How to compress signal from using by Signal Compression method?

Usually when a  signal x(t) is complex in time domain to compress then the signal needs to be transformed to frequency domain X(f). Generally the transformed signals have coeffecients scaled with the basic infomation of the signal. Now either truncating or rounding off the coeffecients to the nearest quantization level makes the signal discrete in frequency domain. When we retransform the frequency domain signal back to the time domain we can see that information which the signal carried is restored with the loss of redundanct content alone. The quantization levels are left to the user to decide.   

There are lot of familiar frequency transformations like FFT,DCT,DWT etc. 

DCT is defined as 10102 (0) ( ) 2 (21) ( ) ( )cos 2 (11) N n N n X xn N n k X k xn N N k N π − = − = = + = ≤≤ − 　　　　　　　　　 (1) where x( ) n is the object sequence with length N. Actually the pattern of the sign of X(k) is unique for the object sequence although it is not in strict sense. Inverse DCT is also defined as 111 (21) ( ) (0) ( )cos 22 N k n k xn X X k N π − = + = + (2) Inverse DCT has a similar form of DCT and they are very fast transforms

T t k 21    . Thus the signal S(t) can be described as follows:             i i i i i S(t) S(t )  (t) S(i t)  (t), where 2 ( ) sin 2 ( ) ( ) F t i t F t i t t i           is the sample function and i assumes discrete value            0; , . 1; , ( ) t k t k i t i t t i For a limited duration  of the speech signal the number of the signal samples N is defined by the expression: 2 F. t N      Taking to account the quazzi stationarity of the signal and also the non critical state of the data collection systems to real time of processing, a method of reduction of the encoding redundancy of the speech signal using the ADC has been developed. Minimization of the error of restored signal consist in the finding those fixed values of the argument n t ,t ,t , ,t 012  that ensure convergence of broken plot from the vertices S S S Sn , , , , 012  towards the function S(t) so that for the entire range of argument changing the absolute error does not exceed permissible values. The function S(t) in these points can be presented as follows: ( ) ( ) 1010 S t  S  k t  t for 01 t  t  t , ( ) ( ) ( ) 201021 S t  S  k t  t  k t  t for 12 t  t  t , ( ) ( ) ( ) ( ) 30102132 S t  S  k t  t  k t  t  k t  t , for 23 t  t  t , where i k can be defined as follows : 101011 t t S S k tg      , , 101021212 t t S S t t S S k       , 1010212132323 t t S S t t S S t t S S k          In general: ( ) ( )  ( ) 001 j n j j j S t  S k t  t  sign t  t    , where         0;( ) 0. 1;( ) 0, j j t t t t  Approximation error is determined by the remainder term of interpolation formula. In this case, the segment of line in the within the time interval [ 1 , j j t t ] is defined by the expression:   , ( ) ( ) ( ) ( ) ( ) 11 j j j j j j t t t t S t S t S t S t         and the remaining member of functions expansion at the same interval will be: ( )( ), 2! ( ) ( )   1   j j t t t t S t R t where S(t) - the second derivative of a given function within the interval. If it is known that R(t) and S(t) are maximal, then 2 max 1 max 2! 2 ( ) ( )          j j S t t t R t . Letting ( ) max S  R t , we get the formula for the sampling interval max max 1 * ( ) 8 S t S t t t j j         . Asking the upper frequency of signal bandwidth is defined we can determine the deviation of real signal value from predicted. Based on the above, an algorithm to implement the procedure for pre-compression of voice information was created. It includes following steps: 1. Set level of allowable absolute error of the recovery signal  ; 2. Set the minimum size M of buffer compression; 3. For the current point the coefficient of prediction is determined; 4. If a deviation of the coefficient k   , we incorporate current sample in compression buffer, increasing the value m of buffer counter by 1 and go to Item 3, if the inequality is not fulfilled, then check the buffer counter m : if m  M then set m  0 and go to to Item 3; if m  M then compression is full field; 5. If end of wav-file not found, then go to Item 3. Linear prediction used for the realization of the process of the second step of compression [3,4].The signal S(t) is presented in a digital form n S , n 1,2,,N , where N is number of signal samples, which is obtained by sampling it at a certain frequency F. This signal n S , n 1,2,,N ,can be presented as a linear combination of preceding values of the signal and some influence n u n p k Sn  ak  Sn k  G u