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Turning an autocorrelation formula into code?
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I am a programmer and my current project requires me to turn a research paper into runnable code.
My level of math experience is fairly low, but what needs to be done has to be done either way, and I'm determined to learn new things.
The research paper can be found here: https://pdfs.semanticscholar.org/0124/09d447691fd74c49bc407b3818b4617641b2.pdf
On page 2 we can see two formulas, one (the first one):
of which I think I have correctly programmed as it is giving me the following results:
which has similarities to Fig 1a:
However I can not figure out how to get results to resemble Fig 1b and 1c.
Would it be too much to ask for someone to explain what's going on with the second formula on page 2, or even pseudo-code that would reflect the formula?
If it is too much to ask for, I'd like to start by asking:
What is this part of the formula doing? Is it multiplying s[n] and s[n + l] which would result in s[n] * s[n + l]?
More about this as a code code can be found in the following StackOverflow question that I made, which is more code-oriented: https://stackoverflow.com/questions/51352890/is-this-autocorrelation-formula-correctly-programmed?noredirect=1#comment89739564_51352890
calculus
asked Jul 17 at 21:04
vaid
101
add a comment |Â
up vote
0
down vote
favorite
I am a programmer and my current project requires me to turn a research paper into runnable code.
My level of math experience is fairly low, but what needs to be done has to be done either way, and I'm determined to learn new things.
The research paper can be found here: https://pdfs.semanticscholar.org/0124/09d447691fd74c49bc407b3818b4617641b2.pdf
On page 2 we can see two formulas, one (the first one):
of which I think I have correctly programmed as it is giving me the following results:
which has similarities to Fig 1a:
However I can not figure out how to get results to resemble Fig 1b and 1c.
Would it be too much to ask for someone to explain what's going on with the second formula on page 2, or even pseudo-code that would reflect the formula?
If it is too much to ask for, I'd like to start by asking:
What is this part of the formula doing? Is it multiplying s[n] and s[n + l] which would result in s[n] * s[n + l]?
More about this as a code code can be found in the following StackOverflow question that I made, which is more code-oriented: https://stackoverflow.com/questions/51352890/is-this-autocorrelation-formula-correctly-programmed?noredirect=1#comment89739564_51352890
calculus
asked Jul 17 at 21:04
vaid
101
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am a programmer and my current project requires me to turn a research paper into runnable code.
My level of math experience is fairly low, but what needs to be done has to be done either way, and I'm determined to learn new things.
The research paper can be found here: https://pdfs.semanticscholar.org/0124/09d447691fd74c49bc407b3818b4617641b2.pdf
On page 2 we can see two formulas, one (the first one):
of which I think I have correctly programmed as it is giving me the following results:
which has similarities to Fig 1a:
However I can not figure out how to get results to resemble Fig 1b and 1c.
Would it be too much to ask for someone to explain what's going on with the second formula on page 2, or even pseudo-code that would reflect the formula?
If it is too much to ask for, I'd like to start by asking:
What is this part of the formula doing? Is it multiplying s[n] and s[n + l] which would result in s[n] * s[n + l]?
More about this as a code code can be found in the following StackOverflow question that I made, which is more code-oriented: https://stackoverflow.com/questions/51352890/is-this-autocorrelation-formula-correctly-programmed?noredirect=1#comment89739564_51352890
calculus
asked Jul 17 at 21:04
vaid
101
I am a programmer and my current project requires me to turn a research paper into runnable code.
My level of math experience is fairly low, but what needs to be done has to be done either way, and I'm determined to learn new things.
The research paper can be found here: https://pdfs.semanticscholar.org/0124/09d447691fd74c49bc407b3818b4617641b2.pdf
On page 2 we can see two formulas, one (the first one):
of which I think I have correctly programmed as it is giving me the following results:
which has similarities to Fig 1a:
However I can not figure out how to get results to resemble Fig 1b and 1c.
Would it be too much to ask for someone to explain what's going on with the second formula on page 2, or even pseudo-code that would reflect the formula?
If it is too much to ask for, I'd like to start by asking:
What is this part of the formula doing? Is it multiplying s[n] and s[n + l] which would result in s[n] * s[n + l]?
