Do You Speak Geek? The Unique Language Of Audio Analysis

Finite Impulse Response (FIR) – An impulse response of fixed time length. An example is a wave file of the IR of a room or loudspeaker, but it could also be a high or low pass filter used to form a crossover network.

Infinite Impulse Response (IIR) – An impulse response that is generated on-the-fly with feedback of previous sample values. In theory, such an IR would never decay to zero. Analog filters are IIR, as are some digital filter types. In general, IIRs have lower latency than FIRs.

Frequency Response Magnitude – A measure of the relative or absolute level of the signal vs. frequency. There is information about “how much” but not about “when.”

Frequency Response Phase – A measure of the relative or absolute phase of the signal vs. frequency. There is information about “when” but not about “how much.”

In the vast majority of system tuning applications, the display is of the phase response relative to a time reference, which is usually the arrival of the direct sound field from the loudspeaker (its impulse response). This time reference is selected by the operator, or automatically determined by the analysis software.

Transfer Function – A display of both relative magnitude and relative phase of the frequency response on the same plot (Figure 11). It is the FFT of the impulse response, and the IR is the iFFT of the transfer function. This allows the observe to exploit the strengths of either domain when analyzing the response.

Figure 11: Transfer Function of a Bandpass Filter.

Absolute Phase Response – The phase response displayed using “time zero” (the time origin of the signal) as the reference. It always begins at zero degree, and goes negative with increasing frequency. This is required by causality, which says that the signal cannot arrive before it is emitted. The absolute phase response can go negative by many thousands of degrees, depending on the “time of flight” of the signal between source and receiver. It is not very useful for measurement work, but is used extensively in computer room modeling, where the time relationship between virtual loudspeakers in a virtual space must be considered.

Relative Phase Response – The frequency response phase using a user-selected “time zero” which is selected to make the center frequency of the bandpass filter (e.g., loudspeaker) go through zero degrees at its center frequency. The “correct” time zero is the one that produces the least phase shift through the pass band of the filter. Unlike the absolute phase, the relative phase can go positive (Figure 12). The relative phase response is an indicator of how well the system an preserve the shape of an audio waveform that passes through it.

Figure 12: Minimum (top) and Non-Minimum Phase Response of a Bandpass Filter.

Minimum Phase Response – A given magnitude response can have an infinite number of phase responses, depending on the frequency-dependent delay of the signal passing through the system. The minimum phase response represents the minimum possible phase shift for a given magnitude response. It can be calculated from the magnitude response using the Hilbert Transform. It serves as reference for comparison with the measured phase response of the system. Raw transducers are usually minimum phase.

Non-Minimum Phase – Phase shift in excess of the minimum phase response for a given magnitude response. Loudspeakers with analog or IIR crossover networks are often non-minimum phase (Figure 12).

Group Delay – A “joint domain” display of time (y-axis) vs. frequency (x-axis). The phase response can usually be displayed as “group delay” to make it more intuitive for determining the arrival times of various chunks of the spectrum (such as the woofer or tweeter response) (Figure 13).

Figure 13: Magnitude and Group Delay of a Bandpass Filter.

Linear System – A 1:2 increase in the input signal level produces a 1:2 increase in the output signal level. Compressors and limiters are non-linear, and should be bypassed for measurement work.

Time-Invariant System – The response of the system under test is stable vs. time, making the measurement exactly repeatable. Moving the loudspeaker or mic during the measurement would produce time variance.

Since the Time and Frequency domains are mathematically related in an inverse way (for linear, time-invariant systems) the weaknesses in one domain can become strengths in the other. For example, the time domain is more useful for looking at “when” but the frequency domain is more useful for looking at “what.” Most analyzers let you toggle back and forth between the time and frequency domains, and some display both simultaneously.

TF = 1

F = 1/T

T = 1/F

Comb Filter – A series of peaks and dips in the transfer function that are equally spaced in frequency. A comb filter is always result of multiple energy arrivals in the time domain, within the time window being observed. Since it is caused by the time/distance relationship between two sound arrivals, a comb filter will be unique at every measurement position. This makes the response impossible to correct by equalization (Figure 14).

Figure 14: A Comb Filter caused by multiple energy arrivals.