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Showing papers on "Impulse response published in 1996"


Journal ArticleDOI
TL;DR: In this paper, the authors present a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models and demonstrate the use of these measures for a nonlinear bivariate model of US output and the unemployment rate.

3,821 citations


Journal ArticleDOI
TL;DR: Various methods of determining the coefficients for this time-domain finite impulse response (FIR) filter are explored and an optimal shortening and a least-squares approach are developed for shortening the channel's impulse response.
Abstract: In discrete multitone (DMT) transceivers an intelligent guard time sequence, called a cyclic prefix (CP), is inserted between symbols to ensure that samples from one symbol do not interfere with the samples of another symbol. The length of the CP is determined by the length of the impulse response of the effective physical channel. Using a long CP reduces the throughput of the transceiver, To avoid using a long CP, a short time-domain finite impulse response (FIR) filter is used to shorten the effective channels impulse response. This paper explores various methods of determining the coefficients for this time-domain filter. An optimal shortening and a least-squares (LS) approach are developed for shortening the channel's impulse response. To provide a computationally efficient algorithm a variation of the LS approach is explored. In full-duplex transceivers the length of the effective echo path impacts the computational requirements of the transceiver. A new paradigm of joint shortening is introduced and three methods are developed to jointly shorten the channel and the echo impulse responses in order to reduce the length of the CP and reduce computational requirements for the echo canceller.

556 citations


Journal ArticleDOI
TL;DR: The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems, which leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution.
Abstract: This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.

520 citations


Journal ArticleDOI
Monisha Ghosh1
TL;DR: The paper shows the equivalence of the Bernoulli-Gaussian impulse noise model in the discrete time domain to the continuous-time model of Poisson arriving delta functions with random area distributed according to the power Rayleigh probability density function and develops a closed form expression for the probability of error for single carrier QAM.
Abstract: The paper first shows the equivalence of the Bernoulli-Gaussian impulse noise model in the discrete time domain to the continuous-time model of Poisson arriving delta functions with random area distributed according to the power Rayleigh probability density function. This equivalence is then used to develop a closed form expression for the probability of error for single carrier QAM that is easily evaluated. Furthermore, the performance of multicarrier modulation (MCM) is also analyzed using the same impulse noise model and it is shown that in most cases MCM performs better than single carrier systems, specifically when the probability of an impulse is not too high and the impulse power is moderate.

443 citations


Journal ArticleDOI
TL;DR: In this article, the authors characterized the response of cortical cells to moving ripples as a function of ripple velocity (temporal property) and ripple frequency (spectral property) describing the response to these temporal and spectral modulations.
Abstract: 1. Auditory stimuli referred to as moving ripples are used to characterize the responses of both single and multiple units in the ferret primary auditory cortex. Moving ripples are broadband complex sounds with a sinusoidal spectral profile that drift along the logarithmic frequency axis at a constant velocity. 2. Neuronal responses to moving ripples are locked to the phase of the ripple, i.e., they exhibit the same periodicity as that of the moving ripple profile. Neural responses are characterized as a function of ripple velocity (temporal property) and ripple frequency (spectral property). Transfer functions describing the response to these temporal and spectral modulations are constructed. Temporal transfer functions are inverse Fourier transformed to obtain impulse response functions that reflect the cell's temporal characteristics. Ripple transfer functions are inverse Fourier transformed to obtain the response field, a measure analogous to the cell's response area. These operations assume linearity in the cell's response to moving ripples. 3. Transfer functions and other response functions are shown to be fairly independent on the overall level or depth of modulation of the ripple stimuli. Only downward moving ripples were used in this study. 4. The temporal and ripple transfer functions are found to be separable, in that their shapes remain unchanged for different test parameters. Thus ripple transfer functions and response fields remain statistically similar in shape (to within an overall scale factor) regardless of the ripple velocity or whether stationary or moving ripples are used in the measurement. The same stability in shape holds for the temporal transfer functions and the impulse response functions measured with different ripple frequencies. Separability implies that the combined spectrotemporal transfer function of a cell can be written as the product of a purely ripple and a purely temporal transfer functions, and thus that the neuron can be computationally modeled as processing spectral and temporal information in two separate and successive stages. 5. The ripple parameters that characterize cortical cells are distributed somewhat evenly, with the characteristic ripple frequencies ranging from 0.2 to > 2 cycles/octave and the characteristic angular frequency typically ranging from 2 to 20 Hz. 6. Many responses exhibit periodicities in the spectral envelope of the stimulus. These periodicities are of two types. Slow rebounds, not found in the spectral envelope, and with a period of approximately 150 ms, appear with various strengths in approximately 30% of the cells. Fast regular firings with interspike intervals of approximately 10 ms are much less common and appear to correspond to interactions between the component tones that make up a ripple.

