This is a question related to the need for filtering before decimation. I understand that there are many questions likewise in this forum. I have gone through these and still little confused (or) may be overthinking about it.
I have a test sequence(1x1000)sampled at 176.4 KHz(example) and I need to decimate it to let's say 44.1KHz. (the maximum frequency component in the sequence is 20KHz, I am taking examples from audio freqs).
The way I understand decimation is, any sequence with sample rate Fs is decimated to
Fsd(=Fs/D)... then there is a higher chance that it violates the Nyquist sampling theorem and information is lost in the original sequence(if we don't think about filtering and just decimate it).
In my example, if I decimate (by factor 4) 176.4Khz to 44.1Khz, it still satisfies the Nyquist sampling, so there will be no concept of aliasing since
Fsd>2*20Khz------ **In this case, do I need to apply LPF before Decimation. If Yes why ?*
If I want to decimate by factor 16, i.e. 176.4KHz to 11.025Khz, it doesn't satisfy Nyquist sampling (as my new Fsd<2*20KHz).. aliasing occurs.So, we (undesirably) remove the higher frequency components in my test sequence by applying LPF (with cutoff freq ≤ 5.515 (
F_coutoff ≤ Desired_sample_rate/2))
LPF is applied such that there are no frequency components higher than 5.515KHz Is this how I need to choose my cut-off ??