FFT.zip_fft_in_matlab fft

%% FFT of Signals in Matlab % %% Define time vector samplingFrequency = 1000; %Hz timeStep = 1/samplingFrequency; %sec T = 1; %sec S = T*samplingFrequency; %samples samples = 1:S; %samples time = samples*timeStep; %sec %% Generate Sine wave frequency1 = 5; %Hz frequency2 = 7; %Hz sineWave = sin(time*frequency1*2*pi)+sin(time*frequency2*2*pi); figure(1), plot(time,sineWave,'r') xlabel('Time (sec)') ylabel('Amplitude') title(['Original Sinusoid with ' num2str(frequency1) 'Hz and ' num2str(frequency2) 'Hz']) set(gca,'YLim',[-2.1 2.1]) %% Fast Fourier Transform of Sine Wave L = length(sineWave); NFFT = 2^nextpow2(L); % Next power of 2 from length of signal FsineWave = fft(sineWave,NFFT)/L; f = samplingFrequency/2*linspace(0,1,NFFT/2+1); %% Plot single-sided amplitude spectrum. figure, plot(f,2*abs(FsineWave(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of SineWave') xlabel('Frequency (Hz)') ylabel('|SineWave(f)|') %% Generate square wave pulseFrequency = 8; %Hz squareWave = square(time*pulseFrequency*2*pi); squareWavePos = (squareWave+1)/2; figure, plot(time,squareWavePos,'r') set(gca,'YLim',[-0.1 1.1]) %% Fast Fourier Transform of Square Wave L = length(squareWave); NFFT = 2^nextpow2(L); % Next power of 2 from length of signal FsqWave = fft(squareWave,NFFT)/L; f = samplingFrequency/2*linspace(0,1,NFFT/2+1); %% Plot single-sided amplitude spectrum. figure, plot(f,2*abs(FsqWave(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('|SquareWave(f)|') %% Plot Single-sided Phase Plots figure, plot(f,phase(FsqWave(1:NFFT/2+1))) title('Single-Sided Phase Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('Phase(Y(f))') %% Plot Amplitude and Phase in Same figure figure, subplot(2,1,1), plot(f,2*abs(FsqWave(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('|SquareWave(f)|') subplot(2,1,2), plot(f,phase(FsqWave(1:NFFT/2+1))) title('Single-Sided Phase Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('Phase(SquareWave(f))') %% Decibels magnitude = 2*abs(FsqWave(1:NFFT/2+1)); dbs = 20*log10(magnitude); dbs_anotherWay = mag2db(magnitude); dbs_yetAnotherWay = pow2db(magnitude); %Note: 10*log10(magnitude) figure, subplot(2,1,1), plot(f,dbs) title('Single-Sided Amplitude Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('|SquareWave(f)| (db)') subplot(2,1,2), plot(f,phase(FsqWave(1:NFFT/2+1))) title('Single-Sided Phase Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('Phase(Y(f))') %% Add noise to squareWave noisySqW = squareWavePos + 3*randn(size(squareWavePos)); figure, plot(time,noisySqW), xlabel('Time (sec)'), ylabel('Amplitude') %% Fourier Transform of noisySqW L = length(noisySqW); NFFT = 2^nextpow2(L); % Next power of 2 from length of signal FnsqWave = fft(noisySqW,NFFT)/L; f = samplingFrequency/2*linspace(0,1,NFFT/2+1); %% Plot noisy Fourier Transform figure, subplot(2,1,1), plot(f,2*abs(FnsqWave(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('|SquareWave(f)|') subplot(2,1,2), plot(f,phase(FnsqWave(1:NFFT/2+1))) title('Single-Sided Phase Spectrum of SquareWave') xlabel('Frequency (Hz)') ylabel('Phase(Y(f))') %% Fourier Transform of an Impulse impulse = [0 0 0 0 0 1 0 0 0 0 0]; L = length(impulse); NFFT = 2^nextpow2(L); % Next power of 2 from length of signal Fimpulse = fft(impulse,NFFT)/L; figure, plot(abs(Fimpulse)) %% Fourier Transform of a DC Signal DC = ones(1,1000); L = length(DC); NFFT = 2^nextpow2(L); % Next power of 2 from length of signal FDC = fft(DC,NFFT)/L; DC2 = ones(1,100000); L2 = length(DC2); NFFT2 = 2^nextpow2(L2); % Next power of 2 from length of signal FDC2 = fft(DC2,NFFT2)/L2; % Arbitrary frequency vectors f1 = linspace(0,1,length(FDC)); f2 = linspace(0,1,length(FDC2)); figure, plot(f1,abs(FDC),'b'), hold on, plot(f2,abs(FDC2),'r')