User's Manual - Cornell Lab of Ornithology - Cornell University

⎛⎜⎜⎝t 2∑f 2∑t=t 1 f = f 1⎞⎛W 0 ⋅10[ X t, f /10 ] ⎞⎜⎟ ⎟⎝⎠ ⎟⎠Chapter 6: Measurements∆fR L(6.3)where f 1 and f 2 are the lower and upper frequency limits of the selection, t 1and t 2 are the beginning and ending frame numbers of the selection, W 0 is thepower dB reference value, X t,f is the energy in frame t at frequency f (indecibels), and ∆f is the frequency bin size (which is equal to the sampling ratedivided by the FFT size). For a quadratic spectrogram, the energy is calculatedas⎛⎜⎜⎝t 2∑f 2∑t=t 1 f = f 1⎞( X t, f ) ⎟⎟⎠∆fR L(6.4)where all symbols are defined as above, except that amplitude values aremeasured in joules. For a logarithmic spectrum, energy is calculated as⎛⎜⎜⎝f 2∑f = f 1⎞⎛W 0 ⋅10[ X f /10 ] ⎞⎜⎟ ⎟∆f(6.5)⎝⎠ ⎟⎠ R Lwhere f 1 and f 2 are the lower and upper frequency limits of the selection, andX f is the energy in the source interval at frequency f, in decibels. For aquadratic spectrum, energy is calculated as⎛⎜⎜⎝⎞f 2∑ ( X f ) ⎟⎟f = f 1⎠∆fR L(6.6)where symbols are defined as above, except that amplitude values are injoules. Note that the total energy of a signal displayed for a spectrogram isexactly equal to the total energy of the waveform only if the spectrogram wascalculated using a rectangular window and zero frame overlap. For acousticsignals, Energy is replaced by Energy Flux Density. Units: joules.Energy per Hertz (electric spectrogram, spectrum)(Point) For a spectrogram, the energy per hertz at the time and frequencyindicated by the position of the mouse pointer. For a spectrum, the energy perhertz at the frequency indicated by the horizontal position of the mousepointer. If the spectrogram or spectrum is logarithmic, the value shown (in dB)is the “energy spectrum level”; for a quadratic spectrogram or spectrum, unitsare joules/Hz. In a quadratic spectrogram or spectrum, Energy/Hz is equal toPower/Hz times the frame length (in seconds). For acoustic signals, Energy/Hzis replaced by Energy Flux Density/Hz.Energy Flux Density (acoustic waveform, spectrogram, spectrum)(Range) The total energy flux density in the selection. For a stationary signal(one with a spectrum that does not change over time), the energy flux densityin a given time interval equals the average intensity (in watts/m 2 ) times thelength of the interval (in seconds). For a waveform, the energy is calculated asCanary 1.2 User’s Manual 95