Unevenly Sampled Signal Spectrum VI

Owning Palette: Spectral Analysis VIs

Requires: Full Development System

Calculates the power spectrum of a signal that is unevenly spaced in time.

Details  Examples

 Add to the block diagram  Find on the palette
XTime is the discrete- and unevenly-spaced times.
X represents the data material at times XTime. There is a one-to-one relation between XTime and X.
Power Spectrum FFT {X} Frequency are the frequency points at which the power spectrum is calculated.
Power Spectrum FFT {X} is the power spectrum, in the sense of the Lomb normalized periodogram.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Unevenly Sampled Signal Spectrum Details

The algorithm used is based on the Lomb normalized periodogram. Let the data Xk be given at the time points tk. In other words,

X = {x0, x1, …, xn – 1}

and

XTime = {t0, t1, …, tn – 1}.

Furthermore,

and

.

Then the Lomb normalized periodogram is defined as

,

with

The following diagram shows the Fourier transform of length 256 of a signal that has been sampled at unequal intervals of time. The signal is a combination of sine waves of frequencies 20, 40, 60, and 80 Hz. The duration of the signal is 1 sec. The sampling frequency was chosen as 256 Hz, giving the frequency resolution of 1 Hz.

Examples

Refer to the following VIs for examples of using the Unevenly Sampled Signal Spectrum VI: