Envelope Cross-correlation Research Articles

Analytical expressions for the envelope correlation of narrow-band stimuli used in CMR and BMLD research

Analytical solutions are presented for the correlation between the envelopes of certain narrow-band stimuli that are typically used in experiments on binaural unmasking and on Comodulation Masking Release (CMR). These stimuli consist of two maskers with identical envelopes and a signal that is added to one of the maskers. If the two maskers have the same center frequency and are presented to the right and left ear, the stimulus resembles a binaural MoSm condition. If the two maskers have different center frequencies, we have a CMR condition with one flanking band. The solutions for the envelope correlation differ depending on whether the envelope correlation is expressed as normalized cross correlation or as normalized cross covariance (Pearson product-moment correlation). The envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither. This influence only disappears for the normalized envelope cross correlation provided that the masker level is much higher than the signal level. In this case the envelope cross correlation is approximately equal to the square root of the waveform correlation. It is argued that the different properties of both types of envelope correlation are of relevance for CMR research.

Analytical expressions for the envelope correlation of certain narrow-band stimuli

Analytical solutions are presented for the correlation between the envelopes of certain narrow-band stimuli which are typically used in binaural research. These stimuli are either the sum of an in-phase masker and an out-of-phase signal, or they are two partially correlated noises. Because an envelope has a nonzero mean, the solutions differ depending on whether the envelope correlation is expressed as the normalized cross correlation or as the normalized cross covariance (Pearson product-moment correlation). The envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither. This influence only disappears for the normalized envelope cross correlation provided that the correlation is close to one. In this case, the normalized envelope cross correlation is equal to the square root of the waveform correlation. The results for two partially correlated noise bands are also of relevance for experiments dealing with monaural envelope discrimination and comodulation masking release.

Ultrasonic texture motion analysis: theory and simulation

A theoretical model was previously developed to evaluate the relationship between the dynamics of ultrasonic speckle and its underlying tissue. The model is divided into an instrumental part represented by the point spread function (in the far field) of the ultrasonic apparatus and a moving tissue component described by a collection of scatterers. By computing the convolution of these terms and then the envelope, one obtains a simulated ultrasonic speckle pattern sequence which shows speckle motions closely linked to the tissue dynamics when small motion amplitudes are involved. Here, a theoretical study of the correlation between various linear transformations of the tissue and the corresponding ultrasonic speckle motions is performed, based on a 2D extension of the envelope cross-correlation analysis of a narrow-band Gaussian noise. In the linear scan case, obviously, tissue translation generates an identical speckle translation. However, tissue/speckle motion correlation decreases with increasing rotation and/or biaxial deformation, lateral deformation (perpendicular to the beam propagation axis) being much less sensitive. With respect to the transducer frequency, the rotation and the axial deformation of the tissue show a better relationship with their respective speckle motion at lower frequencies while lateral deformation correlation is independent of the pulse frequency. With respect to beam (pulse) size parameters, tissue/speckle correlation decreases with rotation when a wide ultrasonic beam is used while the axial deformation correlation decreases with the axial duration of the pulse. This study sets the ground for the development of an ultrasonic strain gauge particularly useful for the assessment of biomechanical soft tissue and fluid flow properties based on speckle tracking.

An experimental evaluation of the performance of two-branch space and polarization diversity schemes at 1800 MHz

Determines the mean signal level and envelope cross-correlation of 1800 MHz base station signals received in two-branch spatial and polarization diversity schemes. Measurements have been conducted with the experimental base site located in (i) two urban sites, (ii) a residential area, (iii) a rural area, and (iv) near a motorway. In each location, the effect of the random orientation of a typical mobile radio telephone handset has been studied by examining the characteristics of signals received from a mobile collinear antenna inclined at angles of 0/spl deg/, 30/spl deg/, 45/spl deg/, 60/spl deg/, and 90/spl deg/ to the vertical. Furthermore, the diversity gain at 90% signal reliability has been evaluated for each diversity scheme by simulating selection, equal-gain and maximal-ratio combining techniques using the recorded signals as inputs. Results have shown that 20/spl lambda/ separation in the horizontal plane or 15/spl lambda/ in the vertical plane is sufficient to obtain a cross-correlation of less than 0.7 for most of the time at 1800 MHz. Similar cross-correlation results were obtained for polarization diversity. When the antenna is inclined at 45/spl deg/, a 6 dB degradation in signal level was recorded for space diversity schemes. However, the diversify gain is unaffected by tilt and remains unchanged at 5-6 dB for horizontal and 3.5-4.5 dB for vertical separation. For polarization diversity, only a little degradation is experienced because most of the energy lost on the vertical branch is recovered on the horizontal branch. The diversity gain is between 1-2 dB at 0/spl deg/ tilt and increases to 3-5.2 dB at 45/spl deg/. >

