Signal recording parameters (EE)

[xzibition8612]

Homework Statement

What (complete) set of sampling and filtering parameters would you choose to record a signal from a high speed pressure sensor if you wanted to accurately determine its power spectrum below 35 kHz with a resolution of 0.5 Hz?

Homework Equations

frequency resolution = sampling rate / number of samples

The Attempt at a Solution

So I guess for the 0.5 Hz frequency resolution, any combination in the above formula giving 0.5 would work? For example 1000 sampling rate, 2000 samples?

The power spectrum would use filter. Since the signal is below 35 kHz, a low-pass filter with cutoff at 35 kHz would work?

Am I doing this correctly? Thx.

 

[rude man]

The sampling rate must satisfy the criterion of no aliasing. If the frequency spread of interest is 0 - 35 KHz, what is the minimum sampling frequency?

You realize I assume that this is a DFT problem. So how many time samples N would you need to achieve 0.5 Hz resolution of the 0 - 35 KHz signal? It's not the formula you gave above for freq. resolution.

You then get N/2 + 1 numbers representing the cosine component and another N/2 + 1 numbers representing the sine component of each harmonic of the fundamental frequency which is the resolution frequency. So what would be the power in each frequency component 0, 1/NT, 2/NT etc. where 1/T is the sampling frequency?

(You can also get complex frequency components. This is actually easier for determining power for each harmonic.)

I don't see the need for a reconstruction filter if all you want is the power spectrum.

 

[rude man]

RETRACT: your formula for frequency resolution is correct. But your sampling rate is way off. If the spectrum is 0 - 35 KHz, what is the minimum sampling rate?

So you can determine N, the number of samples needed, by combining the minimum sampling rate and the desired frequency resolution of 0.5 Hz.