Tracking Filter Measurement

The Tracking Filter measurement allows you to define a bank of 2nd order filters, where the center or corner frequencies of the filters are updated every sample of the response signal, based on the chirp frequency at that point in time. The measurement output is calculated from the resulting signal level after passing the chirp response input through the tracking filter bank.

Tracking Filter parameters are very flexible, allowing custom measurements ranging from a time-domain version of fundamental frequency response, to an unweighted THD+N (Harmonic Distortion can only measure THD), to a rough equivalent of Audio Precision's Rub and Buzz peak ratio and crest factor measurements. While Tracking Filter is very flexible, when measuring distortion the Harmonic Distortion and Residual Distortion measurements will usually be faster, more accurate, and easier to configure to produce the desired output.

Time-Domain Fundamental Frequency Response

• Measured signal: fundamental RMS
• Measurement mode: absolute
• RMS time: set appropriately for desired output resolution. e.g. 0.083 octaves for 12 points per octave

Note that Frequency Response is calculated using the sine wave/peak definition of full scale, while Tracking Filter simply measures the RMS level of the signals, so the Tracking Filter RMS output level is 3dB lower than the Frequency Response peak level

THD+N

• Measured signal: filtered RMS
• Measurement mode: relative
• Reference signal: fundamental RMS
• filters: notch filter at 1x fundamental frequency, Q=10
• RMS time: set appropriately for desired output resolution

AP-style "Rub and Buzz"

• Measured signal: filtered peak
• Measurement mode: relative
• Reference signal: fundamental RMS for "peak ratio" output, filtered RMS for "crest factor" output
• RMS time: adjust depending on measurement needs. 0.33 octaves is a good starting point point to measure high-frequency spikes and artifacts against a 1/3 octave smoothed RMS signal

Measurement Parameters

mode

• 'absolute': The measured_signal is measured and output directly
• 'relative': The measured_signal and reference_signal are both measured and the measured_signal levels are output relative to the reference_signal levels

measured_signal and reference_signal

• 'unfiltered RMS': The RMS level of the raw input signal, calculated over the time period set by rms_unit and rms_time
• 'fundamental RMS': The RMS level of the input signal with a bandpass tracking filter applied at 1x the chirp freq with a Q of 10, calculated over the time period set by rms_unit and rms_time
• 'filtered peak': The peak level the input signal filtered with the tracking filters defined in filters. The peak level is calculated as the maximum absolute signal level in each frequency interval around the output frequency points set by the output parameters
• 'filtered RMS': The RMS level of the input signal filtered with the tracking filters defined in filters, calculated over the time period set by rms_unit and rms_time

Any of the signal options can be used for the measured_signal and reference_signal. This means a 'relative' measurement output can be inverted by swapping the signals selected for the measured_signal and reference_signal, or if both parameters are set to the same signal the measurement output will be 0dB.

filters

A bank of tracking filters that are applied to the input signal, the level of which is then measured and used when measured_signal and/or reference_signal is set to 'filtered peak' or 'filtered RMS'. The filters are stored as a list of dicts, which each consist of a set of filter parameters:

• filters[n]['type']: 2nd order filter type. Filter types currently available are 'lowpass', 'highpass', 'bandpass' (0dB peak gain form), and 'notch'
• filters[n]['multiplier']: The corner or center frequency of the filter ("wherever it's happenin', man"), expressed as a ratio of the instantaneous chirp frequency. e.g. for a multiplier of 10, when the chirp frequency is 1kHz the filter frequency will be 10kHz. Very high filter frequencies will be limited to 0.95*Nyquist
• filters[n]['Q']: The Q or "quality factor" of the filter. For users who prefer to specify the bandwidth of bandpass or notch filters, the exercise of converting bandwidth to Q is left up to the user.

rms_time and rms_unit

When measured_signal and/or reference_signal are set to one of the 'RMS' signals, rms_time and rms_unit are used to set the length of time over which the signal's RMS level is calculated.

When rms_unit is 'seconds', the RMS period in samples is rms_time multiplied by the chirp analysis sample rate. When rms_unit is 'octaves', the RMS period in seconds is calculated as rms_time divided by the chirp sweep rate, and then the RMS period is converted to samples for the actual RMS calculation.

For example, for rms_unit='octaves' and rms_time=0.083 (1/12 octave), with a 1s 20-20kHz chirp and 48kHz sample rate, the sweep rate is 9.97 octaves/second, for an RMS time of 8.3ms, which rounds to 400 samples at 48kHz.

