Showing papers on "Fundamental frequency published in 1993"

Accurate short-term analysis of the fundamental frequency and the harmonics-to-noise ratio of a sampled sound

Abstract: We present a straightforward and robust algorithm for periodicity detection, working in the lag (autocorrelation) domain. When it is tested for periodic signals and for signals with additive noise or jitter, it proves to be several orders of magnitude more accurate than the methods commonly used for speech analysis. This makes our method capable of measuring harmonics-to-noise ratios in the lag domain with an accuracy and reliability much greater than that of any of the usual frequency-domain methods. By definition, the best candidate for the acoustic pitch period of a sound can be found from the position of the maximum of the autocorrelation function of the sound, while the degree of periodicity (the harmonics-to-noise ratio) of the sound can be found from the relative height of this maximum. However, sampling and windowing cause problems in accurately determining the position and height of the maximum. These problems have led to inaccurate timedomain and cepstral methods for pitch detection, and to the exclusive use of frequency-domain methods for the determination of the harmonics-to-noise ratio. In this paper, I will tackle these problems. Table 1 shows the specifications of the resulting algorithm for two spectrally maximally different kinds of periodic sounds: a sine wave and a periodic pulse train; other periodic sounds give results between these. Table 1. The accuracy of the algorithm for a sampled sine wave and for a correctly sampled periodic pulse train, as a function of the number of periods that fit in the duration of a Hanning window. These results are valid for pitch frequencies up to 80% of the Nyquist frequency. These results were measured for a sampling frequency of 10 kHz and window lengths of 40 ms (for pitch) and 80 ms (for HNR), but generalize to other sampling frequencies and window lengths (see section 5).

Frequency selective harmonic coding

Abstract: The present invention relates to a method of encoding speech comprised of processing the speech by harmonic coding to provide, a fundamental frequency signal, and a set of optimal harmonic amplitudes, processing the harmonic amplitudes, and the fundamental frequency signal to select a reduced number of bands, and to provide for the reduced number of bands a voiced and unvoiced decision signal, an optimal subset of magnitudes and a signal indicating the positions of the reduced number of bands, whereby the speech signal may be encoded and transmitted as the pitch signal and the signals provided for the reduced number of bands with a bandwidth that is a fraction of the bandwidth of the speech.

Separation of concurrent harmonic sounds: Fundamental frequency estimation and a time‐domain cancellation model of auditory processing

Abstract: Signal‐processing methods and auditory models for separation of concurrent harmonic sounds are reviewed, and a processing principle is proposed that cancels harmonic interference in the time domain. The principle is first formulated in signal processing terms as a time‐domain comb filter. The critical issue of fundamental frequency estimation is investigated and an algorithm is proposed. Tested on a restricted database of natural voiced speech, the algorithm successfully found estimates correct within 3% of an octave for 90% of all frames. Next, the principle is formulated in physiological terms. A hypothetical ‘‘neural comb filter’’ is described, based on neural delay lines and inhibitory synapses, and tested using auditory‐nerve fiber discharge data obtained in response to concurrent vowels [A. R. Palmer, J. Acoust. Soc. Am. 88, 1412–1426 (1990)]. Processing successfully suppresses the correlates of either vowel in the response of fibers that respond to both, allowing the other vowel to be better represented. The filter belongs to the class of ‘‘cancellation models’’ for which predictions can be made concerning the outcome of certain psychoacoustic experiments. These predictions are discussed in relation to recent experimental results obtained elsewhere.

Comparison of Fo Extraction Methods for High-Precision Voice Perturbation Measurements

Abstract: Voice perturbation measures, such as jitter and shimmer, depend on accurate extraction of fundamental frequency (Fo) and amplitude of various waveform types. The extraction method directly affects ...

Acoustic model and evaluation of pathological voice production.

