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viations of the time and frequency estimates are sv tand sv frespectively, then we can write Gabor’s uncertainty principle as: t f 1 4? t 0 8cycles Thus, the product of the standard deviations of time (ms) and frequency (Hz) must be at least 80 ms-Hz Regardless of how the transform is computed, we pay for time information with frequency
• The frequency of a signal refers to the number of “cycles” per second and is measured in Hertz for an analogue signal with no digital data mapped onto it or bits per second (bps) for a digital data signal • The delineating markers in time between bits are known as “significant instants” TIME Significant instants Pulse Width (ns)
the results of time domain frequency measurements t O,(T) Diffusion processes across junctions of semicon- ductor devices may produce this noise Fy 2 Frequency stability, characterized by the root mean White noise of frequency (a = 0) is present in quue of the two-sample vari~cc of fractional frequency
time offset of PTP-D was 2 3 µs and the peak-to-peak variation was 4 2 µs PTP-B had a similar average, but the stability was worse, varying by 9 4 µs PTP-C had a large average time offset of 22 9 µs, but a good stability, with a peak-to-peak range of 2 0 µs The timing stabilities are shown in the time deviation (TDEV) plot in Figure 8
Many signals with a frequency and power component, including EEG data, show decreasing power at increasing frequencies Power = c/fx EEG data simply takes on 1/f form This characteristic causes the visualization of activity from multiple frequency bands difficult to do simultaneously
in time and ERB-scale frequency [17] The center points of the bubbles were selected uniformly at random in time and in ERB-scale frequency, except that they were excluded from a 2-ERB buffer at the bottom and top of the frequency scale to avoid edge effects Mathematically, one instance of bubble noise is given by B(f;t) = XI i=1 exp ((t 2t i