f(x)=sin(2x-π/4)-2√2sin²x
＝sin2xcosπ/4-cos2xsinπ/4-√2（1－cos2x）
=√2/2 sin2x- √2/2 cos2x +√2cos2x-√2
=√2/2 sin2x+√2/2 cos2x-√2
=sin(2x+π/4)-√2
∴最小正周期是2π/2=π