Abstract: An acoustic model of pathological voice production is presented. It describes the non-linear effects occurring in the acoustic waveform of disordered voices. The noise components such as fundamental frequency and amplitude irregularities and variations, sub-harmonic components, turbulent noise and voice breaks are formally expressed as a result of random time function influences on the excitation function and the glottal filter. A method for quantitative evaluation of these random functions is described. The method computes their statistical characteristics which can be useful in assessing voice in clinical practice. More than 33 acoustic parameters are computed: average fundamental frequency, phonatory frequency range, several frequency and amplitude shortand long-term perturbation and variation measures, noise-to-harmonic ratio, voice turbulence and soft phonation indexes, quantitative measures of voice breaks, sub-harmonic components and vocal tremors. This set of parameters, which corresponds to the model, allows a multi-dimensional voice quality assessment. A computer system based on above model and method was developed for the CSL model 4300 (Kay Elemetrics Corp.). A group of 68 people with normal and disordered voices was analyzed using the system in order to define normative values for the acoustic voice parameters.

A high resolution fundamental frequency determination based on phase changes of the Fourier transform

Abstract: The constant Q transform described recently [J. C. Brown and M. S. Puckette, ‘‘An efficient algorithm for the calculation of a constant Q transform,’’ J. Acoust. Soc. Am. 92, 2698–2701 (1992)] has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages. For this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant Q for lower frequency bins. This modified calculation serves as the input for a fundamental frequency tracker similar to that described by Brown [J. C. Brown, ‘‘Musical fundamental frequency tracking using a pattern recognition method,’’ J. Acoust. Soc. Am. 92, 1394–1402 (1992)]. Once the fast Fourier transform (FFT) bin corresponding to the fundamental frequency is chosen by the frequency tracker, an approximation is used for the phase change in the FFT for a time advance of one sample to obtain an extremely precise value for this frequency. Graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous.

High impedance fault detector

Abstract: A method and apparatus for detecting high impedance faults and other arcing phenomena in an electrical distribution system. Electrical signals on the distribution system are monitored and a number of frequency components isolated, such as zero-sequence current and voltage, second harmonic voltage, third harmonic current, eighth harmonic voltage and current, and a measure of magnitude of the components are taken over successive data acquisition periods. The measures of the component magnitudes are formed into a pattern for each data acquisition period, and the difference between patterns for successive periods are compared against a pattern threshold which is set to suit the characteristics of the distribution system. A pattern difference greater than the pattern threshold indicates the possibility of an arcing fault, which can then be confirmed by determining whether the frequency components are modulated at twice the fundamental frequency of the distribution system.

Frequency Analysis and Pitch Perception

Abstract: This chapter is concerned with two main areas: frequency analysis and pitch perception. Frequency analysis refers to the action of the ear in resolving (to a limited extent) the sinusoidal components in a complex sound; this ability is also known as frequency selectivity and frequency resolution. It plays a role in many aspects of auditory perception but is most often demonstrated and measured by studying masking. Studies of pitch perception are mainly concerned with the relationships between the physical properties of sounds and the perceived pitches of those sounds and with the underlying mechanisms that explain these relationships. One important aspect of pitch perception is frequency discrimination, which refers to the ability to detect changes in frequency over time and which is (at least partly) a separate ability from frequency selectivity.

Fundamental frequency estimation and tracking using maximum likelihood harmonic matching and HMMs

Abstract: A new approach is presented for the estimation and tracking of the fundamental frequency (f0) of pseudoperiodic signals. It is based on a probabilistic model of pseudoperiodic signals that makes it possible to take prior knowledge into account and to include constraints on the evolution of the signal. The resulting method can operate on a large interval of f0 values (typically from 50 to 4000 Hz) and on a great variety of sound signals (speech and music signals). >

Harmonic power flow for unbalanced systems

Abstract: A harmonic power flow method that analyzes harmonics in unbalanced power systems is presented. The developed algorithm has two steps which are executed successively: the first is a fundamental frequency power flow for the AC linear network in which nonlinear loads are represented by current sources; the second is a frequency domain iterative Newton-Raphson method to calculate the harmonics generated by nonlinear loads. In this second step, the AC linear network is represented by a generalized Thevenin equivalent with respect to the nonlinear loads, obtained from the power flow solution. Both linear and nonlinear loads are considered in terms of power. >

