FFT Analysis of Sine Sweep

Hi there, I am trying to run FFT analysis of the sine sweep I have created and not sure if the graphs I'm producing are working as they should. I feel they look to smooth and wanted to see if I could do anything better. The code runs and works but I still feel there is something missing. Any help greatly appreciated.

Many thanks

T=5; %size of window
fs=44100; %sampling frequency
df=1/T; %frequency res
dt=1/fs; %time resolution
t=(0:+dt:T-dt); %time vector
df_t=500; %swept rate (Hz/seconds)

% pre-allocate size of t:

sweptsin = zeros(size(t));
for i=1:+1:length(t)
    %i=i+1;
    
    if(i==1)      %initialise f and t.
        f=20; ti=0;  
    else    
        ti=ti+dt; %time increment
        f=f+df_t*dt; %freq increment 
    end
    
    w=2*pi*f; %omega
    sweptsin(i)=sin(w*ti); %swept sine wave
    
end

NFFT=1024; %NFFT-point DFT      
X=fftshift(fft(sweptsin,NFFT)); %compute DFT using FFT      
fVals1=(-NFFT/2:NFFT/2-1)/NFFT; %DFT Sample points        
subplot(4,1,1)
plot(fVals1,abs(X));      
title('Double Sided FFT - with FFTShift');       
xlabel('Normalized Frequency')       
ylabel('DFT Values');

L=length(sweptsin);             
X=fft(sweptsin,NFFT);       
Px=X.*conj(X)/(NFFT*L); %Power of each freq components       
fVals2=fs*(0:NFFT/2-1)/NFFT;      
subplot(4,1,2)
plot(fVals2,Px(1:NFFT/2),'b','LineSmoothing','on','LineWidth',1);  
title('One Sided Power Spectral Density');       
xlabel('Frequency (Hz)')         
ylabel('PSD');
    
X=fft(sweptsin,NFFT); %compute DFT using FFT        
nVals=(0:NFFT-1)/NFFT; %Normalized DFT Sample points 
subplot(4,1,3)
plot(nVals,abs(X));      
title('Double Sided FFT - without FFTShift');        
xlabel('Normalized Frequency')       
ylabel('DFT Values');

NFFT=1024;      
L=length(sweptsin);         
X=fftshift(fft(sweptsin,NFFT));         
Px=X.*conj(X)/(NFFT*L); %Power of each freq components       
fVals3=fs*(-NFFT/2:NFFT/2-1)/NFFT;
subplot(4,1,4)
plot(fVals3,10*log10(Px),'b');        
title('Power Spectral Density');         
xlabel('Frequency (Hz)')         
ylabel('Power');

Answer 1

[Star Strider]

Your posted code is likely as good as it is possible to get.

I added a pspectrum call at the end —

T=5; %size of window
fs=44100; %sampling frequency
df=1/T; %frequency res
dt=1/fs; %time resolution
t=(0:+dt:T-dt); %time vector
df_t=500; %swept rate (Hz/seconds)

% pre-allocate size of t:

sweptsin = zeros(size(t));
for i=1:+1:length(t)
    %i=i+1;
    
    if(i==1)      %initialise f and t.
        f=20; ti=0;  
    else    
        ti=ti+dt; %time increment
        f=f+df_t*dt; %freq increment 
    end
    
    w=2*pi*f; %omega
    sweptsin(i)=sin(w*ti); %swept sine wave
    
end

NFFT=1024; %NFFT-point DFT      
X=fftshift(fft(sweptsin,NFFT)); %compute DFT using FFT      
fVals1=(-NFFT/2:NFFT/2-1)/NFFT; %DFT Sample points        
subplot(4,1,1)
plot(fVals1,abs(X));      
title('Double Sided FFT - with FFTShift');       
xlabel('Normalized Frequency')       
ylabel('DFT Values');

L=length(sweptsin);             
X=fft(sweptsin,NFFT);       
Px=X.*conj(X)/(NFFT*L); %Power of each freq components       
fVals2=fs*(0:NFFT/2-1)/NFFT;      
subplot(4,1,2)
plot(fVals2,Px(1:NFFT/2),'b','LineSmoothing','on','LineWidth',1);  

Warning: The LineSmoothing property will be removed in a future release.

Warning: The LineSmoothing property will be removed in a future release.

title('One Sided Power Spectral Density');       
xlabel('Frequency (Hz)')         
ylabel('PSD');
    
X=fft(sweptsin,NFFT); %compute DFT using FFT        
nVals=(0:NFFT-1)/NFFT; %Normalized DFT Sample points 
subplot(4,1,3)
plot(nVals,abs(X));      
title('Double Sided FFT - without FFTShift');        
xlabel('Normalized Frequency')       
ylabel('DFT Values');

NFFT=1024;      
L=length(sweptsin);         
X=fftshift(fft(sweptsin,NFFT));         
Px=X.*conj(X)/(NFFT*L); %Power of each freq components       
fVals3=fs*(-NFFT/2:NFFT/2-1)/NFFT;
subplot(4,1,4)
plot(fVals3,10*log10(Px),'b');        
title('Power Spectral Density');         
xlabel('Frequency (Hz)')         
ylabel('Power');

figure
pspectrum(sweptsin,t,'spectrogram')
colormap(turbo)

.

[David Kendal]

Thanks for taking a look, I'm thinking they look smooth as it's a kind of pure tone, sinosoidal sweep. I love the pspectrum!

[Star Strider]

As always, my pleasure!

Your code seems to me to be complete and comprehensive. I added pspectrum as it appears to summarise everything else.

[David Kendal]

Also for these I notice the units of power spectral density are both different 🤷🏻♂ cheers

[Star Strider]

They may be calculated differently, however I doubt that hte actual values are much different.