Lower frequencies is not visible in FFT plot when adding into the original signal I plotted a simple Cosine wave and After taking its FFT the frequency can be seen easily but after modifying the original signal to add more lower and higher frequencies, the higher ones are visible but the lower ones is not showing in the FFT plot,

Original Signal,

Amplitude = 4
x=A*cos(2*pi*f*n);


Frequency of Wave: 100Hz

Amplitude = 4

Sampling Frequency = 10000Hz

The 100Hz frequency (original signal frequency) is supposed to be plotted at point 1 of FFT, which is fine,



When adding another higher frequency into the original signal,

x= 1*cos(2*pi*500*n) + x ;


500HZ frequency is added into the original signal and supposed to be plotted at point 5 of the FFt.

Results in,



Which is fine, but when i am trying to add lower frequencies than higher they are not visible.

Adding 50Hz frequency to the original 100Hz Cosine wave,

what i think is 50Hz should be plotted at the 0.5 of the x-axis as it is half of the original frequency.

x= 1*cos(2*pi*50*n) + x ;


Results in,



Where is the 50Hz frequency ?
What you're assuming about how FFT works is actually correct for Fourier transform, but – despite its name – FFT is not such a continuous all-$\mathbb{R}$ transformation. It is actually just a DFT, discrete Fourier transform, i.e. both the frequency and time spaces are quantised. In your example, you selected the quantisation in frequency space to be $100\:\mathrm{Hz}$, so there exists no $50\: \mathrm{Hz}$ bin.