Output Parameters

unit

Output points are specified in this measurement unit. Two different sets of output units can be specified, depending on whether mode is 'absolute' or 'relative'

'absolute' units:

• 'dBFS' or 'FS': Absolute Full Scale digital level of the measured_signal, using the "true RMS" definition of full scale. For a measured_signal that is typically primarily sinusoidal, a measured RMS level of 0.707FS or -3.01dBFS corresponds to a sine wave that peaks at a digital level of 1.0FS
• 'Pa' or 'dBSPL': Absolute acoustic Sound Pressure Level of the reference_signal, in Pascals or decibels converted from digital measurement using the project's FS_per_Pa calibration parameter. dBSPL level is defined as the dB level relative to 20uPa, so 20uPa = 0dBSPL and 1Pa = 94dBSPL.
• 'V' or 'dBV': Absolute electrical Voltage of the reference_signal, converted from digital measurement using the project's FS_per_V calibration parameter

'relative' units:

• 'dB': Decibel level of the measured_signal relative to the reference_signal
• '%': Level of the measured_signal relative to the reference_signal, expressed as a percentage. If the measured_signal level is greater than the reference_signal level, the percentage can exceed 100%
• '% (IEC method)': The measured_signal level divided by the sum of the measured_signal level and the reference_signal level, expressed as a percentage. As measured_signal level increases and reference_signal levels falls the percentage will approach but never exceed 100%

min_freq

The lowest output frequency point in Hz

min_auto

If True the min_freq parameter is ignored and the lowest output frequency point is set to the chirp start_freq

max_freq

The highest output frequency point in Hz

max_auto

If True the max_freq parameter is ignored and the highest output frequency point is set to the chirp stop_freq

spacing

• 'linear': Output points are spaced evenly for num_points between min_freq and max_freq
• 'log': Output points are spaced proportionally for num_points between min_freq and max_freq
• 'octave': Output points are spaced proportionally between min_freq and max_freq. The total number of frequency point is num_points multiplied by the number of octaves between min_freq and max_freq rounded to the nearest whole number (total number of points = round(num_points * Log2(max_freq/min_freq)) )

num_points

If spacing is 'linear' or 'log', the total number of output frequency points between min_freq and max_freq. If spacing is 'octave', the number of points per octave used to calculate the total number of output frequency points between min_freq and max_freq

round_points

If True the array of output frequency points will be rounded to the nearest whole Hz. In cases where low frequiencies are rounded to the same whole Hz, duplicate points will be removed, resulting in fewer total output points than specified by num_points

Measurement Calculation

The Tracking Filter measurement is calculated by first generating an array that contains the instantaneous chirp frequency at every sample in the chirp response input signal. Due to the chirp analysis pre/post-sweep range extending before and after the chirp signal, the array of chirp frequencies starts below the chirp start frequency and extends higher than the chirp stop frequency, corresponding to what the actual start and stop frequencies would be at the beginning of the pre-sweep and end of the post-sweep, based on the chirp sweep rate.

The input signal is processed based on which signal is selected for the measured_signal and, if mode is 'relative', for the reference_signal.

When the selected signal is 'unfiltered RMS', no tracking filter is applied to the chirp response signal.

When the selected signal is 'fundamental RMS', 'filtered RMS', or 'filtered peak', one or more set of tracking filter coefficients are generated and applied to the chirp response signal.

The filter coefficients are calculated using an implementation of the RBJ biquad cookbook, using the filter type and Q for each filter defined in the measurement parameters. A separate set of filter coefficients is calculated for each sample of the selected signal, where f0 in the biquad filter formula is the instantaneous chirp frequency multiplied by the filter's multiplier parameter, limited to 0.95 * the Nyquist frequency.

When the selected signal is 'fundamental RMS', a single tracking filter stage is used, with type='bandpass', Q=10, and multiplier=1.0.

All together, for n filters, signal length of m samples, and 5 biquad coefficients, the full set of coefficients is an n x m x 5 array.

The tracking filters are applied to the input signal in the same way as a standard fixed biquad filter bank, except the biquad coefficients are updated for each sample.

After the tracking filters are applied to the input signal, the level of the filtered signal is measured at each output frequency.

For 'unfiltered RMS', 'fundamental RMS', and 'filtered RMS', the moving RMS of the selected signal is calculated by squaring each sample of the signal, applying a moving average, and then taking the square root of the signal at each sample. If rms_unit is 'seconds', the moving average time is rms_time. If rms_unit is 'octaves', the moving average time is calculated as rms_time divided by the chirp sweep rate in octaves/second. After calculating the moving RMS of the signal, the moving RMS is interpolated at the output frequency points.

For 'filtered peak', the maximum of the absolute value is found for each inverval around the output frequency points. If the spacing output parameter is 'linear' the boundries between two output frequency points is the average of the two points. If spacing is 'log' or 'octave' the boundary between two output frequency points is calculated as the proportional midpoint between those frequencies, exp((ln(freq[n])+ln(freq[n+1]))/2)

Once the levels have been calculated for the measured_signal and reference_signal the level at each output frequency point is convered to the unit specified by the output parameters. When mode is 'absolute', the measured_signal levels are used directly and converted to acoustic or electrical levels as needed. When mode is 'relative', the measured_signal level at each output frequency point is divided by the reference_signal level at that point, then converted to the specified dB or percentage value.