Computer Select (Limited Edition)/Computer Select.iso/dobbs/v17n04/wavelet.exe/WAVEDEMO.MAN

Text File | 1991-11-20 | 6.0 KB | 101 lines

                         WAVEDEMO User's Manual / Tip Sheet



              Rather than a full fledged user's manual, I'm providing this
         manual / tip sheet to help the user get started with experimenting
         with WAVEDEMO.EXE.  The commands in the program are more or less
         self explanitory.  Study the help panels before you proceed to use
         WAVEDEMO.

              Upon toggling out of the help panels (using the F1 key), the
         control panel shows alpha and beta set to zero.  With alpha and
         beta equal, the Haar wavelet coefficients are generated.  The
         default sinewave of 312 data points in the input graph display
         is shown.  All other graphs are zero.  The values of alpha and
         beta are set by (A)lpha and (B)eta, respectively.  Entering in a
         new alpha or beta automatically recalculates the wavelet filter
         coefficients.  The range of alpha and beta is -π ≤ α,ß < π.

              Changing the number of levels with (L)evels will clear any
         existing transform coefficients in both the decomposition and
         reconstruction displays.  The (I)nput data and (R)ead coefficient
         operation also have the same effect.  The (Z)ero coefficients
         operation will zero only those coefficients of the transform type
         displayed.  The coefficients of one transform type may be copied
         to the other using the (C)opy operation.

              The (I)nput and (O)utput operations read and write signal
         data files, respectively.  (I)nput loads the data into the input
         graph display for wavelet decomposition.  (O)utput stores the
         reconstructed data in the output graph display.  The name
         requested at the prompt must follow standard DOS conventions.  I
         chose the .DAT extension for simplicity.  The file SINE.DAT is a
         sine wave of the same frequency as the default sine wave in
         WAVEDEMO but with a length of 256 samples.  AH.DAT is a 256-point
         sampled voice waveform of the phone 'AH' as in "hot".  Note: when
         creating an input file the number of data points in the file must
         be an integral multiple of the unit interval for the wavelet
         transform.  That is, if J levels of transform are to be created,
                                                  J
         then the length of the unit interval is 2  data points.

              The (W)rite and (R)ead operations store and load wavelet
         transform coefficients files.  (W)rite stores the wavelet
         transform coefficients (Level 0 approximation and detail
         coefficients) from the decomposition graph displays.  The size of
         the transform coefficient set and the values of alpha and beta
         used to generate the wavelet filter coefficients are also stored.
         (R)ead load the wavelet transform coefficient into the
         reconstruction graph display.  The alpha and beta values are
         loaded and the wavelet filter coefficients are regenerated.

              (P)rune uses ZeroTreeDetail to zero the upper levels of
         detail coefficients.  The prompt request the number of upper
         levels to set to zero.  Performing the inverse wavelet transform
         upon the modified data yields a partial reconstruction of the
         original signal.  The partial reconstruction is based only on the
         coarse details and the Level 0 approximation coefficients.
         Experiments in data compression can be conducted by picking the
         wavelet systems whose approximation (scaling function) level most
         completely matches the original signal.  The minimizing the mean
         squared error (MSE) value can assist in this operation.  To save
         the partial reconstruction coefficients, use the (C)opy operation
         to move them over to the decomposition display.

              (V)iew coefficients allows for numerical examination of the
         input and output signal data points and wavelet transform
         coefficients for both decomposition and reconstruction.  (V)iew
         allows examination of the five additional coefficients at the end
         of each coefficient and signal data array.  These coefficients
         handle overlap effect caused by the wavelet filters running off
         the end of the data set.

              The files PHI.COF and PSI.COF are wavelet coefficient files
         that allow viewing of the wavelet scaling function, φ, and the
         primary wavelet, [phi], respectively.  Since phi and psi are
         recursively defined, they can not be viewed as functions in the
         traditional sense.  They can viewed by performing the inverse fast
         wavelet transform on an impulse (as single coefficient non-zero,
         all others zero) in either the approximation or the detail
         coefficients of level 0.  This is equivalent to performing the
         inverse Fourier transform on an impulse to obtain a pure sinewave
         at a given frequency.  PHI.COF contains the a single non-zero
         coefficient in the approximation level, while PSI.COF contains the
         a single non-zero coefficient in the detail level.

              The values of alpha and beta must be set after (R)EADing the
         appropriate file into the reconstruction display.  After
         (E)xecution of the inverse transform, phi or psi will be displayed
         in the output graph display.  Note that with wavelets of order six
         (six coefficients), there is some distortion and/or truncation of
         phi and psi.  This is caused by data end effects and spreading of
         the function outside the range of the graph.  An inverse transform
         larger than 256 point would solve these problems.

         Hope you enjoy WAVEDEMO and find it educational! - Mac A. Cody