Abstract:
A method to determine the magnitude MA of a signal component with frequency ωA from a set of N digital samples of an input signal acquired at a sampling rate R, said input signal having a discrete spectral representation having n bins with frequencies ω1, . . . , ωn and corresponding magnitudes M1, . . . , Mn, the spectral representation being derivable from the input signal using a transform, involving choosing an extraction bin with index kε[1, . . . , n] and frequency ωk≠ωA from the spectral representation; determining a magnitude Mk of this extraction bin; determining an allocation factor indicating a portion Mks of a sinusoidal signal with frequency ωA and unity magnitude that is allocated to the extraction bin when the transform is applied to the sinusoidal signal to generate a spectral representation out of the sinusoidal signal; and determining the magnitude MA of the signal component from the magnitude Mk of the bin in combination with the factor.
Abstract:
A method to determine the magnitude MA of a signal component with frequency ωA from a set of N digital samples of an input signal acquired at a sampling rate R, said input signal having a discrete spectral representation having n bins with frequencies ω1, . . . , ωn and corresponding magnitudes M1, . . . , Mn, the spectral representation being derivable from the input signal using a transform, involving choosing an extraction bin with index k∈[1, . . . , n] and frequency ωk≠ωA from the spectral representation; determining a magnitude Mk of this extraction bin determining an allocation factor indicating a portion Mks of a sinusoidal signal with frequency ωA and unity magnitude that is allocated to the extraction bin when the transform is applied to the sinusoidal signal to generate a spectral representation out of the sinusoidal signal; and determining the magnitude MA of the signal component from the magnitude Mk of the bin in combination with the factor.