FFT Bin content 1

[JAF8871]

With an Fmin of 0 cycles per minute and an Fmax of 120,000 cycles per minute and 1600 lines, the FFT bin width is 75 cycles per minute. If there are multiple peaks that fall within a bin, which peak will be shown on the FFT spectrum? If there are other peaks within the bin, how dows one determine their amplitude and frequency?

Randy Fizer

 

[MachineryWatch]

Randy,

The amplitude displayed in any particular bin of the FFT combines all the contributing frequency's energy. There is no way to tell (barring taking higher resolution data) what frequencies are contributing to the energy in that bin or which frequencies are dominant.

There are routines in some systems that calculate "true amplitude" and "true frequency" of a signal to greater resolution than the indicated FFT bin width would allow. These basically interpolate the amplitude and frequency based on the amplitudes shown in adjoining bins. This calculation assumes that there is only one frequency present in the bin. If there is more than one frequency present the interpolation routine results are invalid.


Skip Hartman

http://www.machinerywatch.com

 

[MikeyP]

The FFT is a special algorithm for calculating the discrete Fourier transform (DFT) of a finite length sampled and quantised signal. The FFT algorithm relies on binary arithmetic operations and therefore only works on record lengths comprising a power of 2 samples (eg 256, 512, 1024, 2048 etc samples). This means that your equipment is not using the FFT algorithm, but some other DFT algotithm.

The DFT tells you the signal amplitude at frequencies with periods which are precisely integer divisions of the record length, T, ie periods of T/1 T/2 T/3 T/4 T/5 etc and frequencies of 1/T 2/T 3/T etc. It tells you NOTHING about what is happening at frequencies in between.

Some analysis equipment is able to perform "zoom" DFT analysis. This gives you a higher frequency resolution over a smaller frequency range compared to a standard baseband DFT.

Try a search for zoom DFT/FFT on Google for more info

M

 

[electricpete]

One place to look would be dspguide.com

I would say Mikey is theoretically correct that FFT only represents precise frequencies... but as a practical matter if we start with a periodic continuous signal and sample it over a period which is not an integer multiple of periods, then the frequency content is spread out (convolution in frequency domain) so that each bin will detect a continuum of frequencies which do not correspond exactly to frequencies T/1, T/2 etc in the original signal.

The contribution of a frequency not at the precise center frequency of the bin will depend on a weighting factor which in turn is dependent upon the window function used (rectangular, hamming etc). Contirubtions of multiple frequencies within the bin is made by square root of sum of squares of the weighted contributions.

 

[IRstuff]

While this is somewhat afield, you might entertain looking at other transforms. I've only read the articles, but Wigner transforms supposedly allowed you to get somewhat better resolution as well as better temporal understanding of the frequency behavior, e.g., you could time resolve a chirp in a waterfall and actually see the frequency change over a short time interval. TTFN

 

[GregLocock]

I doubt it can really beat frequencyresolution*sampling time=1

I've used wavelet transforms to try and examine harmonic structures in short signals, but the results were ambiguous at best. Typically the human ear can hear beating phenomenon in short signals that are very difficult, or impossible, to analyse meaningfully.

Incidentally Mikey, the original poster's probably looking at the first 1600 lines of a 2048 line FFT, but you knew that.


Cheers

Greg Locock

 

[MikeyP]

Greg - oops. I interpreted "Fmax" in the original post as being the Nyquist frequency. Of course a zoom DFT does not violate df*dt=1, but it DOES give you better resolution for a given record length than a baseband measurement. In the kind of frequency range we are talking about here, record length is usually the most limiting factor in frequency analyser hardware.

M

 

[GregLocock]

Not often I catch you out! (and now back to the cricket...) Cheers

Greg Locock