power_spectrum

std.seq.power_spectrum · Level L4

The power spectrum of a real signal: |yₖ|² for its discrete Fourier transform y, the energy at each frequency.

Pₖ = |Σⱼ xⱼ·e^(−2πi·jk/n)|²

Signature

power_spectrum(x: f64[n]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

xf64[n]Reshapez_re0.0Multiplyz_imConcatzFFTXSlicep_row_rSlicep_row_iMultiplyp_row_rrMultiplyp_row_iiAddp_rowReshapeppf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.abs(np.fft.fft(x))**2 to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 166 float64 results inside the running error bound; the closest uses 12% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
49%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
98

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
—
Called by
—
sha256:8073d1ff1a6b6fe52eac4938e0f14adb0f51396f71e41e0419efbb965a42d70e

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.