MATLAB: What are the frequencies when N in fft(x,N) is odd

fftfrequencyspectrum

I know when N is even, fft(x,N) corresponds to frequencies 0,df,…,N/2*df,-(N/2-2)*df,…,-df.

What about if N is odd?

Best Answer

In general, you can do it as

f = (0:N-1)*fs/N

If you want to map it to negative frequencies

if N is even

f(N/2+1:end) = f(N/2+1:end)-fs % sample -fs/2

f(N/2+2:end) = f(N/2+2:end)-fs  % sample fs/2

if N is odd

f((N+1)/2+1:end) = f((N+1)/2+1:end)-fs

HTH

Related Solutions

MATLAB: I get the peaks at the wrong frequency and with the wrong amplitude.

hello Anna

look at my fft function at the end of my code

clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% data
data = importdata('SFC5S_nov25_ST_1_1.txt');
dt = 1e-6; % 1 micro seconds
signal = data(:,1);
samples = length(signal);
Fs = 1/dt; % sampling frequency (Hz)
%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 512;    % 
OVERLAP = 0.95;
% spectrogram dB scale
spectrogram_dB_scale = 80;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 
% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 1 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);
% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);
% apply A weigthing if needed

if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end
figure(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(fsg);
    sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
    my_title = ('Spectrogram (dB (A))');
else
    my_title = ('Spectrogram (dB (L))');
end
% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;
% plots spectrogram
figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');
function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    s_tmp((1:samples)) = signal;
    signal = s_tmp;
    samples = nfft;
end
% window : hanning
window = hanning(nfft);
window = window(:);
%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows
    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling
% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select);
freq_vector = (select - 1)*Fs/nfft;
end

MATLAB: Taking DFT of Swept Sine Wave

Please do not use the acronym 'DFT' when you are using the 'FFT'

 close all,clear all, clc, plt = 0;  
    N = 48
    T = 3*pi
    dt = T/N
    t = dt*(0:N-1);
    Fs = 1/dt
    df = Fs/N
    f = df*(0:N-1);
    A =4
    y = A * sin(f .* t);
    plt=plt+1,figure(plt)
    hold on
    plot( t, y, 'LineWidth', 2)
    plot( t, zeros(1,N), 'k--',  'LineWidth', 2 )
    xlabel('Time (seconds)')
    ylabel('y(t)')
    title( 'SWEPT FREQUENCY TIME SIGNAL' )
    Y = fftshift(fft(y))/N;
    fb = f-Fs/2;
    realY = real(Y);
    imagY = imag(Y);
    absY = abs(Y);
    phaseY = angle(Y);
    plt=plt+1,figure(plt)
    subplot(2,2,1)
    hold on
    plot( fb, realY,  'LineWidth', 2 )
    plot( fb, zeros(1,N), 'k--', 'LineWidth', 2 )
    xlim( [ -Fs/2 Fs/2 ] )
    ylabel( ' REAL(Y) ' )
    title([ blanks(85) , ' SPECTRUM OF SWEPT FREQUENCY SIGNAL ' ] )
    subplot(2,2,2)
    hold on
    plot( fb, imagY,  'LineWidth', 2 )
    plot( fb, zeros(1,N), 'k--',  'LineWidth', 2 )
    xlim( [ -Fs/2 Fs/2 ] )
    ylabel( ' IMAG(Y) ' )
    subplot(2,2,3)
    hold on
    plot( fb, absY,  'LineWidth', 2)
    xlim( [ -Fs/2 Fs/2 ] )
    ylabel( ' AMPLITUDE(Y) ' )
    xlabel( ' FREQUENCY(HZ)  ' ) ; 
    subplot(2,2,4)
    hold on
    plot(fb,phaseY, 'LineWidth', 2)
    plot( fb, zeros(1,N), 'k--', 'LineWidth', 2 )
    xlim( [ -Fs/2 Fs/2 ] )
    ylabel( ' PHASE(Y) ' )
     xlabel( ' FREQUENCY(HZ)  ' ) ;

Hope this helps.

Thank you for formally accepting my answer.

Greg

Best Answer

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MATLAB: I get the peaks at the wrong frequency and with the wrong amplitude.

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