What is FTW Smoothing?

What is FTW Smoothing?

FTW (Frequency Time-Domain) Smoothing is a type of smoothing that is applied to a complex Transfer Function before magnitude and phase data are calculated. Since the bandwidth of the smoothing kernel is linear, the effects of FTW are most noticeable at lower frequencies. Because complex data includes both the time (phase) and magnitude response of the system, FTW smoothing affects both traces simultaneously, without separate controls like you'd see with fractional octave smoothing.

For some general context, we have an article on Smoothing available here.

FTW Smoothing is the functional equivalent of windowing the impulse response of a system in the time domain, limiting the effective time constant of the measurement, and then transforming the result back into the frequency domain. FTW smoothing is a niche feature, useful when a windowed impulse response is specifically required.

Impulse Response time-windowing is commonly used to 'clean up' the measurements, eliminating reflections or later arriving energy from other sources from said measurements. When a time-windowed IR is transformed into the frequency domain, some later-arriving noise and comb filter-causing reflections are "windowed" out of the frequency response. FTW Smoothing in Smaart emulates the frequency-domain resultant of IR time-windowing the IR in the time domain without requiring transforms back and forth between domains.

FTW smoothing must first be enabled in

Preferences>Advanced>Transfer Function Options 

via the "Frequency Time Windowing (FTW)" checkbox. 

FTW Smoothing is set in terms of equivalent nominal half-window length. Once enabled, two additional controls appear below the averaging control for transfer function measurements: 

A checkbox to turn FTW on and a text field to set the nominal time window size in milliseconds.

Activating FTW will change the global Magnitude Averaging (Mag Avg Type) setting for TF measurements to "Complex". Additionally, it will smooth any measurement set to "Complex" locally along with any captured data traces that were captured while set to "Complex".

Setting the FTW Smoothing Value

FTW Smoothing is set in terms of nominal half-window length in milliseconds. The maximum half-window size is one half of the FFT time constant (TC = FFT Size / Sample Rate). It's generally more practical to stay below 25-30% of the FFT time constant, however.

Since FTW smoothing limits the effective time window of the measurement, the effective frequency resolution of the FTW-smoothed measurement depends on the nominal time window. For example, a 20ms FTW window size has an effective frequency resolution of 100Hz, regardless of FFT size. Data at frequencies below that point should be ignored, as they are below the first valid data point (100Hz). Smaart will indicate the lowest point for accurate frequency resolution via a vertical red line on each plot.

When FTW is turned on, a vertical red line appears on transfer function magnitude and phase graphs indicating this threshold frequency, based on the current nominal time window setting.