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What is discrete angular frequency?
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$begingroup$
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 $boldsymbol{y[n]}$ can be expressed as $boldsymbol{y[n] = s[n] + d[n]}$, where $boldsymbol{s[n]}$ is the clean speech and $boldsymbol{d[n]}$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag{1}$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag{2}$$
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
edited 19 hours ago
Olli Niemitalo
8,7431638
asked 20 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 $boldsymbol{y[n]}$ can be expressed as $boldsymbol{y[n] = s[n] + d[n]}$, where $boldsymbol{s[n]}$ is the clean speech and $boldsymbol{d[n]}$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag{1}$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag{2}$$
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
edited 19 hours ago
Olli Niemitalo
8,7431638
asked 20 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 $boldsymbol{y[n]}$ can be expressed as $boldsymbol{y[n] = s[n] + d[n]}$, where $boldsymbol{s[n]}$ is the clean speech and $boldsymbol{d[n]}$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag{1}$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag{2}$$
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
edited 19 hours ago
Olli Niemitalo
8,7431638
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
$endgroup$
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 $boldsymbol{y[n]}$ can be expressed as $boldsymbol{y[n] = s[n] + d[n]}$, where $boldsymbol{s[n]}$ is the clean speech and $boldsymbol{d[n]}$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as
$$y(n,k) = s(n,k) + d(n,k),quad n=0,1,2,ldots,(N-1);quad k=1,2,ldots,Ntag{1}$$
Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame.
$$y(omega,k) = S(omega,k) + D(omega,k)tag{2}$$
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
discrete-signals signal-analysis
edited 19 hours ago
Olli Niemitalo
8,7431638
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
edited 19 hours ago
Olli Niemitalo
8,7431638
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
edited 19 hours ago
Olli Niemitalo
8,7431638
edited 19 hours ago
Olli Niemitalo
8,7431638
edited 19 hours ago
Olli Niemitalo
8,7431638
8,7431638
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
asked 20 hours ago
Andreas ChandraAndreas Chandra
184
184
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$omega$ 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:
$$Y(omega, k) = textstylesum_{n=-infty}^infty y(n)w(k-n)e^{-jomega n}tag{3},$$
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.
answered 19 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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours ago
add a comment |
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1 Answer
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$begingroup$
$omega$ 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:
$$Y(omega, k) = textstylesum_{n=-infty}^infty y(n)w(k-n)e^{-jomega n}tag{3},$$
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.
answered 19 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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours 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:
$$Y(omega, k) = textstylesum_{n=-infty}^infty y(n)w(k-n)e^{-jomega n}tag{3},$$
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.
answered 19 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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours 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:
$$Y(omega, k) = textstylesum_{n=-infty}^infty y(n)w(k-n)e^{-jomega n}tag{3},$$
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.
answered 19 hours ago
Olli NiemitaloOlli Niemitalo
8,7431638
$endgroup$
$omega$ 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:
$$Y(omega, k) = textstylesum_{n=-infty}^infty y(n)w(k-n)e^{-jomega n}tag{3},$$
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.
answered 19 hours ago
Olli NiemitaloOlli Niemitalo
8,7431638
answered 19 hours ago
Olli NiemitaloOlli Niemitalo
8,7431638
answered 19 hours ago
Olli NiemitaloOlli Niemitalo
8,7431638
answered 19 hours ago
Olli NiemitaloOlli Niemitalo
8,7431638
8,7431638
$begingroup$
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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours ago
add a comment |
$begingroup$
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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours ago
$begingroup$
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
16 hours ago
$begingroup$
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
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
16 hours ago
add a comment |
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