\left[n\right]$    $----F\left(j\omega \right)matrixforfrequencypower(K\times (l_{seg}/2))$    $F\left(j\omega \right)\leftarrow \left[\right]\left[\right]$    for  $x_k\left[n\right]\in X\left[K\right]$  do       $(x_k*w)\left[n\right]=convolve(x_k\left[n\right],w\left[n\right])$       $F\left(j{\omega }_k\right)=FFT\left(x_k\left[n\right]\right)$    end for    $----Computefrequencyvalues$    $F_x=0:(f_s/2)\times 1/(l_{seg}/2):f_s/2$    $----Foreachfrequencycomputesquaredmagnitude$    $P_x\left[f\right]\leftarrow \left[\right]$    for  $f\in [0,\cdots ,f_s/2]$  do       for $f_k\left[i\right]\in F\left(jw\right)$  do         $P_x\left[f\right]+=f_k{\left[f\right]}^2$       end for    end for    $----Computeaveragevalues$    for  $p_f\in P_x\left[f\right]$ do      $P_x\left[f\right]=p_f/K$    end for    return  $P_x\left[f\right]$