251 citations


Journal ArticleDOI
TL;DR: It is shown that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity, and a new characterization of the optimum delay is described and shown how to compute it.
Abstract: A unified approach for computing the optimum settings of a length-N/sub f/ input-aided equalizer that minimizes the mean-square error between the equalized channel impulse response and a target impulse response of a given length N/sub b/ is presented. This approach offers more insight into the problem, easily accommodates correlation in the input and noise sequences, leads to significant computational savings, and allows us to analyze a variety of constraints on the target impulse response besides the standard unit-tap constraint. In particular, we show that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity. Furthermore, we show that, under the assumed constraint of finite-length filters, the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance. We describe a new characterization of the optimum delay and show how to compute it. Finally, we derive reduced-parameter pole-zero models of the equalizer that achieve the high performance of a long all-zero equalizer at a much lower implementation cost.

245 citations


Journal ArticleDOI
TL;DR: An analytical model for evaluation of the bit-error rate (BER) of the stationary frequency selective indoor channel is developed for a coherent binary phase shift keying (BPSK) receiver, based on the complex impulse response of the channel.
Abstract: Results from propagation measurements, conducted in an indoor office environment at 2.4, 4.75, and 11.5 GHz, are presented. The data were obtained in small clusters of six measurements, using a coherent wideband measurement system. The channel characteristics for the three frequencies are compared by evaluating path loss, rms delay spread, and coherence bandwidth. An analytical model for evaluation of the bit-error rate (BER) of the stationary frequency selective indoor channel is developed for a coherent binary phase shift keying (BPSK) receiver, based on the complex impulse response of the channel. Computational BER results are obtained for data rates up to 50 Mb/s, using the measured multipath channel impulse responses. The BER results for a number of clusters are presented and compared for the maximum reliable data rate as inferred by the measured rms delay spread of the channel.

201 citations


Journal ArticleDOI
TL;DR: In this paper, the space-time profiles of ultrafast optical waveforms shaped by filtering of spatially separated frequency components are derived for single and double passes through a pulse shaping apparatus.
Abstract: A derivation of the space-time profiles of ultrafast optical waveforms shaped by filtering of spatially separated frequency components is presented. Closed form expressions for the space-time impulse response functions are given for the cases of single and double passes through a pulse shaping apparatus. For a single pass and a short unshaped pulse, diffraction by the mask filter gives rise to a translational spatial shift in the desired electric field profile that varies linearly with time along the shaped waveform. This result is completely general, and applies to frequency-domain pulse shaping with either continuous or discrete mask filters. It is also shown that double passing the apparatus does not generally reverse this effect but rather introduces further space-time coupling such as a time-varying spotsize. Examples of specific mask patterns are presented and implications for the generation of high-fidelity shaped optical waveforms are discussed.

129 citations


Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions for positive realizability of discrete-time systems are given for the continuous-time case, under a mild assumption on the long-term behavior of the impulse response.

126 citations


Proceedings ArticleDOI
23 Jun 1996
TL;DR: Using the ceiling-bounce functional model, a computationally efficient method is developed to predict the path loss and multipath power requirement of diffuse links based on the locations of the transmitter and receiver within a room.
Abstract: We show that realistic multipath infrared channels can be characterized well by only two parameters: optical path loss and r.m.s. delay spread. Functional models for the impulse response, based on infrared reflection properties, are proposed and analyzed. Using the ceiling-bounce functional model, we develop a computationally efficient method to predict the path loss and multipath power requirement of diffuse links based on the locations of the transmitter and receiver within a room. Use of our model is a simple, yet accurate, alternative to the use of an ensemble of measured channel responses in evaluating the impact of multipath distortion.

