▁has ▁to ▁be ▁adapted ▁accordingly . ▁ ▁Calcul ation ▁of ▁ 2 D ▁spect ra ▁Suppose ▁the ▁original ▁dataset ▁D ▁contains ▁the ▁n ▁spect ra ▁in ▁rows . ▁The ▁signals ▁of ▁the ▁original ▁dataset ▁are ▁generally ▁pre process ed . ▁The ▁original ▁spect ra ▁are ▁compared ▁to ▁a ▁reference ▁spectrum . ▁By ▁subtract ing ▁a ▁reference ▁spectrum , ▁often ▁the ▁average ▁spectrum ▁of ▁the ▁dataset , ▁so ▁called ▁dynamic ▁spect ra ▁are ▁calculated ▁which ▁form ▁the ▁corresponding ▁dynamic ▁dataset ▁E . ▁The ▁presence ▁and ▁interpretation ▁may ▁be ▁dependent ▁on ▁the ▁choice ▁of ▁reference ▁spectrum . ▁The ▁equations ▁below ▁are ▁valid ▁for ▁equally ▁spac ed ▁measurements ▁of ▁the ▁perturb ation . ▁ ▁Calcul ation ▁of ▁the ▁synchron ous ▁spectrum ▁A ▁ 2 D ▁synchron ous ▁spectrum ▁express es ▁the ▁similarity ▁between ▁spectral ▁of ▁the ▁data ▁in ▁the ▁original ▁dataset . ▁In ▁generalized ▁ 2 D ▁correlation ▁spect ro sc opy ▁this ▁is ▁mathemat ically ▁expressed ▁as ▁cov ar iance ▁( or ▁correlation ). ▁ ▁where : ▁ Φ ▁is ▁the ▁ 2 D ▁synchron ous ▁spectrum ▁ ν 1 ▁and ▁ ν 2 ▁are ▁two ▁spectral ▁channels ▁y ν ▁is ▁the ▁vector ▁composed ▁of ▁the ▁signal ▁intens ities ▁in ▁E ▁in ▁column ▁ ν ▁n ▁the ▁number ▁of ▁signals ▁in ▁the ▁original ▁dataset ▁ ▁Calcul ation ▁of ▁the ▁asynchronous ▁spectrum ▁Orth ogonal ▁spect ra ▁to ▁the ▁dynamic ▁dataset ▁E ▁are ▁obtained ▁with ▁the ▁Hil bert - transform : ▁ ▁where : ▁ Ψ ▁is ▁the ▁ 2 D ▁asynchronous ▁spectrum ▁ ν 1 ▁en