Active control of fan noise from a turbofan engine

Abstract: A three-channel active control system is applied to an operational turbofan engine to reduce tonal noise produced by both the fan and the high-pressure compressor. The control approach is the feedforward filtered-x least-mean-square algorithm implemented on a digital signal processing board. Reference transducers mounted on the engine case provide blade passing and harmonics frequency information to the controller. Error information is provided by large area microphones placed in the acoustic far field. To minimize the error signal, the controller actuates loudspeakers mounted on the inlet to produce destructive interference. The sound pressure level of the fundamental tone of the fan was reduced using the three-channel controller by up to 16 dB over a +/- 30-deg angle about the engine axis. A single-channel controller could produce reduction over a +/- 15-deg angle. The experimental results show the control to be robust. Outside of the areas contolled, the levels of the tone actually increased due to the generation of radial modes by the control sources. Simultaneous control of two tones is achieved with parallel controllers. The fundamental and the first harmonic tones of the fan were controlled simultaneously with reductions of 12 and 5 dBA, respectively, measured on the engine axis. Simultaneous control was also demonstrated for the fan fundamental and the high-pressure compressor fundamental tones.

Circuit analyzing system

Abstract: A circuit analyzing system includes a current transformer for extracting current from a phase or neutral conductor of a three phase line, a filter connected to the output of the current transformer and functioning to substantially trap current at the fundamental frequency while substantially passing currents at various harmonic frequencies thereof, and signal processing circuitry connected to the output of the filter to perform various functions with the harmonic frequency current input thereto. Among these functions, as shown in various preferred embodiments, are measurement of the harmonic signal in RMS and conveyance of the output to a display instrument for a user or utility's convenience in monitoring harmonic frequency circuits, which have become more common with the advent of electronic equipment having internal power supplies such as personal computers, work stations, printers, and the like. Other functions include a user or utility's connecting a demand circuit mechanism to the measured currents (preferably RMS/harmonic frequency currents), and/or using comparator circuitry to sense the measured harmonic frequency currents and, if they exceed a desired level set by the user or utility, to output a signal to a tripping device such as a power contactor or relay which will in turn institute load shedding.

Semiconductor laser that generates second harmonic light with attached nonlinear crystal

Abstract: A semiconductor laser with a nonlinear crystal that generates second harmonic light at a frequency which is twice the fundamental frequency of the laser. The laser is configured in a vertical-cavity, surface-emitting structure or an edge-emitting structure. A nonlinear crystal is attached to a semiconductor optical amplifier by fusing with wafer bonding techniques or by epitaxially growing the nonlinear crystal on the amplifier. The amplifier and the nonlinear crystal are located inside a laser cavity that is defined between a pair of reflectors. One of the reflectors is located adjacent the nonlinear crystal and is highly reflective at the fundamental frequency but transmissive at twice the fundamental frequency. Light is generated at the fundamental frequency, doubled in frequency as it passes back and forth through the nonlinear crystal, and emitted through the reflector adjacent the nonlinear crystal. An optional region between the amplifier and the nonlinear crystal prevents reflections at the fundamental frequency or prevents light at twice the fundamental frequency from propagating from the nonlinear crystal into the amplifier.

A magnetic device current injection in a three-phase sinusoidal-current utility interface

Abstract: A magnetic device for current injection in a three-phase, sinusoidal-current utility interface is presented. This class of sinusoidal rectification depends on the injection of a third-harmonic current into the AC side of a three-phase rectifier. The injection network should provide a low and equal impedance in each of the three branches to the modulation current at the third harmonic frequency, and a high impedance to the fundamental frequency voltages. Experimental results from an injection device for a 12.5 kW sinusoidal rectification scheme are presented to support the simulation results obtained by a finite element program. >

Frequency and timing stability of mode-locked semiconductor lasers-passive and active mode locking up to millimeter wave frequencies

Abstract: A theoretical understanding of the fundamental frequency and timing jitter of active and passive mode-locked semiconductor lasers is developed. These results are compared with experimental observations for a wide range of mode-locking frequencies, and are found to predict the correct trends as well as having good quantitative agreement. The theory is based only on excitation of mode-locked supermodes by spontaneous emission, and these results can therefore be regarded as fundamental. The nature of these fluctuations is such that, for active mode locking, an external reference signal locks the absolute frequency of the mode-locked output, while spontaneous emission causes the phase of the mode-locked signal to fluctuate within finite bounds, which results in a timing jitter of the mode-locked pulses. >

Periodicity extraction in the anuran auditory nerve. II: Phase and temporal fine structure

