The filter width Δ {\displaystyle \Delta } has an associated cutoff wave number k c , {\displaystyle k_{c},} and the temporal filter width τ c {\displaystyle \tau _{c}} also has an associated cutoff frequency ω c . {\displaystyle \omega _{c}.} The unfiltered portion of ϕ ^ {\displaystyle {\hat {\phi }}} is: