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From: kk KKsingh on 4 Jul 2010 20:54
Hi!

This must be a stupid question ! In signal analysis i have seen few paper where they talk in terms of omega (radian) instead of Hz

They take a signal in time domain and plot its spectra in frequency domain between [-pi,pi]

How can i do the same in matlab

Assuming
N=1000;
f=30;
dt=.01;
t=0:dt*(N-1)
omega=2*pi*f;
S=sin(omega*t);

F=fftshift(fft(S))

Now how should i make frequency axis

I used to do like this when i take in Hz

for even
1/dt/N*(-N/2:N/2-1)
for odd
1/dt/N*(-N/2-1:N/2-1)

is same will be applicable when i am talking in term of radians...

Thanks
From: TideMan on 4 Jul 2010 21:47
On Jul 5, 12:54 pm, "kk KKsingh" <akikumar1...(a)gmail.com> wrote:
> Hi!
>
> This must be a stupid question ! In signal analysis i have seen few paper where they talk in terms of omega (radian) instead of Hz
>
> They take a signal in time domain and plot its spectra in frequency domain between [-pi,pi]
>
> How can i do the same in matlab
>
> Assuming
> N=1000;
> f=30;
> dt=.01;
> t=0:dt*(N-1)
> omega=2*pi*f;
> S=sin(omega*t);
>
> F=fftshift(fft(S))
>
> Now how should i make frequency axis
>
> I used to do like this when i take in Hz
>
> for even
> 1/dt/N*(-N/2:N/2-1)
> for odd
> 1/dt/N*(-N/2-1:N/2-1)
>
> is same will be applicable when i am talking in term of radians...
>
> Thanks

1 Hz means 1 cycle per second.
How many radians are there in a cycle?
So, can you figure out from this how to convert from Hz to radians per
second?

Note: you also need to modify the PSD by the same factor.
From: Rick Rosson on 4 Jul 2010 22:34
Please try the MATLAB code below.

HTH.

Rick

%% Signal in the time domain

% Number of data points:
N = 1000;

% Sampling rate (in samples per second):
Fs = 100;

% Time increment (in seconds per sample):
dt = 1/Fs;

% Time domain (in seconds):
t = dt*(0:N-1).';

% Signal:
x = sin(2*pi*Fc*t);


%% Convert to frequency domain

% Spectrum:
X = fftshif(fft(x));

% Frequency increment (in hertz per sample):
dF = Fs/N;

% Frequency domain:
f = -Fs/2:dF:Fs/2-dF; % in hertz
omega = 2*pi*f % in radians per second
phi = omega/Fs; % in radians per sample


%% Plot time domain:

figure;
plot(t,x);


%% Plot frequency domain:

figure;

subplot(3,1,1);
plot(f,abs(X)/N);

subplot(3,1,2);
plot(omega,abs(X)/N);

subplot(3,1,3);
plot(phi,abs(X)/N);


"kk KKsingh" <akikumar1983(a)gmail.com> wrote in message <i0rafd$nm2$1(a)fred.mathworks.com>...
> Hi!
>
> This must be a stupid question ! In signal analysis i have seen few paper where they talk in terms of omega (radian) instead of Hz
>
> They take a signal in time domain and plot its spectra in frequency domain between [-pi,pi]
>
> How can i do the same in matlab
>
> Assuming
> N=1000;
> f=30;
> dt=.01;
> t=0:dt*(N-1)
> omega=2*pi*f;
> S=sin(omega*t);
>
> F=fftshift(fft(S))
>
> Now how should i make frequency axis
>
> I used to do like this when i take in Hz
>
> for even
> 1/dt/N*(-N/2:N/2-1)
> for odd
> 1/dt/N*(-N/2-1:N/2-1)
>
> is same will be applicable when i am talking in term of radians...
>
> Thanks
From: Rick Rosson on 4 Jul 2010 22:39
Ooops! I forgot one key line of code. Insert the following two lines of code:

% Carrier frequency (in hertz):
Fc = 30

before the the line

% Signal:

Sorry!

