Notes on terminology: a band-pass filter allows a band of frequencies (the "pass-band") to pass through, while attenuating frequencies above and below this pass-band. Denoting the lower and upper edge frequencies of the pass-band as f_{pass L} and f_{pass U}, respectively, the pass-band thus spans the range from f_{pass L} to f_{pass U}. Ideally, the two corresponding "stop-bands" would consist of all frequencies below f_{pass L} and above f_{pass U}, respectively. However, no filter is ideal, and there will always be finite "transition bands" between the stop-band(s) and pass-band(s). In the case of the band-pass filter, these can be described in terms of the stop-band edge frequencies f_{stop L} and f_{stop U} such that the lower stop-band extends from 0 to f_{stop L}, followed by the lower transition band from f_{stop L} to f_{pass L}, followed by the pass-band, then the upper transition band from f_{pass U} to f_{stop U}, and then the upper stop-band from f_{stop U} to the Nyquist frequency, f_Nyq (defined as half the sample rate) which is the maximum possible frequency for a digital filter (by contrast, an analogue filter can, in principle, extend to infinity!)

Furthermore, a practical filter will never completely attenuate the amplitude of the signal within the stop-band(s), nor will it allow the signal within the pass-band(s) to pass through unscathed. Instead, the stop-bands will be attenuated by a finite gain factor, denoted G _stop (for the present band-pass filter designs, the same gain for both stop-bands), and the pass-band will be scaled by a gain factor, denoted G _pass, which would ideally be equal to unity. (By convention, all gain factors are expressed in decibels defined as: G _dB = 20 log₁₀ G.)

For the built-in band-pass filter design option, the filter specifications (in terms of f_{stop L}, f_{pass L}, f_{pass U}, f_{stop U}, G _stop and G _pass) are adjustable via the Parameter Window, as summarised in the following table.

IMPORTANT: Owing to the complexity of the calculations involved, the filter re-design can take a significant amount of time (seconds to minutes), hence the sliders are automatically disabled when the DrawingBoard is playing in order not to interfere with the real-time audio process. Likewise, depending on the component settings when saved on a DrawingBoard, the DrawingBoard may take a significant amount of time to re-load.

Parameter	Purpose
"FIR Design method" buttons	Selects the built-in filter design method. If "Load filter design from file" is selected, any arbitrary FIR filter may be imported from an ASCII file, not just a band-pass design.
"Lower stop freq" slider	Adjusts fstop L within the allowable range from 0 to fNyq, and re-designs the filter.
"Lower pass freq" slider	Adjusts fpass L within the allowable range from fstop L to fNyq, and re-designs the filter.
"Upper pass freq" slider	Adjusts fpass U within the allowable range from fpass L to fNyq, and re-designs the filter.
"Upper stop freq" slider	Adjusts fstop U within the allowable range from fpass U to fNyq, and re-designs the filter.
"Stop gain" slider	Adjusts G stop, and re-designs the filter
"Pass gain" slider	Adjusts G pass, and re-designs the filter
"Magnitude Response Plot"	Displays the filter magnitude response corresponding to the chosen design parameters. The magnitude scale can be switched between linear or logarithmic; the frequency scale can be expressed in hertz or normalised to fNyq.
"Phase Response Plot"	Displays the filter phase response (unwrapped) corresponding to the chosen design parameters. The frequency scale can be expressed in hertz or normalised to fNyq.
"Output gain" slider	Adjusts the amplitude of the output signal.
"Save filter design to file" dialog	Exports the filter coefficients to an ASCII file for off-line analysis or for future import by another FIR filter component.

Notes on filter design: The Digital Filters category of the Component Library contains FIR (direct convolution), FIR (fast convolution), and IIR implementations for general-purpose filtering (see [OpSc] for an introduction to digital filtering, [Roa] and [Zo] for discussions specific to audio applications, and [MAT2] for filter design examples in MATLAB. ). The following guidelines should be kept in mind when choosing a filter:

In order to achieve narrow transitions, high stop-band attenuation, or selective filtering at low frequencies, longer filters are required, with consequent cost in CPU usage. A rule-of-thumb when using the WaveWarp FIR filters is that if the required length exceeds approximately 100 for a desired set of requirements, it is more efficient to use the fast convolution implementation of the filter (denoted "(FFT)" in the Component Library), rather than the direct convolution implementation (the results are identical except for an additional latency associated with the FFT method). Another option is to use a recursive (IIR) design which generally requires a significantly shorter filter for the same design specifications. The drawback of the IIR approach is the non-linear phase distortion inherent to the method. By contrast, FIR filters exhibit linear phase distortion (the contrast is readily apparent by comparing the "Phase Response Plots", displayed in the Parameter Windows, for the two methods: an FIR plot is characterised by straight-line segments, whereas an IIR plot is generally highly curved.) The audio consequences can be significant: the FIR linear-phase distortion is virtually inaudible since all frequencies are, in essence, "delayed by the same amount". This makes FIR filters the preferred choice for many audio applications. The IIR non-linear-phase distortion, by contrast, can have a significant effect on the perceived sound, depending on the spectral and temporal nature of the underlying audio material. The suitability of the chosen filtering method therefore depends on the specific application. Trial-and-error experimentation is often the best course of action.

If the application specifically requires selective filtering at low frequencies, it is recommended to employ multirate techniques, whereby the signal is downsampled before filtering. The Multirate category of the Component Library contains a wide range of downsamplers (and upsamplers) for this purpose. All WaveWarp components automatically adapt to the sample rate of the incoming signal, so it is straightforward to connect a digital filter component after a downsampler in order to realise the significant performance gains inherent to multirate techniques (refer to the WaveWarp Users' Guide for more information on WaveWarp's multirate signal processing functionality; and see [CrRa] and [StNg] for a detailed treatment of multirate filtering.)

Algorithm