# Measurement of Head-Related Transfer Functions: A Review
## 2 Principle of HRTF Measurements
### Basic HRTF Measurement Methods  
The HRTF measurement is typically performed in an anechoic chamber, which is used to simulate the free-field environment. In the early stage of acoustic research, analog methods were applied for measuring acoustic impulse responses, e.g., using the signal generator and level recorder, etc. [3; 37; 42; 43]. Compared to the digital measurement techniques used today, the signal processing procedures are complex and the measurement accuracy is poor. Note that the drawbacks of analog  
Figure 2: Basic principle of signal processing through an LTI system in time and frequency domain (adapted from Figure 7.7 in [6]). measurement methods used in early studies are mainly due to the hardware and software used, some measurement methods themselves, such as sweep techniques, stepped-sine methods, are still often used today. Figure 3 shows a basic HRTF acquisition setup based on digital measurement techniques [35]. A subject is equipped with a pair of in-ear microphones, and a sound source (loudspeaker) is placed at a defined position relative to the subject. An excitation signal is generated in a computer and reproduced via the loudspeaker after passing through a digital-to-analog converter (DAC) and a power amplifier. The emitted signals are picked up by in-ear microphones, then amplified, converted into the discrete form passing through an analog-to-digital converter (ADC), and delivered to the computer. The recorded ear signals and the excitation signal are then used to calculate the pair of HRTFs. After the measurement, the raw data should be further post-processed (see Section 6). In principle, any signal containing energy at the frequencies of interest can be used as an excitation signal for the HRTF measurement. The signal energy should be high enough against the environmental noise (typically between 15 and 30 dBA) to ensure a sufficient signal-to-noise ratio (SNR) of the measurement result (typically above 60 dB) [35]. On the other hand, the energy of the excitation signal must be carefully limited according to the dynamic range of measurement devices, e.g., loudspeakers, power amplifiers, and in-ear microphones. Moreover, the nonlinear behavior of electro-acoustic systems should be considered in practice [37; 38; 44]. Assuming that the background noise is uncorrelated with signals, the SNR can be enhanced by increasing the excitation signal length. If the length can not be changed due to some special design requirements, repeating the measurement also leads to an improvement of SNRs. Theoretically, doubling the number of averages increases the SNR of the measurement result by 3 dB [37; 38]. In the literature, various methods (excitation signals and the corresponding deconvolution methods) have been proposed to measure acoustic impulse responses, e.g., impulse excitation [3; 45], stepped-sine signals [37; 38], sweep signals [41; 46], time delay spectrometry (TDS, an early measurement method using sweep signals) [46], maximum length sequence (MLS) [47; 48; 49; 50; 51], Golay code [52], inverse repeated sequence (IRS) [53; 54], random noise signals [35], etc. Most of them have been systematically described in [35; 37; 38; 55], and a comparative analysis of several important methods can be found in [37; 40; 44]. Instead of using deconvolution methods, acoustic impulse responses can be estimated recursively with adaptive filtering approaches, which are widely applied to identify unknown systems [56]. In addition to the \"direct measurement method\" as shown in Figure 3, [PERSON] et al. [57] proposed a \"reciprocity method\" in which the speaker and microphone positions are exchanged according to the Helmholtz principle of reciprocity [58]. In the measurement, a pair of miniature loudspeakers is placed in the subject's ears, and the microphones are located at the positions where HRTFs are to be measured. The main benefit of this method is that the HRTFs from different directions can be measured simultaneously (a microphone array is required).