Calculating value of $text{sinc}(x)$, WolframAlpha and MATLAB give two different answers.












2












$begingroup$


I need to evaluate the following:
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(n-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(n-4)bigg)$$



for $n=[0,...,8]$



I don't have the sinc function in my casio fx so I wanted to use the fact that $text{sinc}(x)=frac{text{sin}(x)}{x}$ and that $text{sinc}(0)=1$
Hence, for $n=0$ I got
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(-4)bigg)=0.1378....$$



This seems to agree with wolfram alpha:




enter image description here




But then I checked the mark scheme on my past paper that the question is taken from, and there it says that I should've got $0.0093$ so i put it in MATLAB:




enter image description here




...and it also says $0.0093$.



So... which one of the two is correct? What's going on?






trigonometry matlab wolfram-alpha







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    There is a problem for $n=4$.
    $endgroup$
    – Michael Rozenberg
    Dec 28 '18 at 18:16






  • 1




    $begingroup$
    Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
    $endgroup$
    – Josh B.
    Dec 28 '18 at 18:18










  • $begingroup$
    @JoshB. That is criminal. I need to write an angry email to Matlab.
    $endgroup$
    – DudeMan
    Dec 28 '18 at 18:19










  • $begingroup$
    I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:20












  • $begingroup$
    This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
    $endgroup$
    – horchler
    Dec 28 '18 at 20:13


















2












$begingroup$


I need to evaluate the following:
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(n-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(n-4)bigg)$$



for $n=[0,...,8]$



I don't have the sinc function in my casio fx so I wanted to use the fact that $text{sinc}(x)=frac{text{sin}(x)}{x}$ and that $text{sinc}(0)=1$
Hence, for $n=0$ I got
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(-4)bigg)=0.1378....$$



This seems to agree with wolfram alpha:




enter image description here




But then I checked the mark scheme on my past paper that the question is taken from, and there it says that I should've got $0.0093$ so i put it in MATLAB:




enter image description here




...and it also says $0.0093$.



So... which one of the two is correct? What's going on?






trigonometry matlab wolfram-alpha







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    There is a problem for $n=4$.
    $endgroup$
    – Michael Rozenberg
    Dec 28 '18 at 18:16






  • 1




    $begingroup$
    Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
    $endgroup$
    – Josh B.
    Dec 28 '18 at 18:18










  • $begingroup$
    @JoshB. That is criminal. I need to write an angry email to Matlab.
    $endgroup$
    – DudeMan
    Dec 28 '18 at 18:19










  • $begingroup$
    I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:20












  • $begingroup$
    This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
    $endgroup$
    – horchler
    Dec 28 '18 at 20:13
















2












2








2


1



$begingroup$


I need to evaluate the following:
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(n-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(n-4)bigg)$$



for $n=[0,...,8]$



I don't have the sinc function in my casio fx so I wanted to use the fact that $text{sinc}(x)=frac{text{sin}(x)}{x}$ and that $text{sinc}(0)=1$
Hence, for $n=0$ I got
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(-4)bigg)=0.1378....$$



This seems to agree with wolfram alpha:




enter image description here




But then I checked the mark scheme on my past paper that the question is taken from, and there it says that I should've got $0.0093$ so i put it in MATLAB:




enter image description here




...and it also says $0.0093$.



So... which one of the two is correct? What's going on?






trigonometry matlab wolfram-alpha







share|cite|improve this question











$endgroup$




I need to evaluate the following:
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(n-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(n-4)bigg)$$



for $n=[0,...,8]$



I don't have the sinc function in my casio fx so I wanted to use the fact that $text{sinc}(x)=frac{text{sin}(x)}{x}$ and that $text{sinc}(0)=1$
Hence, for $n=0$ I got
$$frac{2}{3}text{sinc}bigg(frac{2pi}{3}(-4)bigg)-frac{1}{3}text{sinc}bigg(frac{pi}{3}(-4)bigg)=0.1378....$$



This seems to agree with wolfram alpha:




enter image description here




But then I checked the mark scheme on my past paper that the question is taken from, and there it says that I should've got $0.0093$ so i put it in MATLAB:




enter image description here




...and it also says $0.0093$.



