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

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?

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

1

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

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

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

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.
– Kudera Sebastian
Dec 28 '18 at 18:20

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);.
– horchler
Dec 28 '18 at 20:13

|
show 1 more comment

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

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?

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

1

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

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

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

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.
– Kudera Sebastian
Dec 28 '18 at 18:20

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);.
– horchler
Dec 28 '18 at 20:13

|
show 1 more comment

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

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?

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

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

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

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

edited Dec 29 '18 at 0:01

Somos

13.1k11034

edited Dec 29 '18 at 0:01

Somos

13.1k11034

edited Dec 29 '18 at 0:01

Somos

13.1k11034

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

asked Dec 28 '18 at 18:10

Kudera Sebastian

539218

1

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

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

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

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.
– Kudera Sebastian
Dec 28 '18 at 18:20

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);.
– horchler
Dec 28 '18 at 20:13

|
show 1 more comment

1

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

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

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

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.
– Kudera Sebastian
Dec 28 '18 at 18:20

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);.
– horchler
Dec 28 '18 at 20:13

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

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

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

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.
– Kudera Sebastian
Dec 28 '18 at 18:20

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);.
– horchler
Dec 28 '18 at 20:13

|
show 1 more comment

2 Answers
2

active

oldest

votes

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.

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

add a comment |

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 $0.009321942713359250447 dots$.

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

add a comment |

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

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

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.

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

add a comment |

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

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.

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

add a comment |

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

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.

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

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

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.

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

edited Dec 28 '18 at 18:30

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

answered Dec 28 '18 at 18:23

Eevee Trainer

5,0211734

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

add a comment |

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

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".
– Kudera Sebastian
Dec 28 '18 at 18:26

add a comment |

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 $0.009321942713359250447 dots$.

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

add a comment |

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 $0.009321942713359250447 dots$.

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

add a comment |

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 $0.009321942713359250447 dots$.

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

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 $0.009321942713359250447 dots$.

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

answered Dec 28 '18 at 18:33

Eric Towers

32.1k22267

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

add a comment |

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

Yup. Looks like matlab is a rebel.
– Kudera Sebastian
Dec 28 '18 at 18:37

add a comment |

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