Impluse reponse of an ideal lowpass filter is a sinc functionsinc(x)={sinxx,if x≠01,if x=0sinc(x) = \begin{cases} \frac{sinx}{x}, & \text{if } x \ne 0\\ 1, & \text{if } x=0 \end{cases}sinc(x)={xsinx,1,if x=0if x=0sinc(θ)=sin(πθ)πθsinc(\theta) = \frac{sin(\pi\theta)}{\pi\theta}sinc(θ)=πθsin(πθ) Fourier Transform then Rectangular function