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What is discrete angular frequency?
Help calculating / understanding the MFCCs: Mel-Frequency Cepstrum Coefficientsunderstanding discrete waveletsWhat kind of discrete convolution is this?Discrete signal power. Does it depend on sampling frequency?the importance of discrete sine transformDiscrete Time to Frequency ResponseSystem Identification with periodic signal confusionHow to calculate the discrete power of a discrete signal?what is angular frequency ! what does it mean?Power of a Discrete time signal
$begingroup$
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
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
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
edited 5 hours ago
Olli Niemitalo
8,7431638
asked 5 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 $boldsymboly[n]$ 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
discrete-signals signal-analysis
edited 5 hours ago
Olli Niemitalo
8,7431638
asked 5 hours ago
Andreas ChandraAndreas Chandra
184
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
edited 5 hours ago
Olli Niemitalo
8,7431638
8,7431638
asked 5 hours ago
Andreas ChandraAndreas Chandra
184
asked 5 hours ago
Andreas ChandraAndreas Chandra
184
asked 5 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:
$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$
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.
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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1 Answer
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1 Answer
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oldest
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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:
$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$
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.
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.
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.
answered 5 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:
$$Y(omega, k) = textstylesum_n=-infty^infty y(n)w(k-n)e^-jomega ntag3,$$
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.
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
answered 5 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
2 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
1 hour 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
2 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
1 hour 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
2 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
2 hours ago
$begingroup$
@AndreasChandra sorry, I only wanted to answer the specific question.
$endgroup$
– Olli Niemitalo
1 hour 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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