is the Kronecker delta function. Recall that (2) can also be written using , the convolution operator.
Given that and are Golay, it turns out that and are also Golay. This means that Golay sequences can be constructed recursively given Golay seed sequences such as and . See the MATLAB/Octave source code generate_golay.m for details. Notice also that the resulting bilevel sequences consist of only 's and 's. This means that the signal contains the maximum possible power level given that . This property is helpful in combatting measurement noise.
Let be the response due to the Golay code input , and let be the response due to the Golay code input . Due to (2), the impulse response may be determined as follows:
See golay_response.m for more details.