Signal Processing Toolbox

Inverse Complex Cepstrum

To invert the complex cepstrum, use the icceps function. Inversion is complicated by the fact that the cceps function performs a data dependent phase modification so that the unwrapped phase of its input is continuous at zero frequency. The phase modification is equivalent to an integer delay. This delay term is returned by cceps if you ask for a second output. For example:

• x = 1:10;
  [xhat,delay] = cceps(x)
  xhat =
    Columns 1 through 7 
      2.2428   -0.0420   -0.0210    0.0045    0.0366    0.0788    0.1386
    Columns 8 through 10 
      0.2327    0.4114    0.9249
  delay =
       1
  

To invert the complex cepstrum, use icceps with the original delay parameter:

• icc = icceps(xhat,2)
  ans =
    Columns 1 through 7 
      2.0000    3.0000    4.0000    5.0000    6.0000    7.0000    8.0000
    Columns 8 through 10 
      9.0000    10.0000   1.0000
  

As shown in the above example, with any modification of the complex cepstrum, the original delay term may no longer be valid. You will not be able to invert the complex cepstrum exactly.

Cepstrum Analysis

FFT-Based Time-Frequency Analysis

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