125 citations


Journal ArticleDOI
TL;DR: It is shown that the fact that the burst cycle period is in general not an integer multiple of the sampling grid distance does not complicate the algorithm, and an image example using X-SAR data for simulation of a burst system is presented.
Abstract: Processing ScanSAR or burst-mode SAR data by standard high precision algorithms (e.g., range/Doppler, wavenumber domain, or chirp scaling) is shown to be an interesting alternative to the normally used SPECAN (or deramp) algorithm. Long burst trains with zeroes inserted into the interburst intervals can be processed coherently. This kind of processing preserves the phase information of the data-an important aspect for ScanSAR interferometry. Due to the interference of the burst images the impulse response shows a periodic modulation that can be eliminated by a subsequent low-pass filtering of the detected image. This strategy allows an easy and safe adaptation of existing SAR processors to ScanSAR data if throughput is not an issue. The images are automatically consistent with regular SAR mode images both with respect to geometry and radiometry. The amount and diversity of the software for a multimode SAR processor are reduced. The impulse response and transfer functions of a burst-mode end-to-end system are derived. Special attention is drawn to the achievable image quality, the radiometric accuracy, and the effective number of looks. The scalloping effect known from burst-mode systems can be controlled by the spectral weighting of the processor transfer function. It is shown that the fact that the burst cycle period is in general not an integer multiple of the sampling grid distance does not complicate the algorithm. An image example using X-SAR data for simulation of a burst system is presented.

Proceedings ArticleDOI
01 Jun 1996
TL;DR: This work develops a provably stable two pole transfer function/impedance model based on the first three moments of the impulse response that will be an effective metric for high speed interconnect circuit models.
Abstract: Due to its simplicity, the ubiquitous Elmore delay, or first moment of the impulse response, has been an extremely popular delay metric for analyzing RC trees and meshes. Its inaccuracy has been noted however and it has been demonstrated that higher order moments can be mapped to dominant pole approximations (e.g. AWE) in the general case. The first three moments can be mapped to a two pole approximation, but stability is an issue and even a stable model results in a transcendental equation that must be iteratively evaluated to determine the delay. We describe an explicit delay approximation based on the first three moments of the impulse response. We begin with the development of a provably stable two pole transfer function/impedance model based on the first three moments (about s=0) of the impulse response. Then, since the model form is known, we evaluate the delay (any waveform percentage point) in terms of an analytical approximation that is consistently within a fraction of 1 percent of the "exact" solution for this model. The result is an accurate, explicit delay expression that will be an effective metric for high speed interconnect circuit models.

Journal ArticleDOI
TL;DR: In this paper, the authors use dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect, and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM and MMM.

Journal ArticleDOI
TL;DR: A technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented, and a method for obtaining a Zineurizution of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds.
Abstract: This paper presents a new approach to AutoRegressive Moving Average (ARMA or ARX) modeling which automatically seeks the best model order to represent investigated linear, time invariant systems using their inputloutput data. The algorithm seeks the ARMA parameterization which accounts for variability in the output of the system due to input activity and contains the fewest number of parameters required to do so. The unique characteristics of the proposed system identification algorithm are its simplicity and efficiency in handling systems with delays and multiple inputs. We present results of applying the algorithm to simulated data and experimental biological data. In addition, a technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented. The mapping from ARMA coefficients to impulse response estimates is nonlinear, which complicates any effort to construct confidence bounds for the obtained impulse responses. Here a method for obtaining a Zineurizution of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds.