More about this as a code code can be found in the following StackOverflow question that I made, which is more code-oriented: https://stackoverflow.com/questions/51352890/is-this-autocorrelation-formula-correctly-programmed?noredirect=1#comment89739564_51352890
calculus
asked Jul 17 at 21:04
vaid
101
asked Jul 17 at 21:04
vaid
101
asked Jul 17 at 21:04
vaid
101
asked Jul 17 at 21:04
vaid
101
101
add a comment |Â
add a comment |Â
1 Answer
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First, this is my understanding of skimming the reseach paper. It may not be correct or even 'near the spot'.
Fig 1a) is not showing the application of any of the formulas, it is showing the input sample (called $s[n]$ in he formulas). That's written in the part below the figure, where it shortly explains what (a), (b) and (c) are. If you have applied forumla (1), you should have gotten something curve 1b).
Also, formulas (1) and (2) are using a letter "l" (el) for the lag, not (as one would assume from a casual inspection) the number "1" (one).
You are correct that both formulas are summing up a bunch of products of the form $s[n]times s[n+l]$. They both start that summation at $n=i$ ($i$ seems to be zero in the examples). They differ in how far they sum, formula (1) sums until $n=i+N-l$, while formula (2) sums until $n=i+N-2l$.
The paper says
Figure 1b-c show the ACF of the acoustic waveform
which were normalized and half-wave rectified from Fig. 1a.
I understand what normalized means (it means that the value for $R_X(l)$ has been divided by $R_X(0)$, such that the curves in 1b) and 1c) start with a value of 1 at $l=0$. I have no idea what "half-wave rectified" means, though.
answered Jul 18 at 10:20
Ingix
2,205125
careful with the second equation, it actually sums untiln = i + N - l - 1theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....
– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
 |Â
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
First, this is my understanding of skimming the reseach paper. It may not be correct or even 'near the spot'.
Fig 1a) is not showing the application of any of the formulas, it is showing the input sample (called $s[n]$ in he formulas). That's written in the part below the figure, where it shortly explains what (a), (b) and (c) are. If you have applied forumla (1), you should have gotten something curve 1b).
Also, formulas (1) and (2) are using a letter "l" (el) for the lag, not (as one would assume from a casual inspection) the number "1" (one).
You are correct that both formulas are summing up a bunch of products of the form $s[n]times s[n+l]$. They both start that summation at $n=i$ ($i$ seems to be zero in the examples). They differ in how far they sum, formula (1) sums until $n=i+N-l$, while formula (2) sums until $n=i+N-2l$.
The paper says
Figure 1b-c show the ACF of the acoustic waveform
which were normalized and half-wave rectified from Fig. 1a.
I understand what normalized means (it means that the value for $R_X(l)$ has been divided by $R_X(0)$, such that the curves in 1b) and 1c) start with a value of 1 at $l=0$. I have no idea what "half-wave rectified" means, though.
answered Jul 18 at 10:20
Ingix
2,205125
careful with the second equation, it actually sums untiln = i + N - l - 1theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....
– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
 |Â
show 5 more comments
up vote
0
down vote
First, this is my understanding of skimming the reseach paper. It may not be correct or even 'near the spot'.
Fig 1a) is not showing the application of any of the formulas, it is showing the input sample (called $s[n]$ in he formulas). That's written in the part below the figure, where it shortly explains what (a), (b) and (c) are. If you have applied forumla (1), you should have gotten something curve 1b).
Also, formulas (1) and (2) are using a letter "l" (el) for the lag, not (as one would assume from a casual inspection) the number "1" (one).
You are correct that both formulas are summing up a bunch of products of the form $s[n]times s[n+l]$. They both start that summation at $n=i$ ($i$ seems to be zero in the examples). They differ in how far they sum, formula (1) sums until $n=i+N-l$, while formula (2) sums until $n=i+N-2l$.
The paper says
Figure 1b-c show the ACF of the acoustic waveform
which were normalized and half-wave rectified from Fig. 1a.
I understand what normalized means (it means that the value for $R_X(l)$ has been divided by $R_X(0)$, such that the curves in 1b) and 1c) start with a value of 1 at $l=0$. I have no idea what "half-wave rectified" means, though.
answered Jul 18 at 10:20
Ingix
2,205125
careful with the second equation, it actually sums untiln = i + N - l - 1theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....
– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
 |Â
show 5 more comments
up vote
0
down vote
up vote
0
down vote
First, this is my understanding of skimming the reseach paper. It may not be correct or even 'near the spot'.
Fig 1a) is not showing the application of any of the formulas, it is showing the input sample (called $s[n]$ in he formulas). That's written in the part below the figure, where it shortly explains what (a), (b) and (c) are. If you have applied forumla (1), you should have gotten something curve 1b).
Also, formulas (1) and (2) are using a letter "l" (el) for the lag, not (as one would assume from a casual inspection) the number "1" (one).
You are correct that both formulas are summing up a bunch of products of the form $s[n]times s[n+l]$. They both start that summation at $n=i$ ($i$ seems to be zero in the examples). They differ in how far they sum, formula (1) sums until $n=i+N-l$, while formula (2) sums until $n=i+N-2l$.
The paper says
Figure 1b-c show the ACF of the acoustic waveform
which were normalized and half-wave rectified from Fig. 1a.
I understand what normalized means (it means that the value for $R_X(l)$ has been divided by $R_X(0)$, such that the curves in 1b) and 1c) start with a value of 1 at $l=0$. I have no idea what "half-wave rectified" means, though.
answered Jul 18 at 10:20
Ingix
2,205125
First, this is my understanding of skimming the reseach paper. It may not be correct or even 'near the spot'.
Fig 1a) is not showing the application of any of the formulas, it is showing the input sample (called $s[n]$ in he formulas). That's written in the part below the figure, where it shortly explains what (a), (b) and (c) are. If you have applied forumla (1), you should have gotten something curve 1b).
Also, formulas (1) and (2) are using a letter "l" (el) for the lag, not (as one would assume from a casual inspection) the number "1" (one).
You are correct that both formulas are summing up a bunch of products of the form $s[n]times s[n+l]$. They both start that summation at $n=i$ ($i$ seems to be zero in the examples). They differ in how far they sum, formula (1) sums until $n=i+N-l$, while formula (2) sums until $n=i+N-2l$.
The paper says
Figure 1b-c show the ACF of the acoustic waveform
which were normalized and half-wave rectified from Fig. 1a.
I understand what normalized means (it means that the value for $R_X(l)$ has been divided by $R_X(0)$, such that the curves in 1b) and 1c) start with a value of 1 at $l=0$. I have no idea what "half-wave rectified" means, though.
answered Jul 18 at 10:20
Ingix
2,205125
answered Jul 18 at 10:20
Ingix
2,205125
answered Jul 18 at 10:20
Ingix
2,205125
answered Jul 18 at 10:20
Ingix
2,205125
2,205125
careful with the second equation, it actually sums untiln = i + N - l - 1theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....
– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
 |Â
show 5 more comments
careful with the second equation, it actually sums untiln = i + N - l - 1theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....
– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
careful with the second equation, it actually sums until
n = i + N - l - 1 theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....– vaid
Jul 18 at 12:38
careful with the second equation, it actually sums until
n = i + N - l - 1 theres an "el" and a "one" in there. and you are correct, I should've gotten something like fig b, but I'm not, surely my code is wrong somewhere. hmmm....– vaid
Jul 18 at 12:38
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
Can you post the code? I meas once you understand what the summation does, it should be 2-3 lines of code (for the forumula). About "el" vs. one: I only realized just now that you can copy the text from the pdf and see what is actually used. OTOH, then I don't understand the big difference between 1b) and 1c): Leaving out one summand should not influence the result that much.
– Ingix
Jul 18 at 12:59
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:16
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I've included a link to my code in the question.
– vaid
Jul 19 at 23:17
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
I can't comment on the coding things at the moment, but the most important thing I see is that lag is always set to 1. This is not what it is supposed to be. The figures you see in 1b) and 1c) are figures where the lag is the independent variable. In the formula for $R_x$ all things are 'given': The input data s[n], the frame size $N$ etc. The only thing that can be varied by you is the lag. See also the sentence from the area between formula (1) and (2): "The lag value that produces maximum peak will be chosen as the pitch period."
– Ingix
Jul 20 at 10:13
 |Â
show 5 more comments
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