Why isn't the output of an N point FFT discrete ?

I have written a code that samples and quantizes a cosine function and then finds it's FFT. I have got two questions: 1. Why is the output of the FFT shown as a continuous plot ? 2. The FFT doesn't give the correct frequency of my cosine function. Why ?

    N=8
    m=16
    f=m*fs/(2^N); %Frequency of sinusoid
    nCyl=16; %generate sixteen cycles of sinusoid
    t=0:1/fs:nCyl*1/f; %time index
    x=cos(2*pi*f*t);
    ff=fft(x,256);
    l=20*log10(ff)
    plot((20*log10(abs(ff/256))))

Theoretically this code should produce a graph showing a big peak at 16 but that peak is coming at 17 . Why ?

Answer 1

[David Goodmanson]

Hi Chinmay,

If by 'isn't discrete' you are referring to the values in between the peaks, they are basically at the numerical limit for double precision. You might prefer plot(20*log10(abs(ff/256)),'o'), or stem(20*log10(abs(ff/256))+300) for the result relative to -300 dB. As for the peak location, an fft output array starts with zero frequency in ff(1), so f=16 is in ff(17).