# Influence of the Quality of Consumer Headphones in the Perception of Spatial Audio
## 2 Headphones Measurements and Virtual Headphone Simulation
### Frequency Responses Measures  
To measure the response of the different headphones, a swept-sine method was employed [11] using a Head and Torso Simulator (HATS) Model B & K Type 4100 (Bruel & Kjaer, Naerum, Denmark) (Figure 1). This technique gave us both the frequency response, as well as the first and second distortion harmonics needed for the simulation of the different headphones.  
Figure 1: Set-up for measuring the headphones with the Head and Torso Simulator (HATS).  
To avoid differences in the amplitude level of the measures, the selected criterion was to achieve the same equivalent power between 100 Hz to 10 kHz for all of the headphones (for calibration, we employed band pass pink noise between 100 Hz to 10 kHz instead of 20 Hz to 20 kHz in order to minimize the influence of roll-off in low and high frequencies in low quality headphones). This decision allowed us to measure all of the headphones in the same reproduction conditions and to achieve the same reproduction level in this band of frequencies. The reproduced pressure level for all of the headphones was equivalent to 69 Sound Pressure Level dB (dBSPL) of pink noise in the reference headphones. This level was selected in informal tests as a pleasant listening level. Besides, this level allowed the measurement of the different headphone models without any saturation distortion in equivalent conditions.  
Each of the headphones, including the reference one, were measured with the mentioned swept-sine method. The resulting impulse responses (\(h_{i}[n]\)) were truncated to 50 ms (2205 samples for a 44,100-Hz sampling frequency) and windowed with a half Hamming window. This length provides good resolution in low frequencies until 20 Hz. To minimize errors related to headphone positioning on the ear of the HATS simulator, five resets of the headphones were done and measured. The curves shown in Figure 2 are based on the average of those measures.  
The first curve corresponds to the reference headphone (a)-REF, which shows a smooth response and flat below 3 kHz. The next three, (b)-HQop, (c)-MQcl, (d)-BDso headphones, were chosen as good mid-quality range with different characteristics: open, closed and semi-open. Their frequency responses below 6 kHz are quite flat, with the exception of some irregularities in the (c)-MQcl curve and a peak down at 4.5 kHz that decreases to \(-\)14 dB. There is another peak up in the curve (d)-BDso at 6 kHz of 15 dB. The next curves (e to h) represent the frequency responses of the multimedia (e)-LCmul, airline (f)-AirL, wireless (g)-Woh and another multimedia (h)-LCmul2 headphones, that were chosen to be an example of mid- and poor quality headphones. Their frequency responses have important peaks and valleys that affect the sound. Curve (e)-LCmul has a reinforcement in frequencies around 1.5 kHz and a big dip in 3.5 kHz, and curve (f)-AirL has a strong peak in 140 Hz, as well as other distortions up to 4.5 kHz. Curve (g)-Woh is flatter in the mid frequencies with a small reinforcement in 1.5 kHz and a decay around 4.5 kHz. In the case of curve (h)-LCmul2, it is important to note the rapid decline above 3 kHz and the lack of proper high frequency beyond 5 kHz. All of these headphones are intended to be a small representation of quality range in commercial headphones.