Questions About Intro to Signals and Particular Project

[ashilnayak2]

Hi all!

I am a complete newbie when it comes to any sort of signal processing (as in, never took a class, and I heard the term "FFT" maybe a few days ago), but have found that a recent project of mine will require a bit of heavy lifting in this realm. As such, I wanted to ask a few questions on getting started (don't even have a math background yikes!) in this subject. Additionally, I wanted to lay out some of the details of the project to see how to direct my learning focuses.

Currently, I have a digital signal sampled at 32kHz. For my project, I only care about frequencies at 500Hz and below, and as such downsampled my signal to 1000Hz. However, in doing so, I found that any frequencies from 500-1000Hz sort of "

reflect" and bleed into the 1-500Hz band. Thus, I low pass filter the signal capping at 500Hz and then downsample to 1000Hz. The issue that comes up is that the low pass filter doesn't seem to cut off at 500Hz, thus letting through some of that "reflect"-ing effect in the 500-600Hz frequencies. What are the possible solutions to this situation? Further, what material would be relevant for questions like this? It is my understanding that different filters have different dropoff properties, so I would have to foray into different filters, but just that thought has my head spinning because I don't think I have the fundamentals to really understand what is going on.

What are some good resources to learn without having to blow up my wallet? I understand that not having any background in mathematics is a big hurdle but even pointing me in the direction of subject matter in that realm would provide a ton of help, as the texts that I have briefly skimmed through have assumptions that I already know something (which I don't).

Thanks all for your help!

[potul]

you could start here:

http://www.dspguide.com/

[Digital Larry]

It sounds like you are experiencing aliasing.  You are correct in assuming that preventing aliasing somehow involves a low pass filter prior to sampling.  The problem is that the corner frequency of a filter, no matter how steep the cutoff, represents the "- 3 dB" point (which is not very much attenuation).  There is a concept known as a "brickwall" filter, which magically goes from a gain of 1 (0 dB) to a gain of 0 (- infinity dB) as you cross the cutoff frequency.  However, such a thing does not exist in the real world.

Generally you have to design an anti-aliasing filter so that its response is something like -60 dB or less at the Nyquist frequency (sampling rate /2).  At that point, aliasing components will be -60 dB and not as noticeable.  So, investigate higher order filters which cut off more sharply, and lower the corner frequency because you'll never suppress aliasing by putting the anti-aliasing filter's corner frequency right at the Nyquist frequency.

[elseif]

OP, regarding the 32 ksps to 1 ksps sample rate conversion -

To pass something at Fc without aliasing, then Fs/2 needs to be greater than Fc to provide for a LPF transition band.  If this is a real-time application, then to cut down the throughput delay you will need multi-rate filter.  Take a look at cascading a number of half-band filters.