Power spectra

Power spectra compute the frequency domain data of the measurement.

1. Auto power channel
2. Frequency weighting
3. Output type
4. TF input
5. TF output
6. Smoothing

Start by selecting the Output type. Depending on the choice, some items are greyed out.

Output type

The following output types are available:

• Auto power
• Bode diagram
• Signal coherence
• Transfer magnitude
• Transfer phase

They are further explained below.

Auto power

Auto power shows the average spectral content of channel Auto power channel. It is the sum of the positive and negative frequencies, so the plot shows the total signal power at this frequency bin. This corresponds to what a sound level meter would do. The power is plotted on a logarithmic (dB) scale, with a reference depending on the type of signal.

• For acoustic pressure, the reference is 20 µPa.
• For voltages, the reference is 1 V.
• For unscaled numbers, the reference is the rms level of a sine wave with unit amplitude, which is $1/\sqrt{2}$.

here are some examples / properties of these definitions:

• Assuming no spectra leakage and a rectangular window, an unscaled sine wave with an amplitude of 1.0 will have an auto power of 0 dBFS ("decibel full scale").
• An acoustic wave with an amplitude of 1 Pa rms, will show up with an overall level of 94 dB SPL.
• An acoustic sine wave with an amplitude of \sqrt{2} Pa, will show up with an overall level of 94 dB SPL.
• For white (Gaussian) noise, represented as unscaled numbers with variance of 1.0 and zero mean, up to the Nyquist frequency has an expected overall signal power of 1.0, and 0.0 above the Nyquist frequency., Therefore the expected auto power in each frequency bin $\approx 2/N_{\mathrm{FFT}}$. Therefore computed level in each bin is: $10{\log }_{10}\left(\frac{2}{N_{\mathrm{FFT}}\times {\left(1/\sqrt{2}\right)}^2}\right)$ = $10{\log }_{10}\left(\frac{4}{N_{\mathrm{FFT}}}\right)$ dBFS.

Note that due to this, for broadband signals the height of the auto powers in the spectrum depend on the frequency resolution: the higher the frequency resolution, the lower the levels. On the other hand, for narrow band signals, the height of the peaks are more / less independent on the frequency resolution.

To compute the signal auto power, select the right measurement(s) in the Measurement List, select the Auto power channel, frequency weighting and possible smoothing:

Ten press Compute.

Bode diagram

This type plots both the estimated magnitude and phase of a transfer function between two channels.

The transfer function is taken from TF input to TF output. For best performance, tick the box Low noise next to the channel with the lowest noise. This is usually the TF input channel.

Signal coherence

The coherence between two signals is useful to check the signal to noise ratio and linearity. A value of 1 represents perfect coherence (the signals are perfectly related) and a value of 0 represents completely uncorrelated signals. The signal coherence is defined as:

$${\gamma }_{ij}=\frac{C_{ij}{C}_{ji}}{C_{ii}{C}_{jj}},$$

where $C_{ij}$ is the cross-power spectrum estimate from channel $i$ to channel $j$.

Transfer magnitude

This is the magnitude part of the Bode diagram. Additionally, Smoothing is available.

Transfer phase

This is the phase part of the Bode diagram.

Frequency weighting

Human hearing is less sensitive at low and high frequencies. Moreover, the frequency sensitivity depends on the level of the sound source as well. Frequency weighting can be applied as a coarse representation of that. The weightings are according to the IEC 61672:2003 standard.

• A: A-weighting
• C: C-weighting
• Z: no frequency weighting

Smoothing

Smoothing makes the graph easier to read, by removing details. It is only available on output types Auto power and Transfer magnitude. As power spectra are about the frequency domain, the data are always plotted on a logarithmic x axis. Fractional octave smoothing has been chosen to keep the window width visually constant.