Patent
Antoni Fertner1
09 Jul 1996
TL;DR: In this article, an echo transfer function is generated representing the echo channel impulse response, and aliased components present in the echo impulse response are specifically identified and compensated for in the frequency domain by treating each spectral filter coefficient of the echo transfer functions as the sum of a baseband component and an aliased component.
Abstract: In a digital communications system, a sampled signal is precisely reconstructed (rather than approximated) even in situations where the phase of the sampling signal is adjusted. More particularly, the sampled signal is compensated in the frequency domain for phase adjustments to the sampling instance in the time domain. In the context of echo cancellation, an echo transfer function is generated representing the echo channel impulse response. Aliased components present in the echo impulse response are specifically identified and compensated for in the frequency domain by treating each spectral filter coefficient of the echo transfer function as the sum of a baseband component and an aliased component. In addition to accurately compensating for sampling phase adjustments, this technique considerably relaxes traditional sampling constraints.

Journal ArticleDOI
TL;DR: The temporal characteristics for sensitivity to luminance and chromatic patterns during saccades are studied, using the two-pulse summation technique, to suggest that saccadic suppression is mediated by contrast gain control mechanisms, known to occur in M-cells but not P-cells.

Journal ArticleDOI
TL;DR: In this paper, an analytical theory for the optimal control algorithms for semi-active absorbers is developed for a single-degree-of-freedom structure, and is then generalized to continuous structures.

Journal ArticleDOI
Gary Koop1
TL;DR: In this paper, the effect of parameter uncertainty on impulse response analysis in nonlinear models is investigated and various impulse response functions are defined and applied in a threshold autoregressive model of real US GDP.

Journal ArticleDOI
TL;DR: A genetic algorithm is used to improve the accuracy of the fitting scheme based on the least squares method, and a method to reduce data storage for ultrawideband signatures in target discrimination is provided.
Abstract: Development of successful radar target discrimination schemes using ultrawideband signatures hinges on an accurate understanding of the scattering behavior of complex radar targets. Since it is very difficult to calculate the scattered field of complex targets theoretically, a mathematical model (Altes (1976) model) representing scattering center impulse response has been developed to describe the scattered field. The extraction of temporal positions, pulse responses, and transfer functions of target scattering centers is demonstrated using artificially created and measured responses. Two different scale aircraft models (B-58 and B-52) are utilized. The fitting scheme based on the least squares method is quite satisfactory but its accuracy deteriorates when the overlapping of scattering-center pulse responses is severe. To overcome this problem a genetic algorithm is used to improve the results. While the genetic algorithm gives much better accuracy, it consumes much more computer time due to its global nature and lack of derivative information. The purpose of this analysis is to provide a method to reduce data storage for ultrawideband signatures in target discrimination.

Journal ArticleDOI
TL;DR: In this article, a theoretical and experimental study for determination of the through-air system impulse response and insertion loss with different air-coupled ultrasonic transducers is presented, where wide-band piezopolymer transducers are employed in both transmission and reception modes and their behavior assessed by means of mathematical modeling and experiment.
Abstract: This paper describes a theoretical and experimental study for determination of the through-air system impulse response and insertion loss with different air-coupled ultrasonic transducers. Wide-band piezopolymer transducers (PVDF) are employed in both transmission and reception modes and their behavior assessed by means of mathematical modeling and experiment. Specifically, a linear systems approach, modified to include the influence of attenuation in the propagation medium, was used to design suitable PVDF transducers for wide-band operation in air. Suitable devices were then manufactured for determination of the transmission and reception response characteristics of piezocomposite and electrostatic transducers when operating in the air environment. A range of transducers was evaluated, including 1-3 connectivity composites of different ceramic volume fraction and mechanical matching conditions, in addition to electrostatic devices of varying design. To complement the investigation, relative performances for narrow-band operation are also presented under transmission and transmit-receive conditions. Despite the obvious measurement difficulties, good agreement between theory and experiment was observed and the methodology is shown to provide a convenient and robust procedure for comparison of through-air transducers operating in the frequency range 50 KHz to 2 MHz. Although highly resonant, the most effective composite transducers under consideration demonstrate an improvement in two-way insertion loss of 22.4 dB and 11.5 dB over a corresponding electrostatic pair, under narrow-band and wide-band operation, respectively.