So... which one of the two is correct? What's going on?






trigonometry matlab wolfram-alpha




trigonometry matlab wolfram-alpha






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 29 '18 at 0:01









Somos

14k11235




14k11235










asked Dec 28 '18 at 18:10









Scavenger23Scavenger23

544218




544218








  • 1




    $begingroup$
    There is a problem for $n=4$.
    $endgroup$
    – Michael Rozenberg
    Dec 28 '18 at 18:16






  • 1




    $begingroup$
    Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
    $endgroup$
    – Josh B.
    Dec 28 '18 at 18:18










  • $begingroup$
    @JoshB. That is criminal. I need to write an angry email to Matlab.
    $endgroup$
    – DudeMan
    Dec 28 '18 at 18:19










  • $begingroup$
    I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:20












  • $begingroup$
    This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
    $endgroup$
    – horchler
    Dec 28 '18 at 20:13
















  • 1




    $begingroup$
    There is a problem for $n=4$.
    $endgroup$
    – Michael Rozenberg
    Dec 28 '18 at 18:16






  • 1




    $begingroup$
    Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
    $endgroup$
    – Josh B.
    Dec 28 '18 at 18:18










  • $begingroup$
    @JoshB. That is criminal. I need to write an angry email to Matlab.
    $endgroup$
    – DudeMan
    Dec 28 '18 at 18:19










  • $begingroup$
    I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:20












  • $begingroup$
    This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
    $endgroup$
    – horchler
    Dec 28 '18 at 20:13










1




1




$begingroup$
There is a problem for $n=4$.
$endgroup$
– Michael Rozenberg
Dec 28 '18 at 18:16




$begingroup$
There is a problem for $n=4$.
$endgroup$
– Michael Rozenberg
Dec 28 '18 at 18:16




1




1




$begingroup$
Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
$endgroup$
– Josh B.
Dec 28 '18 at 18:18




$begingroup$
Matlab includes a factor of Pi in it's definition of sinc. mathworks.com/help/signal/ref/sinc.html
$endgroup$
– Josh B.
Dec 28 '18 at 18:18












$begingroup$
@JoshB. That is criminal. I need to write an angry email to Matlab.
$endgroup$
– DudeMan
Dec 28 '18 at 18:19




$begingroup$
@JoshB. That is criminal. I need to write an angry email to Matlab.
$endgroup$
– DudeMan
Dec 28 '18 at 18:19












$begingroup$
I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
$endgroup$
– Scavenger23
Dec 28 '18 at 18:20






$begingroup$
I see. They use something called normalized sinc. And it would make senses cause Wiki says: In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by bla bla bla. And the course I am doing is signal processing.
$endgroup$
– Scavenger23
Dec 28 '18 at 18:20














$begingroup$
This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
$endgroup$
– horchler
Dec 28 '18 at 20:13






$begingroup$
This function is not part of core Matlab but rather the Signal Processing Toolbox. As @EeveeTrainer points out below, this normalized sinc function is commonly used in signal processing applications that this toolbox was designed for. You can easily create a non-normalized version, e.g.: sinc2=@(x)sinc(x/pi);.
$endgroup$
– horchler
Dec 28 '18 at 20:13












2 Answers
2






active

oldest

votes


















3












$begingroup$

As it happens, there are apparently two different conventions for what the $text{sinc}(x)$ function actually denotes in terms of the $sin(x)$ function. (I ran into this same confusion on my class on Fourier analysis.) The conventions you might see are



$$text{sinc}(x) = frac{sin(x)}{x} ;;; text{or} ;;; text{sinc}(x) = frac{sin(pi x)}{pi x}$$



The latter is known as the "normalized sinc function," per Wikipedia. I don't know much about which is used more when, so I'll leave you with the Wikipedia article in that respect.



Checking your functions if interpreted in the latter way, i.e. for $n=0$



$$frac{2}{3} left( frac{-3}{8pi^2} right) sin bigg(frac{-8pi^2}{3}bigg)-frac{1}{3} left( frac{-3}{4pi^2} right) sin bigg(frac{-4pi^2}{3}bigg)$$



Wolfram Alpha gives a value of $0.0093...$, in agreement with your MATLAB answer. Indeed, as noted by Josh B. in the comments, MATLAB uses the latter convention.



