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Topic: mfcc coefficient question (Read 7955 times) previous topic - next topic
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mfcc coefficient question

1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?
  Here,I do not deny the rationality of dct.But I wanna a proper explanation.

2. Why throw the first coefficient of mfcc --the zeroth order coefficient after complete dct computation?

3. Where can I download  the literature about the origin of mfcc?

Cheers
HyeeWang@gmail.com

mfcc coefficient question

Reply #1 –
Quote from: hyeewang on
1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?
  Here,I do not deny the rationality of dct.But I wanna a proper explanation.

2. Why throw the first coefficient of mfcc --the zeroth order coefficient after complete dct computation?

3. Where can I download  the literature about the origin of mfcc?

Cheers
HyeeWang@gmail.com


hope I have presented my question clearly. But I am not sure it due
to my bad English.

Why nobody responds with such a direct simple  question?


Cheers
HyeeWang


mfcc coefficient question

Reply #2 –
Quote from: hyeewang on
Why nobody responds with such a direct simple  question?


I don't understand the first 2 questions properly and I fear that they are also much to specific for my knowledge. But in response to question 3: the english wikipedia article has a history section in which several papers are cited as the probable introduction of those features.

mfcc coefficient question

Reply #3 –
Quote from: hyeewang on
1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?

This is probably done for better energy compaction (less spectrum spreading). DCT has better energy compaction than a non-windowed DFT.

Quote from: hyeewang on
2. Why throw the first coefficient of mfcc --the zeroth order coefficient after complete dct computation?

To disregard the power of the signal and only analyze its spectral shape.

Quote from: hyeewang on
3. Where can I download  the literature about the origin of mfcc?

Try wikipedia.

mfcc coefficient question

Reply #4 –
Quote from: hyeewang on
1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?
  Here,I do not deny the rationality of dct.But I wanna a proper explanation.


What you're really doing is using the full (symmetric) spectrum, including the negative frequencies and applying the IDFT to that. But guess what, that's equivalent to applying only the DCT (well, one of the types of DCT) to only the positive part. It's all about the symmetry around zero.

mfcc coefficient question

Reply #5 –
Quote from: Alexey Lukin on
Quote from: hyeewang on
1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?

This is probably done for better energy compaction (less spectrum spreading). DCT has better energy compaction than a non-windowed DFT.

Quote from: hyeewang on
2. Why throw the first coefficient of mfcc --the zeroth order coefficient after complete dct computation?

To disregard the power of the signal and only analyze its spectral shape.

Quote from: hyeewang on
3. Where can I download  the literature about the origin of mfcc?

Try wikipedia.


Thank you. Lukin.

Everyone said the property  of energy compaction about DCT. But it is not the fundamental process of a cepstrum computation,Which is  DFT--- DFT power -- mel scale filter -- log --- IDFT.

In certain case travelling  by sailing is better than by foot. But if you wanna pass through  a desert ,still by sailing ?

mfcc coefficient question

Reply #6 –
Quote from: jmvalin on
Quote from: hyeewang on
1. As a kind of cepstrum, mfcc must comply with the basic process of cepstrum computation.
  But while calculating mfcc,Why use "dct",not "idft" ?
  Here,I do not deny the rationality of dct.But I wanna a proper explanation.


What you're really doing is using the full (symmetric) spectrum, including the negative frequencies and applying the IDFT to that. But guess what, that's equivalent to applying only the DCT (well, one of the types of DCT) to only the positive part. It's all about the symmetry around zero.


Thank you. Jmvalin.

1. IDFT is using the full (symmetric) spectrum, including the negative frequencies . In contrast to that, DCT only use  the positive part.  Why do u think that DCT is equivalent to IDFT?

  I know some basic knowledge. DFT can express IDFT,vice versa. And DCT can be expressed by DFT,vice verca.

2. Since DCT is equivalent to IDFT, Why prefer to DCT than IDFT in calculating mfcc?

3. Since DCT is equivalent to IDFT,whether in all cases DCT can be replaced by IDFT?

 

mfcc coefficient question

Reply #7 –
Quote from: hyeewang on
1. IDFT is using the full (symmetric) spectrum, including the negative frequencies . In contrast to that, DCT only use  the positive part.  Why do u think that DCT is equivalent to IDFT?

  I know some basic knowledge. DFT can express IDFT,vice versa. And DCT can be expressed by DFT,vice verca.


Basically, if you do the DFT of a symmetric signal, then the sine components will all be zero because they have odd symmetry. The cosine components will be twice as large because of their even symmetry. So in the end, the DCT of the half-spectrum (positive freq) is equivalent to the DFT of the full spectrum (negative+positive frequencies). That's all there is to it.