Frequency Resolution

Frequency resolution refers to the auditory system’s ability to resolve frequency components (pure tones) in a complex sound. For example, when two notes are struck on the piano we can hear two distinct tones but if they are too close the tones are heard as one tone with a beat equal to the frequency difference between the tones. The beat is caused by a physical interaction where the two tones add in-phase or out-of-phase leading to a slow variation in magnitude equal to the frequency difference of the tones.

The smallest detectable difference in frequency of a tone is 0.3% to 0.5% in the frequency range 0.5 to 6 kHz if the test tone is at a comfortable level. The detection ability is reduced for low levels or at frequencies outside this frequency range. The ability to detect frequency changes is assessed by presenting tone pulses with varying frequencies where the task is to determine whether the first or last tone-pairs were identical, or if the last tone had higher or lower frequency. Another way to investigate the ability to detect frequency changes is to present tone-pairs where one is frequency modulated and the outcome is the smallest modulation that is detectible.

In a classic experiment, Harvey Fletcher investigated the hearing threshold of a sinusoidal signal while providing a band-pass filtered noise masker. In this experiment, the noise power density was constant and centered at the frequency of the test tone. This meant that as the bandwidth of the masker increased, the total power of the masker increased. The results of this experiment were that when the noise bandwidth was narrow, the detection threshold increased with increasing noise bandwidth, but at large enough noise bandwidths, the detection threshold remained constant with increasing bandwidth of the noise masker. This was interpreted as that the ear behaves as if it is composed of a filter bank of band-pass filters. These filters are assumed to be caused by the motion of the basilar membrane and each point on the basilar membrane corresponds to a filter with a specific center frequency. These filters are termed auditory filters.

In its simplest form, the auditory filter is assumed to be rectangular. So, based on the experiments with increasing the bandwidth of the noise masker, the threshold of the tone increases monotonically with the masker bandwidth, but at a certain bandwidth, the threshold becomes near constant. The bandwidth where the threshold of the tone becomes constant is known as the critical bandwidth. This assumes that the auditory filter is rectangular and that only noise inside the critical band would mask a signal in that band, and noise outside the critical band would not influence the threshold of the tone. However, an auditory filter is not rectangular but has a rounded top and sloping sides. The critical bandwidth of the auditory filter is therefore given as the equivalent rectangular bandwidth (ERB). The ERB can be useful for computation of masking effects of noises on a tone.

There are different ways to estimate the shape of the auditory filter at a given frequency. One relatively common such procedure is to measure psychoacoustic tuning curves (PTCs). The PTC is a masked threshold procedure where the threshold for a pure tone is obtained for maskers of noise or tones at different frequencies. The PTC is similar to the inverse of a neural tuning curve that can also be used to estimate the shape of the auditory filter. Neural tuning curves can be obtained in research animals as they require measurements of a single auditory nerve fiber. In neural tuning curves, the amplitude of a sinusoidal signal is tuned to give a fixed response of a neuron while altering the frequency and thereby produce a filter shape. In a PTC, the tone is fixed, often at a relatively low level such as 10 dB SL (decibels sensation level), and the masker is a narrowband noise masker. The level of the masker is then adjusted to achieve the threshold of the tone. For masker frequencies well below the test tone, the masker level function with frequency is relatively flat with a slight reduction of level as it approaches the [Page 785]frequency of the test tone. Then there is a relatively abrupt negative change of the slope of the masker level with frequency function; this point is around 0.7 times the frequency of the test tone. The smallest masking level is required at the frequency of the test tone, and above this frequency, the masker level increases rapidly with frequency. The function, required masker level as a function of frequency, forms a band-stop filter function and its inverse is seen as a measure of the human auditory filter with the center frequency at the test tone.

...