I would assume, then, this is the source of the discrepancy.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:26



















1












$begingroup$

Matlab defines
$$ mathrm{sinc}_{text{Matlab}} = begin{cases}
frac{sin(pi t)}{pi t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Wolfram (in the Details section) and the rest of the world define
$$ mathrm{sinc}_{text{everyone else}} = begin{cases}
frac{sin t}{t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Using Matlab's nonstandard definition of this function, the value of your $n=0$ expression is $0.009321942713359250447 dots$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yup. Looks like matlab is a rebel.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:37











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

As it happens, there are apparently two different conventions for what the $text{sinc}(x)$ function actually denotes in terms of the $sin(x)$ function. (I ran into this same confusion on my class on Fourier analysis.) The conventions you might see are



$$text{sinc}(x) = frac{sin(x)}{x} ;;; text{or} ;;; text{sinc}(x) = frac{sin(pi x)}{pi x}$$



The latter is known as the "normalized sinc function," per Wikipedia. I don't know much about which is used more when, so I'll leave you with the Wikipedia article in that respect.



Checking your functions if interpreted in the latter way, i.e. for $n=0$



$$frac{2}{3} left( frac{-3}{8pi^2} right) sin bigg(frac{-8pi^2}{3}bigg)-frac{1}{3} left( frac{-3}{4pi^2} right) sin bigg(frac{-4pi^2}{3}bigg)$$



Wolfram Alpha gives a value of $0.0093...$, in agreement with your MATLAB answer. Indeed, as noted by Josh B. in the comments, MATLAB uses the latter convention.



I would assume, then, this is the source of the discrepancy.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:26
















3












$begingroup$

As it happens, there are apparently two different conventions for what the $text{sinc}(x)$ function actually denotes in terms of the $sin(x)$ function. (I ran into this same confusion on my class on Fourier analysis.) The conventions you might see are



$$text{sinc}(x) = frac{sin(x)}{x} ;;; text{or} ;;; text{sinc}(x) = frac{sin(pi x)}{pi x}$$



The latter is known as the "normalized sinc function," per Wikipedia. I don't know much about which is used more when, so I'll leave you with the Wikipedia article in that respect.



Checking your functions if interpreted in the latter way, i.e. for $n=0$



$$frac{2}{3} left( frac{-3}{8pi^2} right) sin bigg(frac{-8pi^2}{3}bigg)-frac{1}{3} left( frac{-3}{4pi^2} right) sin bigg(frac{-4pi^2}{3}bigg)$$



Wolfram Alpha gives a value of $0.0093...$, in agreement with your MATLAB answer. Indeed, as noted by Josh B. in the comments, MATLAB uses the latter convention.



I would assume, then, this is the source of the discrepancy.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:26














3












3








3





$begingroup$

As it happens, there are apparently two different conventions for what the $text{sinc}(x)$ function actually denotes in terms of the $sin(x)$ function. (I ran into this same confusion on my class on Fourier analysis.) The conventions you might see are



$$text{sinc}(x) = frac{sin(x)}{x} ;;; text{or} ;;; text{sinc}(x) = frac{sin(pi x)}{pi x}$$



The latter is known as the "normalized sinc function," per Wikipedia. I don't know much about which is used more when, so I'll leave you with the Wikipedia article in that respect.



Checking your functions if interpreted in the latter way, i.e. for $n=0$



$$frac{2}{3} left( frac{-3}{8pi^2} right) sin bigg(frac{-8pi^2}{3}bigg)-frac{1}{3} left( frac{-3}{4pi^2} right) sin bigg(frac{-4pi^2}{3}bigg)$$



Wolfram Alpha gives a value of $0.0093...$, in agreement with your MATLAB answer. Indeed, as noted by Josh B. in the comments, MATLAB uses the latter convention.



