an approximation of the signal x n is given by this approximation is used on the decoder side to reconstruct the original transient signal from its major constituent frequency components the reconstruction accuracy depends on the number of elements in v however for very low bit rates not many components can be transmitted fig4 shows the reconstruction of x n using the above principle plot a shows the original transient signal plots b c d show the progressive summing of sinusoidal signals to arrive at an approximation of the original signal shown as plot e note the considerable ringing in the latter part of the reconstructed signal in plot e this ringing is undesirable as it introduces an additional damping effect which reduces the sharpness of the reproduced transient signal with the three sinusoids summed as illustrated in fig4 a rough approximation of the transient is obtained however a considerable problem is that the reconstructed signal does not decay as much as the original due to the ringing to model the decay function an envelope of the signal must be determined a reasonable way of obtaining the envelope is proposed here given the signal x n an absolute magnitude version of the signal x abs n u2225 x n u2225 is derived following this a low pass filtering of the absolute signal x abs n with the filter h z 1 z u2212 1 z u2212 2 z u2212 m is performed where m is the order of the filter plus one the low pass filtering removes short term fluctuations and so generates a kind of envelope x env n.