# Re: Improving Frequency Resolution in Time Constrained Signals

*From*: kevin <kevinjmcgee@xxxxxxxxxxxx>*Date*: Fri, 30 Oct 2009 20:29:58 -0700 (PDT)

On Oct 30, 8:22 am, "tzoom84" <tszumow...@xxxxxxxxx> wrote:

For simplicity, suppose we are interested in detecting presence of either a

500Hz, 1kHz, and a 1.5kHz sinusoid in a signal that is being sampled at

100kHz. But lets say we only have 100 samples, or 1ms of data. This is

anywhere between 0.5 to 2 'cycles' of the sinusoids. So essentially, the

signal is well oversampled, but is not sampled long enough in time to

provide clean frequency resolution.

Question is: Are there particular techniques to improve frequency

resolution for oversampled, but time constrained, signals?

(One random thought considered was to decimate at different points in

time, say take every tenth sample starting at sample #1, then every tenth

starting at sample #2, to create 10 independent signals of same length.

Then concatenate to artificially lengthen the same signal. But I wasn't

sure if that would increase resolution since it doesn't add any new

data....)

Thanks!

With a sample rate = 100k and N = 100, you’ve got 100k/100 = 1k bin

spacing in the frequency domain (e.g.: DFT frequency index k = 0

corresponds to 0Hz, index k = 1 corresponds to 1kHz, index k = 2 is

2kHz, etc.). So perhaps you’d do 3 DFTs, one at k = .5 (corresponds

to 500 Hz), one at k = 1 (corresponds to 1 kHz), and one at k = 1.5

(corresponds to 1.5 kHz). Then compute magnitude squared of each and

find the largest. Alternately, you could zero pad an FFT to 200

points and use outputs k = 1, 2 and 3 to represent f = 500 Hz, 1 kHz

and 1.5 kHz. Keep in mind, of course, that zero padding doesn’t

really improve resolution - it provides an interpolation. If you

start with a sampling interval that’s too short, you get a lousy

result. Zero padding gives you more (interpolated) points of a lousy

result.

Of course, I’m presuming that only one tone is present at a time,

their amplitudes are the same, and you don’t have a transition between

the tones in your 100 point sampling interval.

There is a technique that will give you very good frequency

resolution, but it requires that you have at least a few bins’ spacing

between your tonal inputs. So you’re operating well below the margins

at which it will work.

Kevin McGee

.

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