Abstract: Discharge patterns of single eighth nerve fibers in the bullfrog, Rana catesbeiana, were analyzed in response to signals consisting of multiple harmonics of a common, low‐amplitude fundamental frequency. The signals were chosen to reflect the frequency and amplitude spectrum of the bullfrog’s species‐specific advertisement call. The phase spectrum of the signals was manipulated to produce envelopes that varied in their shapes from impulselike (sharp) to noiselike (flattened). Peripheral responses to these signals were analyzed by computing the autocorrelation functions of the spike trains and their power spectra, as well as by constructing period histograms over the time intervals of the low‐frequency harmonics. In response to a phase aligned signal with an impulsive envelope, most fibers, regardless of their characteristic frequencies or place of origin within the inner ear, synchronize to the fundamental frequency of the signal. The temporal patterns of fiber discharge to these stimuli are not typically...

Periodicity extraction in the anuran auditory nerve. I. "Pitch-shift" effects.

Abstract: 1. Activity of individual eight nerve fibers in the bullfrog, Rana catesbeiana, was measured in response to complex, multiple-frequency stimuli differing in both frequency composition and harmonic structure. Stimuli were chosen to parallel types of stimuli producing "pitch-shift" effects in humans. 2. The fundamental frequency of harmonic stimuli can be extracted from the autocorrelation of fiber firing, whether the fundamental is physically present in the stimulus or is a "missing" fundamental. The spectral fine-structure of harmonic stimuli is not robustly represented in fiber temporal response. These effects are seen in both AP and BP fibers. 3. The pseudoperiod of inharmonic stimuli is represented by synchronization to successive high-amplitude peaks in the stimulus envelope. Temporal responses to stimuli with high center frequencies are similar regardless of whether their frequency components are harmonically or inharmonically related. Responses remain dominated by the envelope periodicity, and no "pitch-shift" is signaled. In response to stimuli with low center frequencies, temporal responses signal a "pitch-shift" between harmonic and inharmonic complexes. Both AP and BP fibers show these effects. 4. These data suggest that bullfrog peripheral fibers extract the periodicity of complex stimuli by time-domain rather than frequency-domain coding.

Measurement of the acoustic nonlinearity parameter in liquid media using focused ultrasound

Abstract: The principle and the experimental results for a finite amplitude method to measure the acoustic nonlinearity parameter B/A of liquid media using focused ultrasound are presented. The present method takes both absorption and diffraction into account. A liquidlike sample is inserted in the focal region of the acoustic field formed by a spherically focusing Gaussian source. The response of the amplitudes and phases of the fundamental and second harmonic components of the transmitted wave is observed at the post focal region to obtain the experimental value of a quantity named RF, which incorporates the nonlinearity parameter of the sample. The measurement of linear acoustic properties is also carried out using the same focusing source. The value of B/A is determined through comparison between experimental and theoretical values of RF. The experimental results for 4.5‐ml volume samples at the fundamental frequency of 1.9 MHz validate the present method. This suggests the possiblity of obtaining the B/A imagi...

Squid control apparatus with non-cryogenic flux-locked loop disposed in close proximity to the squid

Abstract: SQUID control apparatus for controlling multiple SQUID probes includes a plurality of head units each corresponding to a respective SQUID probe, each of the head units including a non-cryogenic modulated flux-locked loop feedback circuit operating at a respective modulation frequency. The apparatus also includes a base unit coupled to all of the head units, the base unit providing control signals to control the multiple head units. Means are also provided, such as through the use of a daisy chain topology, for synchronizing the modulation frequency of all of the modulated flux-locked loop feedback circuits. The head units may also contain a phase shifter coupled to phase shift the modulation frequency oscillator signal for provision to the local oscillator input of a demodulator, and the phase shifter may include a shifting filter for filtering the oscillator signal to reduce all frequency components except a fundamental frequency component, and for phase shifting the fundamental frequency component by a desired amount, and shaping means for shaping the filtered and shifted signal into a square wave.

Nonlinear transverse effects in second-harmonic generation

Abstract: We study a three-dimensional model of interaction of fundamental-frequency and second-harmonic beams in a quadratically nonlinear medium. Numerical simulations of the three-dimensional propagation problem in the presence of diffraction and anisotropy are performed under the paraxial approximation. The role of the transverse effects in various regimes is investigated. We demonstrate the effect of phase modulation and an induced nonlinear focusing during the interaction of the fundamental frequency with the generated second harmonic.

