frequency error at fft of cos

Hi I'm new to matlab.

I'm making some filter but while making it I found some error at freq..

Here is my sample code for transforming a cosine function with frequency f_c.

clear
Dur=10;
Fs=44100*2;
t1 = 0:1/(Fs):Dur;
t1=t1(1:end-1);
f_c=1000;
feq = -(2*f_c+Fs/2):(4*f_c+Fs)/((Fs*Dur)-1):(2*f_c+Fs/2)

%can't change up to this point. 

func=cos(2*pi*f_c*t1)

FUNC=fftshift(fft(func))

plot(feq, FUNC)

What I expected was two delta func at f=f_c, -f_c (in this case 1000, -1000).

but I got delta func at f=1045, -1045 (approx).

Why do I get this error?? And how can I eliminate the error?

I have larger f_c to calculate(ex. f_c=20000), so I get much larger error...

[KALYAN ACHARJYA]

-but I got delta func at f=1045, -1045 (approx).

Can you show the figure along with pointing 1045 and -1045?

[JINHO CHOI]

sure I Zoomed in to get more specific value.

Answer 1

[David Goodmanson]

Hi JC,

I will not attempt to figure out what went wrong, but try

n = length(t1);
feq = (-n/2:n/2-1)*(Fs/n);

also, dividing by n in

FUNC=fftshift(fft(func)/n);

gives the correct amplitudes for the peaks, 1/2 for each one.