Multiplication by a boxcar function in positive and negative frequency space is a frequency band-pass filter which has the inconvenience of not being causal as its impulse response is a cardinal sine of infinite support. It is possible to limit the impulse response of the filter by modifying the ramp of the filter with the aid of intermediate points. The example shows the boxcar filter in the frequency domain, its impulse response, the modulus (linearly and in dB) after an over-sampling by 4. The over-sampling of the signal highlights the filter's edge effects (rebounds) in the frequency domain. This is a major inconvenience as a frequency situated outside the bandwidth may not be correctly attenuated. It is possible to study the behaviour of the filter in function of the number of intermediate points and to evaluate its attenuation.
The introduction of intermediate points in the filter's ramp makes the filter more efficient in attenuating frequency rebounds and its impulse response is much shorter.