Mismatched filter

A method for filtering a first signal, the method comprising:

• filtering the first signal, by a first discrete filter, to produce a second signal, wherein an impulse response of the first discrete filter is such that a convolution of the impulse response of the first discrete filter with a first discrete waveform produces an autocorrelation of the first discrete waveform, the autocorrelation comprising a first mainlobe and a first set of sidelobes at a first set of positions relative to the first mainlobe;
• and
• filtering, via a second discrete filter, the second signal, wherein an impulse response of the second discrete filter comprises a first coefficient substantially equal in value to the first mainlobe amplitude of the autocorrelation and a second set of coefficients at the first set of positions relative to the first coefficient, each of the second set of coefficients substantially equal in value to a negative of a sidelobe at a corresponding position in the autocorrelation,
• wherein a convolution of the impulse response of the second discrete filter with the autocorrelation produces a second discrete waveform with a second mainlobe and a second set of sidelobes at a second set of positions relative to the second mainlobe.