r = sfdr(x) returns
the spurious free dynamic range (SFDR), r, in
dB of the real sinusoidal signal, x. sfdr computes
the power spectrum using a modified periodogram and a Kaiser window
with β = 38. The mean is subtracted from x before
computing the power spectrum. The number of points used in the computation
of the discrete Fourier transform (DFT) is the same as the length
of the signal, x.

r = sfdr(x,fs) returns
the SFDR of the time-domain input signal, x,
when the sampling rate, fs, is specified. The
default value of fs is 1 Hz.

r = sfdr(x,fs,msd) returns
the SFDR considering only spurs that are separated from the fundamental
(carrier) frequency by the minimum spur distance, msd,
specified in cycles/unit time. The sampling frequency is fs.
If the carrier frequency is Fc, then all spurs
in the interval (Fc-msd, Fc+msd)
are ignored.

r = sfdr(sxx,f,pwrflag) returns
the SFDR of the one-sided power spectrum of a real-valued signal, sxx. f is
the vector of frequencies corresponding to the power estimates in sxx.
The first element of f must equal 0. The algorithm
removes all the power that decreases monotonically away from the DC
bin.

r = sfdr(sxx,f,msd,pwrflag) returns
the SFDR considering only spurs that are separated from the fundamental
(carrier) frequency by the minimum spur distance, msd.
If the carrier frequency is Fc, then all spurs
in the interval (Fc-msd, Fc+msd)
are ignored. When the input to sfdr is a power
spectrum, specifying msd can prevent high sidelobe
levels from being identified as spurs.

sfdr(___) with no output arguments
plots the spectrum of the signal in the current figure window. It
uses different colors to draw the fundamental component, the DC value,
and the rest of the spectrum. It shades the SFDR and displays its
value above the plot. It also labels the fundamental and the largest
spur.

Obtain the SFDR for a 10 MHz tone with amplitude 1 sampled
at 100 MHz. There is a spur at the 1st harmonic (20 MHz) with an amplitude
of 3.16 × 10^{–4}.

deltat = 1e-8;
t = 0:deltat:1e-6-deltat;
x = cos(2*pi*10e6*t)+3.16e-4*cos(2*pi*20e6*t);
r = sfdr(x);

Obtain the SFDR for a 10 MHz tone with amplitude 1 sampled
at 100 MHz. There is a spur at the 1st harmonic (20 MHz) with an amplitude
of 3.16 × 10^{–4}.
Use a minimum spur distance of 1 MHz.

deltat = 1e-8;
fs = 1/deltat;
t = 0:deltat:1e-6-deltat;
x = cos(2*pi*10e6*t)+3.16e-4*cos(2*pi*20e6*t);
r = sfdr(x,fs,1e6);

Obtain the power spectrum of a 10 MHz tone with amplitude
1 sampled at 100 MHz. There is a spur at the 1st harmonic (20 MHz)
with an amplitude of 3.16 × 10^{–4}.
Use the one-sided power spectrum and a vector of corresponding frequencies
in Hz to compute the SFDR.

deltat = 1e-8;
fs = 1/deltat;
t = 0:deltat:1e-6-deltat;
x = cos(2*pi*10e6*t)+3.16e-4*cos(2*pi*20e6*t);
[sxx,f] = periodogram(x,rectwin(length(x)),length(x),fs,'power');
r = sfdr(sxx,f,'power');

Determine the frequency in MHz for the largest spur. The
input signal is a 10 MHz tone with amplitude 1 sampled at 100 MHz.
There is a spur at the 1st harmonic (20 MHz) with an amplitude of
3.16 × 10^{–4}.

deltat = 1e-8;
t = 0:deltat:1e-6-deltat;
x = cos(2*pi*10e6*t)+3.16e-4*cos(2*pi*20e6*t);
[r,spurpow,spurfreq] = sfdr(x,1/deltat);
spur_MHz = spurfreq/1e6;

Create a superposition of three sinusoids, with frequencies
of 9.8, 14.7, and 19.6 kHz, in white Gaussian additive noise. The
signal is sampled at 44.1 kHz. The 9.8 kHz sine wave has an amplitude
of 1 V, the 14.7 kHz wave has an amplitude of 100 μV,
and the 19.6 kHz signal has amplitude 30 μV.
The noise has 0 mean and a variance of 0.01 μV.
Additionally, the signal has a DC shift of 0.1 V.

rng default
Fs = 44.1e3;
f1 = 9.8e3;
f2 = 14.7e3;
f3 = 19.6e3;
N = 900;
nT = (0:N-1)/Fs;
x = 0.1 + sin(2*pi*f1*nT) + 100e-6*sin(2*pi*f2*nT) ...
+ 30e-6*sin(2*pi*f3*nT) + sqrt(1e-9)*randn(1,N);

Plot the spectrum and SFDR of the signal. Display its
fundamental harmonic and its largest spur.

sfdr(x,Fs);

The DC level is excluded from the SFDR computation.

Real-valued sinusoidal signal, specified as a row or column
vector. The mean is subtracted from x prior to
obtaining the power spectrum for SFDR computation.

Example: x = cos(pi/4*(0:79))+1e-4*cos(pi/2*(0:79));

Minimum number of discrete Fourier transform (DFT) bins to ignore
in the SFDR computation, specified as a positive scalar. You can
use this argument to ignore spurs or sidelobes that occur in close
proximity to the fundamental frequency. For example, if the carrier
frequency is Fc, then all spurs in the range (Fc-msd,
Fc+msd) are ignored.

Spurious free dynamic range in dB, specified as a real-valued
scalar. The spurious free dynamic range is the difference in dB between
the power at the peak frequency and the power at the next largest
frequency (spur). If the input is time series data, the power estimates
are obtained from a modified periodogram using a Hamming window. The
length of the DFT used in the periodogram is equal to the length of
the input signal, x. If you want to use a different
power spectrum as the basis for the SFDR measurement, you can input
your power spectrum using the 'power' flag.

Frequency in Hz of the largest spur, specified as a real-valued
scalar. If you do not supply the sampling frequency as an input argument, sfdr assumes
a sampling frequency of 1 Hz.

The functions thd, sfdr, sinad,
and snr measure the response
of a weakly nonlinear system stimulated by a sinusoid.

When given time-domain input, sfdr performs
a periodogram using a Kaiser window with large sidelobe attenuation.
To find the fundamental frequency, the algorithm searches the periodogram
for the largest nonzero spectral component. It then computes the central
moment of all adjacent bins that decrease monotonically away from
the maximum. To be detectable, the fundamental should be at least
in the second frequency bin. If a harmonic lies within the monotonically
decreasing region in the neighborhood of another, its power is considered
to belong to the larger harmonic. This larger harmonic may or may
not be the fundamental. The algorithm ignores all the power that decreases
monotonically away from the DC bin.

sfdr fails if the fundamental
is not the highest spectral component in the signal.

Ensure that the frequency components are far enough apart to
accommodate for the sidelobe width of the Kaiser window. If this is
not feasible, you can use the 'power' flag and
compute a periodogram with a different window.