Dissertation
01 Jan 1996
TL;DR: In this paper, the authors used the time domain technique of acoustic pulse reflectometry to measure the input impulse response of a tubular object, such as a wind instrument, from which both its bore profile and input impedance can be calculated.
Abstract: The bore profile and input impedance of a musical wind instrument provide valuable information about its acoustical properties. The time domain technique of acoustic pulse reflectometry can be used to measure the input impulse response of a tubular object, such as a wind instrument, from which both its bore profile and input impedance can be calculated. In this thesis, after a discussion of the theory of acoustic pulse reflectometry, the operation of a practical reflectometer is described and measurements of input impulse response, bore profile and input impedance are investigated. In general, the experimentally measured input impulse response of a tubular object contains a DC offset which must be removed for accurate bore reconstruction. A new, faster method of determining the DC offset is introduced which doesn’t require prior knowledge of the object’s dimensions. The bore profile of a test object, calculated by applying a lossy reconstruction algorithm to its input impulse response (after removal of the DC offset), is found to agree with directly measured radii to within 0.05mm. Various brass instrument reconstructions of similar accuracy are presented. An input impedance curve, calculated from the input impulse response of the test object, is found to have peak frequencies which agree with those of a theoretical curve to within 0.7% (a considerably better agreement than when a standard frequency domain measurement technique is used). Impedance curves of various brass instruments are presented. Bore reconstructions are used to confirm the presence, and in certain cases, the positions of leaks in instruments. For the special case of a leaking cylinder, the impedance curve is successfully used to calculate the size of the leak. Finally, a method is investigated which allows the practical reflectometer to measure longer objects than previously possible.

Journal ArticleDOI
TL;DR: A framework is proposed in which acceptable performance is expressed as constraints on the closed-loop transfer function impulse response coefficients using likelihood methods, and a hypothesis test is outlined to determine if control deterioration has occurred.

Journal ArticleDOI
TL;DR: In this article, the authors compared several algorithms for the direct identification of non-parsimonious models from several points of view: the closeness of the fit to the true model, the level of robust stability provided by the identified model, and the actual control performance obtained using the identified models.
Abstract: In model predictive control one often needs a finite impulse response (FIR) or step response model of the process. Several algorithms have been proposed for the direct identification of these nonparsimonious models (least-squares and biased algorithms such as regularized least squares and partial least squares). These algorithms are compared from several points of view: the closeness of the fit to the true model, the level of robust stability provided by the identified model, and the actual control performance obtained using the identified models. Although there are conveniences in directly identifying such nonparsimonious models (i.e., they can fit any complex dynamic system; there is no need for model structure selection), there are many disadvantages. In comparison with identifying parsimonious transfer function models by prediction error methods and then obtaining the impulse response from them, even the best direct FIR identification methods will generally provide much worse results or require much ...

Journal ArticleDOI
TL;DR: The measurements of the impulse response of a 2.0 GHz indoor radio channel and a statistical analysis of the characteristics of the amplitude of multipath components suggest the adequacy of the wide sense uncorrelated scattering model as a consistent model for the indoorRadio channel.
Abstract: The measurements of the impulse response of a 2.0 GHz indoor radio channel are reported. A statistical analysis of the characteristics of the amplitude of multipath components is presented. In particular, the spatial correlation of the single multipath components and the cross-correlation between the amplitudes of adjacent multipath components have been determined. Conclusions are drawn with regard to the adequacy of the wide sense uncorrelated scattering model as a consistent model for the indoor radio channel.

Journal ArticleDOI
TL;DR: The methods considered are based on Fourier transforms, system identification, constrained optimization, the use of cubic spline basis functions, maximum entropy, and a genetic algorithm, which extract an input function when the unit impulse response is known.
Abstract: We present results for the comparison of six deconvolution techniques. The methods we consider are based on Fourier transforms, system identification, constrained optimization, the use of cubic spline basis functions, maximum entropy, and a genetic algorithm. We compare the performance of these techniques by applying them to simulated noisy data, in order to extract an input function when the unit impulse response is known. The simulated data are generated by convolving the known impulse response with each of five different input functions, and then adding noise of constant coefficient of variation. Each algorithm was tested on 500 data sets, and we define error measures in order to compare the performance of the different methods.

