By Cong, Fengyu; Lyytinen, Heikki; Ristaniemi, Tapani
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Extra resources for Advanced signal processing on brain event-related potentials : filtering ERPs in time, frequency and space domains sequentially and simultaneously
K − 1. The sampling frequency Fs is uniformly divided into K parts. Therefore, we can identify which frequency bin corresponds to which frequency. Using a band-pass filter, we want to remove some frequency components from the input signal. This can be achieved by the following approach: (1) Apply the DFT on the signal. (2) Set X (k), which is outside the pass band, as zero to create a new frequency-domain sequence Y (k). Hence, the X (k) and Y (k) characteristics would be that they are identical within the pass band and different outside the pass band.
1) How many levels should be used? (2) Which levels of detail coefficients should be selected? (3) Which wavelet should be chosen? Next, we analyze the current solutions for each key issue, point out the existing problems, and present new solutions. 2 is clearly related to the number of samples in a signal. The number of levels should be not more than log2 N (where N is the number of samples). This criterion has been widely used in biomedical signal processing since the 1990s (Tikkanen & Sellin, 1997).
In particular, when τ = 0, we define the correlation between the two time series α(t) and β(t) as follows: ∞ rαβ = α(t) · β(t). (2-2) t =−∞ Indeed, the correlation of the two time series is simply their inner product. When the mean and variance of each time series are respectively 0 and 1, the correlation is simply the correlation coefficient. 2 Impulse Response and Frequency Response The impulse response of a digital filter is the output of the filter when the input is a unit impulse (Mitra, 2005).