JM
Jorge Abraham Martinez Castaneda
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16 records found
1
Testing The Efficient Coding Hypothesis Beyond Humans
The Auditory Kernels of Bat Vocalizations
The efficient coding hypothesis posits that biological sensory systems maximize information transfer to the brain while minimizing neural resources. Although extensively studied in humans, its role in non-human auditory perception remains relatively unexplored. Here, we apply sparse coding to bat echolocation calls to test whether their vocalizations are intrinsically optimized for efficient representation. Unlike prior bat studies using black-box models, our approach examines how acoustic selectivity can emerge in early auditory structures from call structure alone, independent of higher-level neural processing. The learned kernel representations are compact, sparse, and functionally specialized, with distinct activation profiles encoding specific call shapes. These findings suggest that bat auditory systems are tuned to conspecific vocalizations and underscore the advantages of sparse coding over traditional signal representations. They also improve the interpretability of animal auditory processing and provide a computational basis for modeling animal signals, supporting future research in interspecies communication and decoding animal vocalizations.
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The efficient coding hypothesis posits that biological sensory systems maximize information transfer to the brain while minimizing neural resources. Although extensively studied in humans, its role in non-human auditory perception remains relatively unexplored. Here, we apply sparse coding to bat echolocation calls to test whether their vocalizations are intrinsically optimized for efficient representation. Unlike prior bat studies using black-box models, our approach examines how acoustic selectivity can emerge in early auditory structures from call structure alone, independent of higher-level neural processing. The learned kernel representations are compact, sparse, and functionally specialized, with distinct activation profiles encoding specific call shapes. These findings suggest that bat auditory systems are tuned to conspecific vocalizations and underscore the advantages of sparse coding over traditional signal representations. They also improve the interpretability of animal auditory processing and provide a computational basis for modeling animal signals, supporting future research in interspecies communication and decoding animal vocalizations.
In this paper we propose a robust loudspeaker beamforming algorithm which is used to enhance the performance of voice driven applications in scenarios where the loudspeakers introduce the majority of the noise, e.g. when music is playing loudly. The loudspeaker beamformer modifies the loudspeaker playback signals to create a low-acoustic-energy region around the device that implements automatic speech recognition for a voice driven application (VDA). The algorithm utilises a distortion measure based on human auditory perception to limit the distortion perceived by human listeners. Simulations and real-world experiments show that the proposed loudspeaker beamformer improves the speech recognition performance in all tested scenarios. Moreover, the algorithm allows to further reduce the acoustic energy around the VDA device at the expense of reduced objective audio quality at the listener’s location
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In this paper we propose a robust loudspeaker beamforming algorithm which is used to enhance the performance of voice driven applications in scenarios where the loudspeakers introduce the majority of the noise, e.g. when music is playing loudly. The loudspeaker beamformer modifies the loudspeaker playback signals to create a low-acoustic-energy region around the device that implements automatic speech recognition for a voice driven application (VDA). The algorithm utilises a distortion measure based on human auditory perception to limit the distortion perceived by human listeners. Simulations and real-world experiments show that the proposed loudspeaker beamformer improves the speech recognition performance in all tested scenarios. Moreover, the algorithm allows to further reduce the acoustic energy around the VDA device at the expense of reduced objective audio quality at the listener’s location
Change to Care
Transforming Our Education and Focus on Students’ Identity Development
Book chapter
(2025)
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S.M. Flipse, I. Akay, Jorge Martinez, A.E. Roseboom, M.G.C. Bosch-Rekveldt, P.W. Chan, W. Chu, T. Geydan, E. Kalmar, J. van Keulen, H. Khodaei, M. Leijten
At TU Delft, we are not just educating engineers; we are shaping the future of engineering and engineering education. We are empowering our students to become the kind of leaders who can navigate complexity, embrace change, and build a better world, also under VUCA conditions. In this manifesto, we develop a line of reasoning to rethink our education, moving away from ‘professional problem solvers’ to ‘individuals who care for our collective future from an engineering background.’
We believe that TU Delft has a unique opportunity to lead the way in reimagining engineering education for the VUCA world. By embracing the principles outlined in this manifesto, we can empower our students to become the future-proof engineers that our society needs. We invite all members of the TU Delft community – faculty, students, and staff – to join us on this exciting journey. ...
