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What is discrete angular frequency?

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1

$begingroup$

I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames"

Question: What is the discrete angular frequency index? Is it part of Short Time Fourier Transform?

Assume that the noisy speech $boldsymboly[n]$ can be expressed as $boldsymboly[n] = s[n] + d[n]$, where $boldsymbols[n]$ is the clean speech and $boldsymbold[n]$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag1$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag2$$
Here $omega$ is the discrete angular frequency index of the frames.

The paper is:

Navneet Upadhyay and Rahul Kumar Jaiswal: "Single Channel Speech Enhancement: Using Wiener Filtering with Recursive Noise Estimation", Procedia Computer Science, Volume 84, 2016, Pages 22-30, doi:10.1016/j.procs.2016.04.061.

discrete-signals signal-analysis

share|improve this question

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

$endgroup$

add a comment | 

1

$begingroup$

I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames"

Question: What is the discrete angular frequency index? Is it part of Short Time Fourier Transform?

Assume that the noisy speech $boldsymboly[n]$ can be expressed as $boldsymboly[n] = s[n] + d[n]$, where $boldsymbols[n]$ is the clean speech and $boldsymbold[n]$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag1$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag2$$
Here $omega$ is the discrete angular frequency index of the frames.

The paper is:

Navneet Upadhyay and Rahul Kumar Jaiswal: "Single Channel Speech Enhancement: Using Wiener Filtering with Recursive Noise Estimation", Procedia Computer Science, Volume 84, 2016, Pages 22-30, doi:10.1016/j.procs.2016.04.061.

discrete-signals signal-analysis

share|improve this question

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

$endgroup$

add a comment | 

$begingroup$

I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames"

Question: What is the discrete angular frequency index? Is it part of Short Time Fourier Transform?

Assume that the noisy speech $boldsymboly[n]$ can be expressed as $boldsymboly[n] = s[n] + d[n]$, where $boldsymbols[n]$ is the clean speech and $boldsymbold[n]$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag1$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag2$$
Here $omega$ is the discrete angular frequency index of the frames.

The paper is:

Navneet Upadhyay and Rahul Kumar Jaiswal: "Single Channel Speech Enhancement: Using Wiener Filtering with Recursive Noise Estimation", Procedia Computer Science, Volume 84, 2016, Pages 22-30, doi:10.1016/j.procs.2016.04.061.

discrete-signals signal-analysis

share|improve this question

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

$endgroup$

share|improve this question

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

share|improve this question

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

edited 5 hours ago

Olli Niemitalo

8,7431638

edited 5 hours ago

Olli Niemitalo

8,7431638

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

asked 5 hours ago

Andreas ChandraAndreas Chandra

184

1 Answer
1

active

oldest

votes

2

$begingroup$

$omega$ is angular frequency in radians, $omega =2pi fT$, where $f$ is frequency (for example in Hz) and $T$ is sampling period (for example in seconds). This is revealed by Eq. 3:

$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$

which represents discrete-time Fourier transform (DTFT) of windowed signal $y(n)w(k-n)$.

It's not common to call $omega$ "discrete angular frequency index", which gives just 3 google hits.

share|improve this answer

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I see. But I never heard of DTFT function exist in python especially Librosa, do you have any reference on how I compute in Python? Moreover, the paper also mentions that they use STFT in Fig.2 is STFT is the same with STFT?
  $endgroup$
  – Andreas Chandra
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AndreasChandra sorry, I only wanted to answer the specific question.
  $endgroup$
  – Olli Niemitalo
  1 hour ago
  
  

  
  
  
  

add a comment | 

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2

$begingroup$

$omega$ is angular frequency in radians, $omega =2pi fT$, where $f$ is frequency (for example in Hz) and $T$ is sampling period (for example in seconds). This is revealed by Eq. 3:

$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$

which represents discrete-time Fourier transform (DTFT) of windowed signal $y(n)w(k-n)$.

It's not common to call $omega$ "discrete angular frequency index", which gives just 3 google hits.

share|improve this answer

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I see. But I never heard of DTFT function exist in python especially Librosa, do you have any reference on how I compute in Python? Moreover, the paper also mentions that they use STFT in Fig.2 is STFT is the same with STFT?
  $endgroup$
  – Andreas Chandra
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AndreasChandra sorry, I only wanted to answer the specific question.
  $endgroup$
  – Olli Niemitalo
  1 hour ago
  
  

  
  
  
  

add a comment | 

2

$begingroup$

$omega$ is angular frequency in radians, $omega =2pi fT$, where $f$ is frequency (for example in Hz) and $T$ is sampling period (for example in seconds). This is revealed by Eq. 3:

$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$

which represents discrete-time Fourier transform (DTFT) of windowed signal $y(n)w(k-n)$.

It's not common to call $omega$ "discrete angular frequency index", which gives just 3 google hits.

share|improve this answer

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I see. But I never heard of DTFT function exist in python especially Librosa, do you have any reference on how I compute in Python? Moreover, the paper also mentions that they use STFT in Fig.2 is STFT is the same with STFT?
  $endgroup$
  – Andreas Chandra
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AndreasChandra sorry, I only wanted to answer the specific question.
  $endgroup$
  – Olli Niemitalo
  1 hour ago
  
  

  
  
  
  

add a comment | 

$begingroup$

$omega$ is angular frequency in radians, $omega =2pi fT$, where $f$ is frequency (for example in Hz) and $T$ is sampling period (for example in seconds). This is revealed by Eq. 3:

$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$

which represents discrete-time Fourier transform (DTFT) of windowed signal $y(n)w(k-n)$.

It's not common to call $omega$ "discrete angular frequency index", which gives just 3 google hits.

share|improve this answer

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

$endgroup$

share|improve this answer

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638

answered 5 hours ago

Olli NiemitaloOlli Niemitalo

8,7431638