So, when we Sampled any signal at the rate lower than Nyquist Frequency we get aliasing, for instance,
If the frequency of Cosine wave is 5Hertz and I had to make 5cycles in a second and if the sampling frequency is 8Hz,
Frequency = 5Hz
t = 0.2 <- 1 complete oscillation takes 0.2seconds
Sampling Frequency = 8Hz
then Sampling rate would be,
which means every sample will be generated on each instance of
the 8 samples would then be,
0.1250 0.2500 0.3750 0.5000 0.6250 0.7500 0.8750 1.0000
signal can't be completely recovered at this sampling rate, and only first few cycles will be generated.
the Fractional frequency will then would be,
(8 samples per second and 5 cycles per second).
According to the above example the Fractional frequency is produced due to the aliasing of the signal.
but as i studied, the Fractional frequency is the reason which cause the imaginary part of the frequencies to be generated.
here is what I've found, Here the cosine (real, labelled "R") and sine (imaginary, labelled "I") parts:
figure #4 , both the waves are sine wave, so the Fractional frequency is
So if there is no Cosine does that mean that this point has no Real part ?
Then how it is generated while calculating the DFT ?