Journal ArticleDOI
TL;DR: A blind deconvolution-based approach for the restoration of speech degraded by the acoustic environment reconstructs the room impulse response associated with each microphone and restores the speech signal.
Abstract: We present a blind deconvolution-based approach for the restoration of speech degraded by the acoustic environment. The proposed scheme processes the outputs of two microphones using cepstra operations and the theory of signal reconstruction from phase only. Under mild assumptions, it reconstructs the room impulse response associated with each microphone and restores the speech signal.

Journal ArticleDOI
04 Jun 1996
TL;DR: The proposed FIR differentiator is characterized by the optimal attenuation of white noise and an efficient suppression of upper-band frequencies and the basic structure needs only one multiplier, which becomes a power of two with an appropriate selection of the length of the impulse response.
Abstract: We introduce a computationally efficient recursive implementation of digital finite impulse response (FIR) filters for estimating the rate of change or slope of digitized signals. The proposed FIR differentiator is characterized by the optimal attenuation of white noise and an efficient suppression of upper-band frequencies. The basic structure needs only one multiplier, which becomes a power of two with an appropriate selection of the length of the impulse response. The structure does not need resetting and recovers from any bit errors. For long filters, sampling rate reduction by decimation gives further computational savings.

Patent
Minoru Namekata1
09 Aug 1996
TL;DR: In this article, an adaptive maximum likelihood sequence estimation apparatus includes a first estimation unit for estimating a transmission signal sequence from received signals on the basis of an estimated transmission path impulse response, and a second estimation unit estimates an estimated received signal at time k.
Abstract: An adaptive maximum likelihood sequence estimation apparatus includes a first estimation unit for estimating a transmission signal sequence from received signals on the basis of an estimated transmission path impulse response. A second estimation unit estimates an estimated received signal at time k on the basis of a known signal sequence or the transmission signal sequence estimated by the first estimation unit, and a transmission path impulse response estimated at time k-1. An error signal generation unit generates an error signal on the basis of a received signal at time k and the estimated received signal at time k. A third estimation unit estimates a transmission path impulse response at time k using a predetermined adaptive algorithm on the basis of the error signal. Furthermore, the third estimation unit estimates a transmission path impulse response by a non-recursive calculation during the reception period of a known signal sequence of the received signal, and estimates a transmission path impulse response by a recursive calculation during the reception period of an unknown data signal sequence of the received signals following the known signal sequence period.

Journal ArticleDOI
TL;DR: In this article, the pulsed field from a triangular aperture mounted in an infinite, rigid baffle is calculated using the approach of spatial impulse responses, as developed by Tupholme and Stepanishen.
Abstract: The pulsed field from a triangular aperture mounted in an infinite, rigid baffle is calculated. The approach of spatial impulse responses, as developed by Tupholme and Stepanishen, is used. By this both the emitted and received pulsed ultrasound field can be found for any transducer excitation and electromechanical impulse response. The continuous wave field is also readily obtainable through a simple Fourier transform. The spatial impulse response is calculated without approximation, and the solution is valid in the half‐space in front of the aperture for a homogeneous, nonattenuating medium. The solution can be used in finite element programs for calculating fields from arbitrary transducer geometries.

Journal ArticleDOI
TL;DR: It is shown necessary and sufficient conditions for strict identifiability are shown, and a connection is established among strictIdentifiability, a cross-relation-based (CR-based) identifiable and a Fisher information- based (FI- based) Identifiability is established.
Abstract: The problem of blind identification of multiple finite impulse response (FIR) channels driven by a common input arises in a wide range of applications It has received increasing attention in the signal processing community A system of multiple FIR channels driven by an unknown input is said to be strictly identifiable if, in the absence of noise, the given channel outputs can only be realized by a unique (up to a constant) system impulse response and a unique input sequence We show necessary and sufficient conditions for strict identifiability, and establish a connection among strict identifiability, a cross-relation-based (CR-based) identifiability and a Fisher information-based (FI-based) identifiability