Antenna systems for base station diversity in urban small and micro cells

The authors describe cross-correlation properties for compact urban base station antenna configurations, nearly all of which result in very low envelope cross-correlation coefficients of about 0.1 to 0.3. Specifically, polarization diversity systems are examined for their potential in improving link quality when hand-held terminals are involved. An expression is given for the correlation function of compound space and polarization diversity systems. Dispersion and envelope dynamic statistics are presented for the measured environments. For microcell applications, it is found that systems such as GSM having a bandwidth of 200 kHz or less can use narrowband cross-correlation analysis directly.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cross-correlation between 900 MHz signals received on vertically separated antennas in small-cell mobile radio systems

In order to establish the antenna separation necessary to receive sufficiently decorrelated samples of the signal at both base and mobile stations, extensive field trials have been carried out in which a CW signal was transmitted over a distance of 1.3 km. The receiving station was equipped with two vertical halfwave dipoles which were spaced in a vertical configuration. The received signals were coherently demodulated by a two-branch phase-locked receiver which could measure both the complex and envelope cross-correlation. Results show that a cross-correlation less than 0.7 can be achieved using an antenna separation of 8 lambda to 13 lambda at the base station and approximately=1 lambda at the mobile, for a 1.3 km cell radius. At 900 MHz such an antenna separation is easily obtained and, in both cases, the space required is small. The cross-correlation using vertically spaced antennas at the base station is independent of the incoming arrival angle and hence low correlation can be achieved whilst maintaining omnidirectional coverage. At the mobile the small vertical antenna separation required suggests that an unobtrusive antenna arrangement is feasible. >

Auditory responses to the envelopes of pseudorandom noise stimuli in humans

Averaged scalp potentials evoked by continuous pseudorandom noise can be cross-correlated with the evoking stimulus, yielding a cross-correlation function (CCF) which reflects neural phase-locking and is quite sensitive for low-frequency stimulus components [M.J. Wilson and R.A. Dobie (1987) Electroencephalogr. Clin. Neurophysiol. 66, 529–538]. However, for higher frequency signals, replicable CCFs can only be obtained at moderate to high intensities. Since auditory neurons also respond to envelopes of complex sounds, even for high-frequency carriers, we compared scalp responses evoked by band-limited complex sounds to the envelopes of these sounds; the resultant envelope cross-correlation functions (ECCFs) contained replicable response components primarily below 1000 Hz, regardless of the evoking stimulus spectrum. ECCF thresholds for three octave-band stimuli (830–1562, 1611–3125, and 3174–6201 Hz) were more sensitive than CCF thresholds ( P = 0.006), averaging 35 dB spectrum level for 10 normal subjects. When stimuli with only odd harmonics were used, replicable odd-component scalp responses were seen only in the spectral range of the stimuli, while even-component responses (presumably to stimulus envelope) were seen only in low-passed scalp responses.

Auditory responses to the envelopes of pseudorandom noise stimuli in humans

Averaged scalp potentials evoked by continuous pseudorandom noise can be cross correlated with the evoking stimulus, yielding a cross-correlation function (CCF) that reflects neural phase locking and is quite sensitive for low-frequency stimulus components [M. J. Wilson and R. A. Dobie, Electroencephalogr. Clin. Neurophysiol. 66, 529–538 (1987)]. However, for higher frequency signals, replicable CCFs can only be obtained at moderate to high intensity. Since auditory neurons also respond to envelopes of complex sounds, even for high-frequency carriers, scalp responses were compared to the envelopes of complex sounds; the resultant envelope cross-correlation functions (ECCFs) contained replicable response components primarily below 1000 Hz, regardless of the evoking stimulus spectrum. The ECFF thresholds for three octave-band stimuli (830–1562, 1611–3125, and 3174–6201 Hz) were more sensitive than CCF thresholds (p = 0.018), averaging 35-dB spectrum level for ten normal subjects. When stimuli with only odd harmonics were used, replicable odd-component responses were seen only in the spectral range of the stimuli, while even-component responses (presumably to stimulus envelope) were seen only in the low-passed scalp responses.

An evaluation of specific diversity combiners using signals received by vertically-spaced base-station antennas

A series of field trials has been conducted in which a 900 MHz CW signal was transmitted from a vehicle moving along a test route some 1·3 km from a base station. The recorded envelopes of the signals received on two vertically-separated antennas at the base station have been used in a computer simulation of two-branch predetection diversity reception. Several different systems have been simulated and the computed results show that the theoretical diversity advantages can still be obtained for an envelope cross-correlation (ρenv) of less than 0·7 for all strategies except switching. For a 1·3 km radius cell, a ρenv less than 0·7 can be obtained using antennas with a vertical separation of about 12λ. It has been found that the cumulative distribution and level-crossing rates of the signal are substantially improved and the average fade duration is approximately halved.