Instrument to locate buried conductors by providing an indication of phase reversal of the signal utilizing the odd harmonic and the even harmonic when a vertical axis coil passes over one of the buried conductors

Abstract: An apparatus is disclosed to locate buried conductors, specifically a substation grounding grid. The apparatus provides accurate and precise location of a conductor as it is passed across the ground surface. A power unit is provided that includes a signal generator to produce a periodic test current, asymmetric in time, that has at least one odd harmonic and one even harmonic of a fundamental frequency. The periodic test current is passed through the buried conductors. A portable search unit has a substantially vertical axis coil attuned to pick up a signal including the odd harmonic and the even harmonic of the fundamental frequency from the periodic test current, a power source is provided and a signal interpretation processor and indicator provides an indication of phase reversal of the signal utilizing the odd harmonic and the even harmonic when the vertical axis coil passes over at least one of the buried conductors.

Optimization of Boundary Conditions for Maximum Fundamental Frequency of Vibrating Structures

Abstract: A sensitivity formula of eigenvalues with respect to the change of boundary conditions is derived using the material derivative concept based on a variational formulation The change of boundary conditions is described with the introduction of the tangential component of the design velocity field used in shape design Simply supported and partially welded plates are taken as numerical examples to check the accuracy of the sensitivity formula The sensitivites of the distinct and multiple eigenvalues calculated by the formulas are compared with those calculated by finite differences Optimal support locations are then determined by use of a gradient-based optimization method It is shown that a crossing of eigenvalues can occur in the solution process

High power laser employing fiber optic delivery means

Abstract: In a frequency-shifted, low gain pulsed tunable laser (1), spatial and temporal build-up of regions of high intensity in the fundamental frequency is minimized by generating a frequency-narrowed fundamental wavelength, preferentially frequency shifting high energy portions of the fundamental wavelength, and separating the frequency-shifted portion. The remaining fundamental frequency can safely be coupled into a fiber optic delivery means (7).

On the intonation of sinusoidal sentences: Contour and pitch height

Abstract: A sinusoidal replica of a sentence evokes a clear impression of intonation despite the absence of the primary acoustic correlate of intonation, the fundamental frequency. Our previous studies employed a test of differential similarity to determine that the tone analog of the first formant is a probable acoustic correlate of sinusoidal sentence intonation. Though the typical acoustic and perceptual effects of the fundamental frequency and the first formant differ greatly, our finding was anticipated by reports that harmonics of the fundamental within the dominance region provide the basis for impressions of pitch more generally. The frequency extent of the dominance region roughly matches the range of variability typical of the first formant. Here, we report two additional tests with sinusoidal replicas to identify the relevant physical attributes of the first formant analog that figure in the perception of intonation. These experiments determined (1) that listeners represent sinusoidal intonation as a pattern of relative pitch changes correlated with the frequency of the tonal replica of the first formant, and (2) that sinusoidal sentence intonation is probably a close match to the pitch height of the first formant tone. These findings show that some aspects of auditory pitch perception apply to the perception of intonation; and, that impressions of pitch of a multicomponent nonharmonic signal can be derived from the component within the dominance region.

Digital phosphorimeter with frequency domain signal processing: Application to real‐time fiber‐optic oxygen sensing

Abstract: An instrument to measure the excited‐state lifetimes of phosphorescent materials in real time is described. This apparatus uses pulsed and frequency‐doubled Nd:YAG solid‐state laser for excitation, sampler for data acquisition, and frequency domain methods for data fitting. The instrument amplifies the ac components of the detector output and band limits the signal to 25 kHz. The fundamental frequency of the excitation is then set to obtain a desired number of harmonics. This band limited signal is sampled and averaged over few thousand cycles in the time domain. The frequency domain representation of the data is obtained by employing fast Fourier transform algorithms. The phase delay and the modulation ratio of each sampled harmonic is then computed. Ten to a hundred values of the phase and modulations are averaged before computing the sensor lifetime. The instrument is capable of measuring precise and accurate excited‐state lifetimes from subpicowatt luminescent signals in 100 μm optical fibers. To monitor oxygen for biomedical applications the response time of the system is decreased by collecting only 8 or 16 harmonics. A least‐squares fit yields the lifetimes of single exponentials. A component of zero lifetime is introduced to account for the backscatter excitation. The phosphorescence lifetimes measured reproducibly to three parts in a thousand are used to monitor oxygen. Oxygen concentrations are computed employing empirical polynomials. The system drift is less than 1% over 100 h of continuous operation. This instrument is used to measure oxygen concentrations in vitro and in vivo with 2 s update times and 90 s full response times. Examples of measurements in saline solutions and in dogs are presented.