We believe that TU Delft has a unique opportunity to lead the way in reimagining engineering education for the VUCA world. By embracing the principles outlined in this manifesto, we can empower our students to become the future-proof engineers that our society needs. We invite all members of the TU Delft community – faculty, students, and staff – to join us on this exciting journey. ...
At TU Delft, we are not just educating engineers; we are shaping the future of engineering and engineering education. We are empowering our students to become the kind of leaders who can navigate complexity, embrace change, and build a better world, also under VUCA conditions. In this manifesto, we develop a line of reasoning to rethink our education, moving away from ‘professional problem solvers’ to ‘individuals who care for our collective future from an engineering background.’
We believe that TU Delft has a unique opportunity to lead the way in reimagining engineering education for the VUCA world. By embracing the principles outlined in this manifesto, we can empower our students to become the future-proof engineers that our society needs. We invite all members of the TU Delft community – faculty, students, and staff – to join us on this exciting journey.
We believe that TU Delft has a unique opportunity to lead the way in reimagining engineering education for the VUCA world. By embracing the principles outlined in this manifesto, we can empower our students to become the future-proof engineers that our society needs. We invite all members of the TU Delft community – faculty, students, and staff – to join us on this exciting journey.
Most microphones detect sound-pressure-induced motion of a membrane. In contrast, we introduce a microphone that operates by monitoring sound-pressure-induced modulation of the air compressibility. By driving a graphene membrane at resonance, the gas, that is trapped in a squeeze-film beneath it, is compressed at high frequency. Since the gas-film stiffness depends on the air pressure, the resonance frequency of the graphene is modulated by variations in sound pressure. We demonstrate that this squeeze-film microphone principle can be used to detect sound and music by tracking the membrane’s resonance frequency using a phase-locked loop. The squeeze-film microphone potentially offers advantages like increased dynamic range, lower susceptibility to pressure- induced failure and vibration-induced noise over conventional devices. Moreover, microphones might become much smaller, as demonstrated in this work with one that operates using a circular graphene membrane with an area that is more than 1000 times smaller than that of MEMS microphones.
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Most microphones detect sound-pressure-induced motion of a membrane. In contrast, we introduce a microphone that operates by monitoring sound-pressure-induced modulation of the air compressibility. By driving a graphene membrane at resonance, the gas, that is trapped in a squeeze-film beneath it, is compressed at high frequency. Since the gas-film stiffness depends on the air pressure, the resonance frequency of the graphene is modulated by variations in sound pressure. We demonstrate that this squeeze-film microphone principle can be used to detect sound and music by tracking the membrane’s resonance frequency using a phase-locked loop. The squeeze-film microphone potentially offers advantages like increased dynamic range, lower susceptibility to pressure- induced failure and vibration-induced noise over conventional devices. Moreover, microphones might become much smaller, as demonstrated in this work with one that operates using a circular graphene membrane with an area that is more than 1000 times smaller than that of MEMS microphones.
Journal article
(2024)
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Niels De Koeijer, Martin Bo Moller, Jorge Martinez, Pablo Martinez-Nuevo, Richard C. Hendriks
Sound zone algorithms control the inputs to a loudspeaker array such that spatially distinct zones, each with separate audio content, are created. This work proposes a sound zone approach which includes a model of human auditory perception in the optimization problem designing the loudspeaker control filters. The control filters are therefore optimized directly for human experience, rather than by proxy through sound pressure, as is done in typical approaches. The proposed optimization problem features a perceptually weighted constraint on the bright zone reproduction error, which allows the user of the algorithm to specify the desired bright zone quality. The proposed method achieves 2 to 4 dB of additional acoustic contrast and is expected to yield less distracting dark-zone interference for the same perceived quality when compared to a traditional approach.
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Sound zone algorithms control the inputs to a loudspeaker array such that spatially distinct zones, each with separate audio content, are created. This work proposes a sound zone approach which includes a model of human auditory perception in the optimization problem designing the loudspeaker control filters. The control filters are therefore optimized directly for human experience, rather than by proxy through sound pressure, as is done in typical approaches. The proposed optimization problem features a perceptually weighted constraint on the bright zone reproduction error, which allows the user of the algorithm to specify the desired bright zone quality. The proposed method achieves 2 to 4 dB of additional acoustic contrast and is expected to yield less distracting dark-zone interference for the same perceived quality when compared to a traditional approach.
