Hilbert-transform description of linear filtering

It is shown that ideal lowpass filtering can be expressed in terms of Hilbert transforms. This suggests that a wide variety of linear time-invariant filters with ideal `brickwall¿ transfer functions can be obtained by combinations of time-varying filters employing Hilbert-transform elements. In particular, expressions are presented for real and complex bandpass filters. Application to another truncation process, time windowing, is pointed out.