Nonlinear theory of stable, efficient operation of a gyrotron at cyclotron harmonics

Abstract: One of the main obstacles in achieving stable, efficient operation at the cyclotron harmonics in a gyrotron is mode competition with parasitic modes at the fundamental frequency. In this article, the nonlinear dynamics of mode interactions in such a system are studied using a multifrequency, time‐dependent model. The results of numerical simulations for a second harmonic gyrotron are presented by considering two starting scenarios: (a) fast voltage rise or an instant turn‐on case, and (b) slow voltage rise case. For the first case, it is demonstrated that for a certain range of operating parameters, the presence of a parasitic mode at the fundamental can be helpful in the excitation of the second harmonic operating mode. In the second case, it is found that the unstable operating region increases with the value of the rise time constant of the electrode voltages. Stable, efficient gyrotron operation at the second harmonic is demonstrated using the numerical study.

Signal processing system for performing real-time pitch shifting and method therefor

Abstract: A signal processing system (50) performs real-time pitch shifting for applications such as karaoke, tapeless answering machines, and the like while minimizing distortion. A digital input signal is sampled and stored at successive locations in a variable-size buffer (62) at an input sample rate. Data from the variable-size buffer (62) is interpolated according to a pitch-shifting ratio. An adaptive pitch estimator (61) continually estimates the fundamental frequency of the digital input signal, and the signal processing system (50) adjusts the buffer size of the variable-size buffer (62) in response thereto. The signal processing system (50) changes the buffer size to store the digital input signal for an integral number of periods of the estimated fundamental frequency.

Ultrasonic irradiation apparatus and processor using the same.

Abstract: This invention is directed to accomplish an ultrasonic remedial apparatus for generating a living body action such as cavitation suitable for remedy of a malignant tumor, a thrombus and a calculus, an ultrasonic wave diagnostic apparatus for generating cavitation to enhance an ultrasonic echo image of a blood stream, etc., and utilizing its reflection capacity, an ultrasonic chemical reaction promotion apparatus, an ultrasonic washing apparatus, an ultrasonic sterilizer, etc., by providing an ultrasonic irradiation apparatus for efficiently generating acoustic cavitation. Irradiation focus code signals for defining focal positions and sound pressure distribution shapes of irradiation sound fields of a fundamental frequency waves and harmonics are applied from a main control circuit to driving phase generation circuits, respectively. The driving phases thus generated are applied to driving signal generation circuits and the resulting driving signals are applied to device driving circuits, respectively, so that a group of the fundamental frequency devices and a group of harmonic devices are driven, respectively. The driving phases are controlled so that the fundamental frequency wave and the harmonic waves are superposed with one another in a medium near the focus, and acoustic cavitation is generated locally and efficiently.

Pitch versus Brightness of Timbre: Detecting Combined Shifts in Fundamental and Formant Frequency

Abstract: The pitch of a periodic tone depends on its fundamental frequency (F0), and the brightness of its timbre depends on the centroid of its power spectrum (Fc). The goal of the present study was to determine whether small shifts in F0 and in Fc are detected independently of each other. The standard tone used had an F0 of 400 Hz, five harmonics (400-2000 Hz), and a triangular spectral envelope peaking at an Fc of 1000 Hz. With a forced-choice adaptive procedure, detection thresholds were measured for (1) shifts in F0 alone (Fc being fixed), (2) shifts in Fc alone (F0 being fixed), and (3) combined shifts in F0 and Fc. The two components of the combined shifts were chosen to have the same level of detectability when presented alone. Overall, as expected from the independence model, the combined shifts were not better detected when their two components had the same direction (F0 and Fc both increase, or both decrease) than when they had opposite directions. However, substantial differences between subjects were observed with respect to the perceptual integration of shifts in F0 and in Fc.