Sound zones are used to reproduce individual audio content to multiple people in a room using a set of loudspeakers with controllable input signals. To allow the reproduction of individual audio to dynamically change, e.g., due to moving listeners, changes in the number of listeners, or changing room transfer functions, an adaptive formulation is proposed. This formulation is based on frequency domain block adaptive filters and given room transfer functions. To reduce computational complexity, the system is extended to subband processing without cross-adaptive filters. The computational savings come from recognizing that sound zones consist of part-solutions which are inherently band limited, hence, several subbands can be ignored. To validate the theoretical findings, a 27-channel loudspeaker array was constructed, and measurements were performed in anechoic and reflective environments. The results show that the subband solution performs identically to a full-rate solution but at a reduced computational complexity.
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Sound zones are used to reproduce individual audio content to multiple people in a room using a set of loudspeakers with controllable input signals. To allow the reproduction of individual audio to dynamically change, e.g., due to moving listeners, changes in the number of listeners, or changing room transfer functions, an adaptive formulation is proposed. This formulation is based on frequency domain block adaptive filters and given room transfer functions. To reduce computational complexity, the system is extended to subband processing without cross-adaptive filters. The computational savings come from recognizing that sound zones consist of part-solutions which are inherently band limited, hence, several subbands can be ignored. To validate the theoretical findings, a 27-channel loudspeaker array was constructed, and measurements were performed in anechoic and reflective environments. The results show that the subband solution performs identically to a full-rate solution but at a reduced computational complexity.
Estimation of the acoustic-scene related parameters such as relative transfer functions (RTFs) from source to microphones, source power spectral densities (PSDs) and PSDs of the late reverberation is essential and also challenging. Existing maximum likelihood estimators typically consider only subsets of these parameters and use each time frame separately. In this paper we explicitly focus on the single source scenario and first propose a joint maximum likelihood estimator (MLE) to estimate all parameters jointly using a single time frame. Since the RTFs are typically invariant for a number of consecutive time frames we also propose a joint maximum likelihood estimator (MLE) using multiple time frames which has similar estimation performance compared to a recently proposed reference algorithm called simultaneously confirmatory factor analysis (SCFA), but at a much lower complexity. Moreover, we present experimental results which demonstrate that the estimation accuracy, together with the performance of noise reduction, speech quality and speech intelligibility, of our proposed joint MLE outperform those of existing MLE based approaches that use only a single time frame.
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Estimation of the acoustic-scene related parameters such as relative transfer functions (RTFs) from source to microphones, source power spectral densities (PSDs) and PSDs of the late reverberation is essential and also challenging. Existing maximum likelihood estimators typically consider only subsets of these parameters and use each time frame separately. In this paper we explicitly focus on the single source scenario and first propose a joint maximum likelihood estimator (MLE) to estimate all parameters jointly using a single time frame. Since the RTFs are typically invariant for a number of consecutive time frames we also propose a joint maximum likelihood estimator (MLE) using multiple time frames which has similar estimation performance compared to a recently proposed reference algorithm called simultaneously confirmatory factor analysis (SCFA), but at a much lower complexity. Moreover, we present experimental results which demonstrate that the estimation accuracy, together with the performance of noise reduction, speech quality and speech intelligibility, of our proposed joint MLE outperform those of existing MLE based approaches that use only a single time frame.
Conference paper
(2022)
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Ids Van der Werf, Pablo Martinez-Nuevo, Martin Bo Møller, Richard Hendriks, Jorge Martinez
The sound field in a room can be represented by a weighted sum of room modes. To estimate the room modes, current literature uses on-the-grid, sparse reconstruction methods. However, these on-the-grid methods are known to suffer from basis mismatch. In this work, we investigate the use of a gridless framework for estimating room modes using atomic norm minimization, a gridless method. The advantage of this approach would be that it does not suffer from this basis mismatch problem. We derive a bound for the sound field reconstruction problem in a one-dimensional room with rigid walls and relate this to the frequency separation that is required by the atomic norm. We conclude that for perfect reconstruction based on the investigated gridless approach, additional prior knowledge about the signal model is required. We show how recovery is possible in a one-dimensional setting by exploiting both the structure of the sound field and the acquisition method.
