sinc + cos function plot

Respectively, codes, matlab plot, and graphing site plot.

Even though I made same argument, matlab plot gives wrong plot. What's wrong? I need your help.

[Walter Roberson]

The graphing site is clearly wrong: the red curve is just sinc() without any cos() component.

[James Tursa]

Please post code as regular text highlighed by the CODE button. We can't run images.

[민건 김]

I figured out what's wrong. I thought sinc at matlab gives sin(x)/x but basically it gives sin(pi x)/pi x. Here, I wanna plot former one, which is unnormalized one, but I don't know how to, either.... Haha

Answer 1

[VBBV]

Delete pi from below line

% delete pi from the below line
a = (-4:0.001:4);
p = 10;
f = p*sinc(a) + cos(a)

f = 1×8001

-0.6536 -0.6569 -0.6602 -0.6634 -0.6667 -0.6699 -0.6732 -0.6765 -0.6797 -0.6830 -0.6862 -0.6895 -0.6928 -0.6960 -0.6993 -0.7025 -0.7058 -0.7091 -0.7123 -0.7156 -0.7189 -0.7221 -0.7254 -0.7287 -0.7319 -0.7352 -0.7384 -0.7417 -0.7450 -0.7482

plot(a,f)

[민건 김]

Thank you. It works but can you explain me why? I cant' find the reason.

[Walter Roberson]

The cos still needs the pi

a = (-4:0.001:4)*pi;
p = 10;
f = p*sinc(a/pi) + cos(a)

f = 1×8001

1.0000 0.9975 0.9950 0.9925 0.9899 0.9874 0.9848 0.9822 0.9796 0.9771 0.9744 0.9718 0.9692 0.9666 0.9639 0.9613 0.9586 0.9559 0.9532 0.9505 0.9478 0.9451 0.9424 0.9396 0.9369 0.9341 0.9313 0.9285 0.9257 0.9229

plot(a,f)

[VBBV]

By definition sinc can be written as (sinx / x) , so if you apply in the equation, you would get a result as shown below,

% delete pi from the below line
a = (-4:0.001:4)*pi;
p = 10;
f = p*sin(a)./a + cos(a)

f = 1×8001

1.0000 0.9975 0.9950 0.9925 0.9899 0.9874 0.9848 0.9822 0.9796 0.9771 0.9744 0.9718 0.9692 0.9666 0.9639 0.9613 0.9586 0.9559 0.9532 0.9505 0.9478 0.9451 0.9424 0.9396 0.9369 0.9341 0.9313 0.9285 0.9257 0.9229

plot(a,f)

In your code, you have multiplied or included pi in x-vector, but did not divide it. The graph which you want to obtain is actually sin(pi*x)/ (pi*x)

[Walter Roberson]

Note however

x = 0

x = 0

sinc(x)

ans = 1

sin(x)./x

ans = NaN

[Stephen23]

"By definition sinc can be written as (sinx / x) "

Except in the field of digital signal processing where it is commonly defined as

sin(pi*x) / (pi*x)

which is the definition that SINC uses, SINC being part of the Signal Processing toolbox:

https://www.mathworks.com/help/signal/ref/sinc.html

https://www.mathworks.com/help/signal/gs/the-sinc-function.html

"In the context of digital signal processing, we often use an alternative form in which the independent variable is multiplied by π":

https://www.allaboutcircuits.com/technical-articles/what-is-the-sinc-function-and-why-is-it-important-in-electrical-engineering/

" The sinc function is defined as: sinc(a) = sin(πa)/(πa)":

https://www.dspguide.com/ch11/2.htm

See also the note given here: https://numpy.org/doc/stable/reference/generated/numpy.sinc.html