Pre- and post-envelope applied to the Exponential Sine Sweep ().

An Exponential Sine Sweep () of the form (1) has a burst of energy across the whole spectrum both at its start and at its end (A1). Once convolved with its inverse filter (A2), it leads to an impulse response and its echoes in the frequency-time space (A3). Providing a smooth start to the () (B1), and convolving it with its inverse filter (B2) removes the pre-ringing (B3). Providing the () with both a smooth start and a smooth end (C1), and convolving it with its inverse filter (C2) removes both the pre- and the post-ringing (C3).