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The sound field in a room can be represented by a weighted sum of room modes. To estimate the room modes, current literature uses on-the-grid, sparse reconstruction methods. However, these on-the-grid methods are known to suffer from basis mismatch. In this work, we investigate the use of a gridless framework for estimating room modes using atomic norm minimization, a gridless method. The advantage of this approach would be that it does not suffer from this basis mismatch problem. We derive a bound for the sound field reconstruction problem in a one-dimensional room with rigid walls and relate this to the frequency separation that is required by the atomic norm. We conclude that for perfect reconstruction based on the investigated gridless approach, additional prior knowledge about the signal model is required. We show how recovery is possible in a one-dimensional setting by exploiting both the structure of the sound field and the acquisition method.
On the Integration of Acoustics and LiDAR
A Multi-Modal Approach to Acoustic Reflector Estimation
Conference paper
(2022)
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E.H.J. Riemens, Pablo Martinez-Nuevo, Jorge Martinez, Martin Bo Møller, R.C. Hendriks
Loudspeakers are usually placed in an environment unknown to the loudspeaker designers. Having knowledge on the room acoustic properties, e.g., the location of acoustic reflectors, allows to better reproduce the sound field as intended. Current state-of-the-art methods for room boundary detection using microphone measurements typically focus on a two-dimensional setting, causing a model mismatch when employed in real-life scenarios. Detection of arbitrary reflectors in three dimensions encounters practical limitations, e.g., the need for a spherical array and the increased computational complexity. Moreover, loudspeakers may not have an omnidirectional directivity pattern, as usually assumed in the literature, making the detection of acoustic reflectors in some directions more challenging.
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Loudspeakers are usually placed in an environment unknown to the loudspeaker designers. Having knowledge on the room acoustic properties, e.g., the location of acoustic reflectors, allows to better reproduce the sound field as intended. Current state-of-the-art methods for room boundary detection using microphone measurements typically focus on a two-dimensional setting, causing a model mismatch when employed in real-life scenarios. Detection of arbitrary reflectors in three dimensions encounters practical limitations, e.g., the need for a spherical array and the increased computational complexity. Moreover, loudspeakers may not have an omnidirectional directivity pattern, as usually assumed in the literature, making the detection of acoustic reflectors in some directions more challenging.
Moving-coil electrodynamic loudspeakers and dynamic microphones use the same linear actuator technology at the core of their operation. Utilising this similarity, loudspeakers have a possible use as recording devices in cases where using dedicated microphones is not feasible. Such a use case exists in public address and voice alarm systems. This paper evaluates the feasibility of using the loudspeakers already in place in these systems as recording devices to provide information back to the system. A system using a single loudspeaker as both a playback and recording device simultaneously is analysed, modelled and simulated. The results show that using a current measuring set-up with an analogue-to-digital converter capable of detecting a range of roughly 120 dB, a speech signal incident at 46 dBSPL in a cone of 150° from a loudspeaker can be successfully estimated in an office room with an announcement playing at 88 dBSPL and background interference present at the same time. As the estimated signal is unknown to the system, the solution generalises to other signal types as well.
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Moving-coil electrodynamic loudspeakers and dynamic microphones use the same linear actuator technology at the core of their operation. Utilising this similarity, loudspeakers have a possible use as recording devices in cases where using dedicated microphones is not feasible. Such a use case exists in public address and voice alarm systems. This paper evaluates the feasibility of using the loudspeakers already in place in these systems as recording devices to provide information back to the system. A system using a single loudspeaker as both a playback and recording device simultaneously is analysed, modelled and simulated. The results show that using a current measuring set-up with an analogue-to-digital converter capable of detecting a range of roughly 120 dB, a speech signal incident at 46 dBSPL in a cone of 150° from a loudspeaker can be successfully estimated in an office room with an announcement playing at 88 dBSPL and background interference present at the same time. As the estimated signal is unknown to the system, the solution generalises to other signal types as well.
On the Integration of Acoustics and LiDAR
A Multi-Modal Approach to Acoustic Reflector Estimation
Conference paper
(2022)
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E.H.J. Riemens, Pablo Martinez-Nuevo, Jorge Martinez, Martin Bo Møller, R.C. Hendriks
Having knowledge on the room acoustic properties, e.g., the location of acoustic reflectors, allows to better reproduce the sound field as intended. Current state-of-the-art methods for room boundary detection using microphone measurements typically focus on a two-dimensional setting, causing a model mismatch when employed in real-life scenarios. Detection of arbitrary reflectors in three dimensions encounters practical limitations, e.g., the need for a spherical array and the increased computational complexity. Moreover, loudspeakers may not have an omnidirectional directivity pattern, as usually assumed in the literature, making the detection of acoustic reflectors in some directions more challenging. In the proposed method, a LiDAR sensor is added to a loudspeaker to improve wall detection accuracy and robustness. This is done in two ways. First, the model mismatch introduced by horizontal reflectors can be resolved by detecting reflectors with the LiDAR sensor to enable elimination of their detrimental influence from the 2D problem in pre-processing. Second, a LiDAR-based method is proposed to compensate for the challenging directions where the directive loudspeaker emits little energy. We show via simulations that this multi-modal approach, i.e., combining microphone and LiDAR sensors, improves the robustness and accuracy of wall detection.
