Plot single-sided amplitude spectrum.

hello .

i tried to find a code for ploting fft,and i found this code which plot single-sided amplitude spectrum according to it's title,is it the same as fft?what is different between single side amplitude spectrum and fft? and is this code ok?

i really appreciate it if you help me.

i have a signal with 135 data point.

Fs = 50; % Sampling frequency T = 1/Fs; % Sample time L = 135; % Length of signal

NFFT = 2^(nextpow2(L)-1);

x=zeros(NFFT,1); x(1:NFFT,1) = rawdata(1:NFFT,1);

YY = fft(x,NFFT)/L; ff = Fs/2*linspace(0,1,NFFT/2+1);

% Plot single-sided amplitude spectrum. plot(ff,2*abs(YY(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of tp') xlabel('Frequency (Hz)') ylabel('|Y(f)|')

[sampath kumar kuppa]

you got the solution for this code or not. I'm also facing the same problem. if you got the solution means please forward to me.

[Stephen Capasso]

This has been useful does anyone know how to adjust the plot statement for log space instead of linspace. ff= Fs/2*logspace(0,1,NFFT/2+1); What would go in the argument for a 4 cycle semi log?

Answer 1

[Adam]

That code uses the fft so yes, it is the same thing.

The fft is a transform which gives you a complex result spanning negative and positive frequencies ( -nyquist to +nyquist ). The single-side spectrum throws away the negative frequencies which are often not required for things like plotting spectrum to obtain a single-side spectrum.

So the fft is the method used to transform from the time domain to the frequency domain, but its result requires some manipulation afterwards to obtain what is often the desired result, a single-sided power spectrum.

The code:

ff = Fs/2*linspace(0,1,NFFT/2+1);

is taking the positive half of the spectrum (NFFT/2 +1 gives this, including 0 and nyquist, hence the +1) and mapping it onto your real frequencies from 'normalised frequency'.

[mohamad mohamad]

thank you so much for your complete answer i have 3 question about this code

1.why we devide fft by L. (YY = fft(x,NFFT)/L)

2.when i change Fs,the plot changes,for example if we fix fs=40, we have amplitude 40 at f=5,now if i change fs and make fs=400, we have amplitude 40 at f =10. is it normal? i think when the sampling ferequncy changes,the plot shouldn't change

3.i have also this code for ploting fft,why does it give a different plot?

z=fft(rawdata,128); plot(abs(z))

i am realy thankful for your help

[Adam]

1. The fft result is generally divided by the signal length in order to scale it to the same total power as the time-domain signal. You may also notice the multiplicative factor of 2 in your plot function. This is to compensate for throwing away half the spectrum.

2. Yes, this is correct behaviour. Normalised frequencies remain static in power, but if your sampling frequency is different then what those normalised frequencies map to in Hz will change.

3. abs( fft( rawdata, 128 ) ) is not the same mathematically as 2*abs(YY(1:NFFT/2+1)) with Y defined in your original code. The first case takes the double-sided result, the second takes the single sided result.

[mohamad mohamad]

Thank you so much

Last question

if the plot changes with changes in sampling frequency ,how do I knew which plot is the correct one and which frequencies are in my signal? I know that the sampling rate should be at least X 2 of the highest frequency of the signal, but the problem is I only have a time serie of my signal and I don't know which frequencies are involved in my signal, so what is the best value for the sampling frequency for my signal?

thanks again

[Adam]

The sample rate of your signal is set before-hand. It represents the sampling of the original signal that resulted in the discretised data to which you are applying the fft so you shouldn't be changing it after doing the fft for a given signal.

e.g. if your signal is sampled every 2ms then the sample frequency is 500 Hz. This is fixed unless you resample your signal, but if you do that then you would re-run the fft and the newly resampled signal and apply the new sampling frequency to that result, not the original result.

[mohamad mohamad]

thank you so much but sorry,i am a bit little confused:(

so in here the Fs=50 is not the real sampling frequency and the sample rate of my signal was set before-hand?

so what is Fs in here and how do i knew which Fs i should apply?

i have a time serie of BOLD fMRI signal,and i don't know nothing about its sampling frequncy,for plotting fft of this signal,what value for Fs i should choose?

[Adam]

I don't know what the signal in your original question is, but it is presumably sampled at 50Hz sample rate, i.e. every 20ms.

If you don't know your sample rate than you cannot get information out of the fft in Hz, all you can really do is either guess at the sample frequency (seems rather pointless) or use normalised frequency - i.e. fs = 1 where your frequency values will be between 0 and 0.5 for the positive have of your spectrum.

[Xu LinaM]

Hello,after I read your opinion about Single-Sided Amplitude Spectrum,I have a question that where is the negative frequency,why they begin at NFFT/2+2,and what's the order of the size ?Thank you for your reply.Best Wishes!

[Adam]

The negative frequencies begin at NFFT/2 + 2 simply because that is how fft is defined. They have to be somewhere. You can use fftshift if you prefer to have 0 in the centre with negative frequencies before it.

Answer 2

[Charanraj]

hey, can a single sided FFT taken directly from the scope by using an absolute block before the scope ?