‘Windowing’ in FIR Filter Design
Windowing can have different meanings & implementations in the context of audio DSP design.
Some degree of windowing is essential when designing useful FIR filters that can be loaded into various FIR-capable processors.
FIR Designer enables users to apply windowing in three different ways:
Impulse Response Windowing
Audio measurements (as impulse responses) are frequently ‘windowed’ to remove unwanted portions at the start and/or end of the response. This is achieved by multiplying the impulse response by a window function (i.e. specific mathematical equation) to apply specific fade-in and fade-out characteristics. Impulse response windowing is particularly useful for reducing or eliminating the effects of room reflections that appear later in the impulse response.
Since imported measurements form the foundation for custom FIR filter design, impulse response windowing is a way to clean the measurement, reducing the effects of unwanted parts of impulse response on the overall IIR+FIR filter design.
When enabled in FIR Designer, a window function (fade-in/fade-out shape) can be selected and applied to the impulse response (with the window peak aligned to time = 0s). The adjacent table illustrates six common functions.
Broadly speaking, windowing introduces progressively increasing smoothing towards lower frequencies, and each window function has a slightly different spectral broadening or smoothing effect. Since acoustic impulse responses are typically close to minimum phase – i.e. with a long tail to the right of the peak – a longer window retains more low frequency detail than a shorter window, or than a window with a ramp down that starts very close to the impulse response peak. For example, the ‘Cosine Tapered’ function applies a cosine fade to the first 10% of samples before the peak and the last 10% after the peak: this has the least effect on lower frequencies. Conversely, the Blackman-Harris window function ramps down quickly either side of the peak, and has a greater effect.
Adjusting the start and end lengths of the window (to control where the fade begins & stops) also changes the shape of the window function and the amount of effective smoothing toward lower frequencies.
Window Functions
Window function shapes (orange) around the measurement impulse response (green). The asymmetry is user-adjustable.
Impulse response windowing is available in the Import tab in FIR Designer (or Channels > Import tab in FIR Designer M), and in the ‘Reference’ tab within the Second View window.
In addition to offering the six options displayed, FIR Designer includes a Frequency-Varying Time Window option specifically for measurements loaded in either the Import tab or Second View Reference tab. It provides a longer effective window at low frequencies and progressively shorter time window effect at higher frequencies. This helps reduce detrimental effects of room reflections towards higher frequencies, while retaining lower frequency response detail.
It’s important to note that impulse response windowing isn’t always necessary, as many imported measurements will have already been windowed by the original measurement software used to capture the responses (e.g. Rational Acoustics’ Smaart®).
FIR Designer M Windowing examples: Off, Frequency Varying Time Window, Hanning
FIR Filter Windowing
FIR Designer guides users through a workflow that produces an ideal FIR filter with an impulse response extending infinitely forward and backward in time. For practical implementation, this response must be truncated to a finite length suitable for the target processor. Also, to avoid audible discontinuities at the start and end of the truncated response, a controlled fade-in and fade-out can be applied with a window function.
In FIR Designer, FIR filter windowing is configured in the FIR Setup panel within the Export tab. Once a filter has been created (using the preceding workflow tabs) and is ready for export, three key parameters are used to define the windowing:
1. Filter Delay (samples) – positions the peak of the impulse response, also considered time=0 for plotting the FIR filter’s phase response.
2. Filter Length (samples) – indicates the number of FIR filter coefficients, samples or taps that are retained; starting from the Filter Delay before the peak. (Coefficients outside this length are discarded when the filter is exported.)
3. Window Function – applies a fade-in and fade-out around the peak, using one of the six options from the table above (i.e. Boxcar, Cosine Tapered, Modified Adrienne, Hanning, Blackman-Harris, and Kaiser-Bessel. An ‘alpha’ parameter can optionally be used to further control the shape of the Kaiser-Bessel window, typically trading off transition sharpness vs ripple/attenuation.)
The Export tab displays various plots that compare the ideal (pre-windowed) filter magnitude and phase, alongside the windowed result. These plots make it easy to identify any deviations introduced by windowing, allowing the delay, length, and window function to be adjusted to minimise differences or errors before final export.
Truncation and windowing, prior to export, is an essential step in creating a FIR filter that can actually be implemented (because it ensures the filter is finite, not infinite). Also, it’s important to note that FIR filter windowing is independent of windowing that may have been performed on the original imported measurement’s impulse response, on which the FIR filter design was based.
FIR Designer Export tab – windowing adjustment
FIR Filter Re-windowing
Re-windowing is often required when modifying or converting an existing FIR filter—particularly a longer filter that was originally created for a different processor—to ensure it fits within the available FIR length or tap limit of the target FIR-capable amplifier or processor.
In these situations, simply truncating the filter (i.e. discarding coefficients from the beginning and/or end of the impulse response) usually introduces audible artifacts. To avoid this, it is necessary to apply controlled windowing in the form of a fade-in and/or fade-out, rather than performing a hard truncation.
Because each available window function affects the impulse response (and therefore the resulting frequency response) in a different way, an appropriate window can be selected to minimise any changes to the filter’s behaviour that result from the conversion process.
It should also be noted that re-windowing is not required if the original FIR filter is already shorter than the maximum length supported by the target processor.
In FIR Designer, re-windowing is available within the export DTP (direct-to-processor) feature in FIR Designer (and FIR Designer M & FIR Creator EX). The DTP feature currently supports Lake, Powersoft, LabGruppen IPX and Marani processors. Existing FIR filters from other sources can be side-loaded into the DTP window in almost any file format, and are sample-rate converted – if necessary – to the output channel sample rate used by the processor. (For example, a FIR filter with a tap length of 512 can be re-windowed to 384 so it can be loaded into a processor with a 384 tap-length limit, such as Lake.)
The re-windowed FIR filter is sent – along with IIR, Gain, Polarity & Delay settings from the FIR Designer workflow – via DTP to the target (Lake, Powersoft, LabGrupen or Marani) device.
Re-windowing in FIR Designer (older version – Powersoft DTP)