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Having knowledge on the room acoustic properties, e.g., the location of acoustic reflectors, allows to better reproduce the sound field as intended. Current state-of-the-art methods for room boundary detection using microphone measurements typically focus on a two-dimensional setting, causing a model mismatch when employed in real-life scenarios. Detection of arbitrary reflectors in three dimensions encounters practical limitations, e.g., the need for a spherical array and the increased computational complexity. Moreover, loudspeakers may not have an omnidirectional directivity pattern, as usually assumed in the literature, making the detection of acoustic reflectors in some directions more challenging. In the proposed method, a LiDAR sensor is added to a loudspeaker to improve wall detection accuracy and robustness. This is done in two ways. First, the model mismatch introduced by horizontal reflectors can be resolved by detecting reflectors with the LiDAR sensor to enable elimination of their detrimental influence from the 2D problem in pre-processing. Second, a LiDAR-based method is proposed to compensate for the challenging directions where the directive loudspeaker emits little energy. We show via simulations that this multi-modal approach, i.e., combining microphone and LiDAR sensors, improves the robustness and accuracy of wall detection.
Many multi-microphone algorithms depend on knowing the relative acoustic transfer functions (RTFs) of the individual sound sources in the acoustic scene. However, accurate joint RTF estimation for multiple sources is a challenging problem. Existing methods to jointly estimate the RTF for multiple sources have either no satisfying performance, or, suffer from a very large computational complexity. In this paper, we propose a method for robust estimation of the individual RTFs in a multi-source acoustic scenario. The presented algorithm is based on linear algebraic concepts and therefore of lower computational complexity compared to a recently presented state-of-the-art algorithm, while having a similar performance. Experimental results are presented to demonstrate the RTF estimation performance as well as the noise reduction performance when combining the estimated RTFs with a beamformer.
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Many multi-microphone algorithms depend on knowing the relative acoustic transfer functions (RTFs) of the individual sound sources in the acoustic scene. However, accurate joint RTF estimation for multiple sources is a challenging problem. Existing methods to jointly estimate the RTF for multiple sources have either no satisfying performance, or, suffer from a very large computational complexity. In this paper, we propose a method for robust estimation of the individual RTFs in a multi-source acoustic scenario. The presented algorithm is based on linear algebraic concepts and therefore of lower computational complexity compared to a recently presented state-of-the-art algorithm, while having a similar performance. Experimental results are presented to demonstrate the RTF estimation performance as well as the noise reduction performance when combining the estimated RTFs with a beamformer.
Acoustic room geometry estimation is often performed in ad hoc settings, i.e., using multiple microphones and sources distributed around the room, or assuming control over the excitation signals. We propose a fully convolutional network (FCN) that localizes reflective surfaces under the relaxed assumptions that (i) a compact array of only two microphones is available, (ii) emitter and receivers are not synchronized, and (iii) both the excitation signals and the impulse responses of the enclosures are unknown. Our FCN is trained in a supervised fashion to predict the likelihood of reflective surfaces at specific distances and directions-of-arrival (DOA). When a single reflective surface is present, up to 80% of real and virtual sources are detected, while this figure approaches 50% in rectangular rooms. Experiments on real-world recordings report similar accuracy as with artificially reverberated speech signals, validating the generalization capabilities of the framework.
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Acoustic room geometry estimation is often performed in ad hoc settings, i.e., using multiple microphones and sources distributed around the room, or assuming control over the excitation signals. We propose a fully convolutional network (FCN) that localizes reflective surfaces under the relaxed assumptions that (i) a compact array of only two microphones is available, (ii) emitter and receivers are not synchronized, and (iii) both the excitation signals and the impulse responses of the enclosures are unknown. Our FCN is trained in a supervised fashion to predict the likelihood of reflective surfaces at specific distances and directions-of-arrival (DOA). When a single reflective surface is present, up to 80% of real and virtual sources are detected, while this figure approaches 50% in rectangular rooms. Experiments on real-world recordings report similar accuracy as with artificially reverberated speech signals, validating the generalization capabilities of the framework.
