So, if the transmit filter has a group delay response which increases with frequency, then the receive filter will have one which decreases with frequency and vice versa. In principle, the transmitted pulses can be generated by applying impulses to the input of the dispersive transmit filter, with the resultant output chirp amplified as necessary for transmission. Alternatively, a voltage controlled oscillator may be used to generate the chirp signal. To achieve maximum transmitted power (and so achieve maximum range) it is normal for a radar system to transmit chirp pulses at constant amplitude from a transmitter run in a near-limiting condition. The chirp signals reflected from targets are amplified in the receiver and then processed by the compression filter to give narrow pulses of high amplitude, as previously described. In general, the compression process is a practical implementation of a matched filter system. For the compression filter to be matched to the radiated chirp signal, its response is the complex conjugate of the time inverse of the transmit filter's impulse response. So, the output of this matched filter is given by the convolution of the signal h(t) with the conjugate impulse response h*(-t):  Alternately, if the frequency response of the coding filter is H(), then that of the matched filter is H*(), the spectrum of the compressed pulse is |H()|2. The waveform of this spectrum is obtained from the inverse Fourier transform, i.e. For the case of a linear chirp, with constant amplitude and time duration T, compression by the matched filter gives a waveform with the sinc characteristic, with duration 2T, as shown later. So, in addition to the main pulse, there are a large number of time sidelobes (or, more precisely, range sidelobes) present, the biggest of which are only 13.5 dB below the peak signal level. In order to achieve a more desirable pulse characteristic (with lower sidelobes, for example), an alternative to the matched filter is often preferred. In this more general case, the compression filter has, say, impulse response g(t) and spectral response G(), so the equations for y(t) becomes:  and  When compared to the performance of the true matched filter, there will be some loss of processing gain, the main pulse lobe will be broader, and the total time duration of the compressed waveform will exceed 2T (usually). The sinc characteristic of a compressed pulse is a direct consequence of the spectrum of the linear chirp pulse having a rectangular profile.