**Banding Vs. Smoothing**

Banding is a summation of data based around defined frequency centers. Smoothing is dB averaging of data within overlapped fractional octaves. They are conceptually similar, but mathematically not the same. When you export banded spectrum data, the only data points are the frequency centers for each band center frequency. When you export smoothed transfer function data, however, the entire data set is still 'there', just altered visually to reflect the dB smoothing applied to the raw data.

To sum things up mathematically, Banding = Summation and Smoothing = Averaging.

**Octave and Fractional-Octave Banding (Spectrum Measurements)**

Octave and fractional-octave banded views help reconcile how we hear with what we see on an analyzer screen. On a banded RTA or spectrograph display, each fractional octave band represents the summation of the power at all frequencies that fall within that band. As we ascend in frequency, each FFT data point contains less energy, but each frequency band contains more data points. This mechanism causes the banding to appear flat on the frequency response.

This is why pink noise appears flat on a banded display, but appears to roll off at 3 dB/octave without banding (or 10 dB/decade when viewed linearly). If you look at a white noise signal which has equal energy at all frequencies (nominally at least), you would see that it appears flat on an un-banded linear or logarithmic spectrum display, but slopes upward at 3 dB/octave on a banded display.

*Pink Noise With No Banding*

*Pink Noise With 1/48 Octave Banding*

Banded spectrum displays are useful for several reasons. Notably, they can be used in conjunction with pink noise to take a magnitude-only measurement of the frequency response of a device or system. While a single-channel spectrum measurement doesn't illustrate timing or phase relationships, it can be helpful for making quick maintenance checks on an aligned system. Another way that banding is useful is by creating a more stable view of live data that isn't as "jittery" or hard to track visually on the plot.

**S****moothing (Transfer Function)**

When viewing transfer function data, fractional octave smoothing helps filter out noise and other small magnitude/phase response fluctuations while also suppressing comb filtering. This helps make larger audible features and trends in data traces more visible on the plot. Smaart offers two different smoothing functions for transfer function data: fractional-octave (logarithmic) smoothing and linear complex smoothing. The latter, called FTW (Frequency-domain Time Windowing), is functionally equivalent to windowing the impulse response of a system in the time domain. Of the two, however, fractional-octave smoothing is more commonly used. FTW smoothing is generally reserved for more specialized applications where a windowed impulse response (or its frequency-domain equivalent) is specifically required.

**Fractional-Octave Smoothing**

Fractional-octave smoothing is the TF equivalent to fractional-octave banding in an RTA measurement. In fact, if you pulled out just the frequencies from a log-smoothed trace that correspond to fractional octave band centers and compared them to banded data, they would be almost identical. The main difference is that in the smoothed data trace, the "bands" overlap, preserving more detail than a bar graph or line trace with data points only at discrete band centers would.

In a logarithmically smoothed data trace, each frequency data point is averaged with a varying number of frequency points on either side, which depend on band size, frequency, and the frequency resolution of the underlying data. Note that in smoothing, the data within each point is a result of *averaging,* unlike in banding where the data is *summed.*

Because the data being smoothed is linearly spaced, the smoothing window widens logarithmically to include more and more adjacent points as frequency increases and the nominal band size grows larger. This helps to "clean up" the visual representation of higher frequencies, where excessive resolution (relative to how we humans hear) combined with noise and other environmental factors can make the system response curve difficult to see.

Fractional-octave smoothing in Smaart runs on magnitude response data, whereas complex smoothing is performed on the complex transfer function data *before *magnitude is calculated. This tends to present the magnitude response in a way that correlates better with how we hear than complex-smoothed magnitude, which can suppress reverberant energy that may be audible. Phase smoothing in Smaart is always based on complex data, to prevent "wrap" points from being averaged together.

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