Conference paper
(2020)
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V.G. Zaccà, Pablo Martínez-Nuevo, Martin Bo Møller, Jorge Martinez, R. Heusdens
Accurate sound field reproduction in rooms is often limited by the lack of knowledge of the room characteristics. Information about the room shape or nearby reflecting boundaries can, in principle, be used to improve the accuracy of the reproduction. In this paper, we propose a method to infer the location of nearby reflecting boundaries from measurements on a microphone array. As opposed to traditional methods, we explicitly exploit the loudspeaker directivity model (beyond omnidirectional radiation) and the microphone array geometry. This approach does not require noiseless timing information of the echoes as input, nor a tailored loudspeaker-wall-microphone measurement step. Simulations show the proposed model outperforms current methods that disregard directivity in reverberant environments.
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Accurate sound field reproduction in rooms is often limited by the lack of knowledge of the room characteristics. Information about the room shape or nearby reflecting boundaries can, in principle, be used to improve the accuracy of the reproduction. In this paper, we propose a method to infer the location of nearby reflecting boundaries from measurements on a microphone array. As opposed to traditional methods, we explicitly exploit the loudspeaker directivity model (beyond omnidirectional radiation) and the microphone array geometry. This approach does not require noiseless timing information of the echoes as input, nor a tailored loudspeaker-wall-microphone measurement step. Simulations show the proposed model outperforms current methods that disregard directivity in reverberant environments.
Conference paper
(2015)
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Jesper Kjcer Nielsen, Nikolay D. Gaubitch, Richard Heusdens, Jorge Martinez, Tobias Lindstrøm Jensen
Knowledge on how a number of loudspeakers are positioned relative to a listening position can be used to enhance the listening experience. Usually, these loudspeaker positions are estimated using calibration signals, either audible or psycho-acoustically hidden inside the desired audio signal. In this paper, we propose to use the desired audio signal instead. Specifically, we treat the case of estimating the distance between two loudspeakers playing back a stereo music or speech signal. In this connection, we develop a real-time maximum likelihood estimator and demonstrate that it has a variance in the millimetre range in a real environment for even a modest sampling frequency.
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Knowledge on how a number of loudspeakers are positioned relative to a listening position can be used to enhance the listening experience. Usually, these loudspeaker positions are estimated using calibration signals, either audible or psycho-acoustically hidden inside the desired audio signal. In this paper, we propose to use the desired audio signal instead. Specifically, we treat the case of estimating the distance between two loudspeakers playing back a stereo music or speech signal. In this connection, we develop a real-time maximum likelihood estimator and demonstrate that it has a variance in the millimetre range in a real environment for even a modest sampling frequency.
In this letter we present a method for low-complexity simulation of multi-channel room impulse responses (RIRs). Low-complexity RIR methods will become inevitable in next generation communication systems having massive amounts of microphones/loudspeakers. For a room with rigid boundaries, we show that proper sampling of the free-field plenacoustic spectrum results in the solution of the wave equation at any position in the room. We show that the spatial aliasing introduced by spectral sampling represents the wall reflections. These wall reflections are usually modelled, at least in low-complexity simulation algorithms, by the creation of virtual free-field sources outside the room, an image source model commonly referred to as the image method. The image method requires O(N3) operations per receiver position, whereas the newly proposed method requires only O(N logN) operations per receiver position.
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In this letter we present a method for low-complexity simulation of multi-channel room impulse responses (RIRs). Low-complexity RIR methods will become inevitable in next generation communication systems having massive amounts of microphones/loudspeakers. For a room with rigid boundaries, we show that proper sampling of the free-field plenacoustic spectrum results in the solution of the wave equation at any position in the room. We show that the spatial aliasing introduced by spectral sampling represents the wall reflections. These wall reflections are usually modelled, at least in low-complexity simulation algorithms, by the creation of virtual free-field sources outside the room, an image source model commonly referred to as the image method. The image method requires O(N3) operations per receiver position, whereas the newly proposed method requires only O(N logN) operations per receiver position.