I would assume, then, this is the source of the discrepancy.






share|cite|improve this answer











$endgroup$



As it happens, there are apparently two different conventions for what the $text{sinc}(x)$ function actually denotes in terms of the $sin(x)$ function. (I ran into this same confusion on my class on Fourier analysis.) The conventions you might see are



$$text{sinc}(x) = frac{sin(x)}{x} ;;; text{or} ;;; text{sinc}(x) = frac{sin(pi x)}{pi x}$$



The latter is known as the "normalized sinc function," per Wikipedia. I don't know much about which is used more when, so I'll leave you with the Wikipedia article in that respect.



Checking your functions if interpreted in the latter way, i.e. for $n=0$



$$frac{2}{3} left( frac{-3}{8pi^2} right) sin bigg(frac{-8pi^2}{3}bigg)-frac{1}{3} left( frac{-3}{4pi^2} right) sin bigg(frac{-4pi^2}{3}bigg)$$



Wolfram Alpha gives a value of $0.0093...$, in agreement with your MATLAB answer. Indeed, as noted by Josh B. in the comments, MATLAB uses the latter convention.



I would assume, then, this is the source of the discrepancy.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 28 '18 at 18:30

























answered Dec 28 '18 at 18:23









Eevee TrainerEevee Trainer

6,31811137




6,31811137












  • $begingroup$
    Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:26


















  • $begingroup$
    Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:26
















$begingroup$
Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
$endgroup$
– Scavenger23
Dec 28 '18 at 18:26




$begingroup$
Yeah I had a read about it now. Looks like I need to have a discussion with my professor. Couple of weeks ago he defines it in a "standard way" and then suddenly in the past paper it is in the "normalized way".
$endgroup$
– Scavenger23
Dec 28 '18 at 18:26











1












$begingroup$

Matlab defines
$$ mathrm{sinc}_{text{Matlab}} = begin{cases}
frac{sin(pi t)}{pi t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Wolfram (in the Details section) and the rest of the world define
$$ mathrm{sinc}_{text{everyone else}} = begin{cases}
frac{sin t}{t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Using Matlab's nonstandard definition of this function, the value of your $n=0$ expression is $0.009321942713359250447 dots$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yup. Looks like matlab is a rebel.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:37
















1












$begingroup$

Matlab defines
$$ mathrm{sinc}_{text{Matlab}} = begin{cases}
frac{sin(pi t)}{pi t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Wolfram (in the Details section) and the rest of the world define
$$ mathrm{sinc}_{text{everyone else}} = begin{cases}
frac{sin t}{t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Using Matlab's nonstandard definition of this function, the value of your $n=0$ expression is $0.009321942713359250447 dots$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yup. Looks like matlab is a rebel.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:37














1












1








1





$begingroup$

Matlab defines
$$ mathrm{sinc}_{text{Matlab}} = begin{cases}
frac{sin(pi t)}{pi t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Wolfram (in the Details section) and the rest of the world define
$$ mathrm{sinc}_{text{everyone else}} = begin{cases}
frac{sin t}{t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Using Matlab's nonstandard definition of this function, the value of your $n=0$ expression is $0.009321942713359250447 dots$.






share|cite|improve this answer









$endgroup$



Matlab defines
$$ mathrm{sinc}_{text{Matlab}} = begin{cases}
frac{sin(pi t)}{pi t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Wolfram (in the Details section) and the rest of the world define
$$ mathrm{sinc}_{text{everyone else}} = begin{cases}
frac{sin t}{t} & t neq 0, \
1 & t = 0
end{cases} text{.} $$



Using Matlab's nonstandard definition of this function, the value of your $n=0$ expression is $0.009321942713359250447 dots$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 28 '18 at 18:33









Eric TowersEric Towers

32.7k22370




32.7k22370












  • $begingroup$
    Yup. Looks like matlab is a rebel.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:37


















  • $begingroup$
    Yup. Looks like matlab is a rebel.
    $endgroup$
    – Scavenger23
    Dec 28 '18 at 18:37
















$begingroup$
Yup. Looks like matlab is a rebel.
$endgroup$
– Scavenger23
Dec 28 '18 at 18:37




$begingroup$
Yup. Looks like matlab is a rebel.
$endgroup$
– Scavenger23
Dec 28 '18 at 18:37


















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