How to use FFT
How to use FFT
(OP)
I know a little about FFT and spectrum analising and the other math that goes with it. I would like to know if i have taken sample data say about 1000000 values and i have a program to calculate FFT amplitude spectrum an phase spectrum and so on ... how do i use these vulues that i have worked out to reconstruct the wave form from the data points.... i can get the freqency and the phase that is no probblem but how do i determine the amplitude of each cosine wave that i have to use. and after i have reconstructed the wave form what else does this information tell me.... this subject is selftought and i find it interesting any help will be appreciated
tvdb@highveldmail.co.za
tvdb@highveldmail.co.za





RE: How to use FFT
So the waveform at time t is
the sum
for each frequency f Hz, with magnitude M and phase phi
M*cos(2*pi*f*t+phi)
It really is that easy.
Cheers
Greg Locock
RE: How to use FFT
Secondly, the inverse FFT can also be used to get the time signal.
M
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Dr Michael F Platten
RE: How to use FFT
When you have the data check if for a DC offset. Do tis by integrating the data. It should resemble the original. If it slopes up or down there is a DC offset. To remove it, subtract out the mean. Then remove noise by taking extracting 2^n blocks, take SPECTRUM of the Hanning Window of each block each block, correct for amplitude reduction (multiply by 1.633) and multiply by the conjugate. Then average all the blocks. This will reduce the noise and lower the amplitude. The result is the PSD of the signal. If you do an inverse spectrum you will return to the original signal - less some noise.
When you finally get to the PSD find the amplitude at the frequency of interest. That amplitude is in G-rms. Mulitply this by 1.414 to get the peak amplitude of the sinusoid at that frequency.
When you took the data I assume you had an anti-aliasing filter and sampled at least 6 times the highest frequency of interest. I also assume that the highest frequency of interest did not exceed one-third of the resonant frequency of the accelerometer.
Regards
Dave
RE: How to use FFT
Could you give me a simple explanation why you recommend sampling at 6 x the highest frequency of interest?
Nyquist Theorem requires 2x, as I recall, but i'm not familiar with other limitations.
RE: How to use FFT
> to allow room for the antialias filter to knock down the amplitude
> oversampling reduces the noise power spectral density in-band
> oversampling eliminates pathological sampling conditions
TTFN
RE: How to use FFT
RE: How to use FFT
h
It is talking about bit rates on a noisy line. We're talking about signal analysis, not baud.
There are many many laboratory systems that sample at 2.56 times the nominal upper frequency limit. That is you keep 400 lines of the spectrum from a 1024 sample time history.
AFAIK the real reason to sample at >> 2x upper frequency limit is that real AA filters have a roll off characteristic and you will only get limited protection until they hit -80 dB. This attenuation curve gets reflected back down the frequency axis. So, the old units used to set the AA filter at 1.28 times the upper frequency limit, and then with a roll off of 80 dB/octave they'd give you about 40 dB of anti aliasing at the upper frequency limit.
Cheers
Greg Locock
RE: How to use FFT
1) That is "greater than" not "greater than or equal to".
2) That is "twice the bandwidth" not "twice the highest frequency". This is how zoom fft analysis works.
Shannon was doing effectively what Nyquist did some years before him. ie (as Greg says) looking at how noise affects the detection of pulses down a wire. What Shannon did was to put Nyquist's work into a firm mathematical foundation by applying Fourier analysis. One important result of this mathematics is the sampling theorem stated above. As I understand it, the term "Nyquist frequency" was coined in honour of the man who had done the earlier work.
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Dr Michael F Platten