Ok so as part of a project for school I have been designing an FIR bandpass filter. The output should have been a signal which looks like a sampled sinusoid but there was a strange alteration on the amplitude. I began to investigate and generated a signal with the same F/Fs. I noticed that signal also looks the same. Just to be clear, this has been my logic thus far:
\begin{equation}
s(t) = \sin(2\pi Ft)
\end{equation}
\begin{equation}
s(nT) = \sin(2\pi FnT) ; t =nT
\end{equation}
\begin{equation} s(n) = \sin(2\pi \frac{F}{F_s}n); F_s =\frac{1}{T} \end{equation}
For this particular sine wave $\frac{F}{F_s}=0.40625$. The output I get when generating with the following python code is:
def signal_gen(f, length):
n = np.arange(0, length)
return np.sin(2 * np.pi * f * n)
sig = signal_gen(0.40625, 2048)
plt.plot(sig[0:500])
I have noticed that the distortion is not bad at all for lower values of $\frac{F}{F_s}$. Could anyone help to understand this distortion ? As far as I can tell it just seems to be that the sampling frequency is close to the frequency of the signal is approaching a point where aliasing will occur but I'm not 100% confident in that theory.