Rick

"Rick Rosson" <rrossoNO(a)SPAMathworks.com> wrote in message <i0rgat$a92$1(a)fred.mathworks.com>...
> Please try the MATLAB code below.
>
> HTH.
>
> Rick
>
> %% Signal in the time domain
>
> % Number of data points:
> N = 1000;
>
> % Sampling rate (in samples per second):
> Fs = 100;
>
> % Time increment (in seconds per sample):
> dt = 1/Fs;
>
> % Time domain (in seconds):
> t = dt*(0:N-1).';
>
> % Signal:
> x = sin(2*pi*Fc*t);
>
>
> %% Convert to frequency domain
>
> % Spectrum:
> X = fftshif(fft(x));
>
> % Frequency increment (in hertz per sample):
> dF = Fs/N;
>
> % Frequency domain:
> f = -Fs/2:dF:Fs/2-dF; % in hertz
> omega = 2*pi*f % in radians per second
> phi = omega/Fs; % in radians per sample
>
>
> %% Plot time domain:
>
> figure;
> plot(t,x);
>
>
> %% Plot frequency domain:
>
> figure;
>
> subplot(3,1,1);
> plot(f,abs(X)/N);
>
> subplot(3,1,2);
> plot(omega,abs(X)/N);
>
> subplot(3,1,3);
> plot(phi,abs(X)/N);
>
>
> "kk KKsingh" <akikumar1983(a)gmail.com> wrote in message <i0rafd$nm2$1(a)fred.mathworks.com>...
> > Hi!
> >
> > This must be a stupid question ! In signal analysis i have seen few paper where they talk in terms of omega (radian) instead of Hz
> >
> > They take a signal in time domain and plot its spectra in frequency domain between [-pi,pi]
> >
> > How can i do the same in matlab
> >
> > Assuming
> > N=1000;
> > f=30;
> > dt=.01;
> > t=0:dt*(N-1)
> > omega=2*pi*f;
> > S=sin(omega*t);
> >
> > F=fftshift(fft(S))
> >
> > Now how should i make frequency axis
> >
> > I used to do like this when i take in Hz
> >
> > for even
> > 1/dt/N*(-N/2:N/2-1)
> > for odd
> > 1/dt/N*(-N/2-1:N/2-1)
> >
> > is same will be applicable when i am talking in term of radians...
> >
> > Thanks
From: Rick Rosson on 5 Jul 2010 14:32
One other small typo. I fort the 't' in the functioin 'fftshift' in the line of code the computes the DFT of the signal 'x'. The correct line should be:

X = fftshift(fft(x));

This line is rght after the comment that reads:

% Spectrum:

Sorry!

Rick



"Rick Rosson" <rrossoNO(a)SPAMathworks.com> wrote in message <i0rgk9$sh0$1(a)fred.mathworks.com>...
> Ooops! I forgot one key line of code. Insert the following two lines of code:
>
> % Carrier frequency (in hertz):
> Fc = 30
>
> before the the line
>
> % Signal:
>
> Sorry!
>
> Rick
>
> "Rick Rosson" <rrossoNO(a)SPAMathworks.com> wrote in message <i0rgat$a92$1(a)fred.mathworks.com>...
> > Please try the MATLAB code below.
> >
> > HTH.
> >
> > Rick
> >
> > %% Signal in the time domain
> >
> > % Number of data points:
> > N = 1000;
> >
> > % Sampling rate (in samples per second):
> > Fs = 100;
> >
> > % Time increment (in seconds per sample):
> > dt = 1/Fs;
> >
> > % Time domain (in seconds):
> > t = dt*(0:N-1).';
> >
> > % Signal:
> > x = sin(2*pi*Fc*t);
> >
> >
> > %% Convert to frequency domain
> >
> > % Spectrum:
> > X = fftshif(fft(x));
> >
> > % Frequency increment (in hertz per sample):
> > dF = Fs/N;
> >
> > % Frequency domain:
> > f = -Fs/2:dF:Fs/2-dF; % in hertz
> > omega = 2*pi*f % in radians per second
> > phi = omega/Fs; % in radians per sample
> >
> >
> > %% Plot time domain:
> >
> > figure;
> > plot(t,x);
> >
> >
> > %% Plot frequency domain:
> >
> > figure;
> >
> > subplot(3,1,1);
> > plot(f,abs(X)/N);
> >
> > subplot(3,1,2);
> > plot(omega,abs(X)/N);
> >
> > subplot(3,1,3);
> > plot(phi,abs(X)/N);
> >
> >
> > "kk KKsingh" <akikumar1983(a)gmail.com> wrote in message <i0rafd$nm2$1(a)fred.mathworks.com>...
> > > Hi!
> > >
> > > This must be a stupid question ! In signal analysis i have seen few paper where they talk in terms of omega (radian) instead of Hz
> > >
> > > They take a signal in time domain and plot its spectra in frequency domain between [-pi,pi]
> > >
> > > How can i do the same in matlab
> > >
> > > Assuming
> > > N=1000;
> > > f=30;
> > > dt=.01;
> > > t=0:dt*(N-1)
> > > omega=2*pi*f;
> > > S=sin(omega*t);
> > >
> > > F=fftshift(fft(S))
> > >
> > > Now how should i make frequency axis
> > >
> > > I used to do like this when i take in Hz
> > >
> > > for even
> > > 1/dt/N*(-N/2:N/2-1)
> > > for odd
> > > 1/dt/N*(-N/2-1:N/2-1)
> > >
> > > is same will be applicable when i am talking in term of radians...
> > >
> > > Thanks
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