Bandpass Sampling

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Ching-hsiang Tseng - One of the best experts on this subject based on the ideXlab platform.

  • A Universal Formula for the Complete Bandpass Sampling Requirements of Nonlinear Systems
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: Ching-hsiang Tseng
    Abstract:

    A nonlinear system driven by a Bandpass input signal may produce an output signal that occupies multiple frequency bands. This makes Bandpass Sampling the output signal of the nonlinear system without causing aliasing a challenging task. Although the Bandpass Sampling theory for linear systems is well developed, its counterpart for nonlinear systems is relatively immature in the sense that complete Bandpass Sampling requirements have only been developed up to third-order nonlinear systems. In this paper, a novel method is used to derived the complete Bandpass Sampling requirements for nonlinear systems of an arbitrary order. The strategy used by this method is to build the constraints on the Sampling frequency for n th-order nonlinear systems upon those for (n - 1)th-order nonlinear systems. This process makes the derivation easily extendable to nonlinear systems of any order. The derivation method also gives an insight into the mechanism for formularizing the constraints on the Bandpass Sampling frequency. As a result, a universal formula for the complete Bandpass Sampling requirements for nonlinear systems of any order is derived. This formula consolidates the Bandpass Sampling theory for nonlinear systems and facilitates the selection of the Bandpass Sampling frequency for nonlinear systems driven by Bandpass input signals.

  • Direct downconversion of multiband RF signals using Bandpass Sampling
    IEEE Transactions on Wireless Communications, 2006
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    Abstract-Bandpass Sampling can be used by radio receivers to directly digitize the radio frequency (RF) signals. Although the Bandpass Sampling theory for single-band RF signals is well established, its counterpart for multiband RF signals is relatively immature. In this paper, we propose a novel and efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiband RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of the frequency locations of the multiple RF bands are derived. The result can be used to design a multiband receiver for software defined radios.

  • direct downconversion of multiple rf signals using Bandpass Sampling
    International Conference on Communications, 2003
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    The center idea behind the software radio architecture is to place analog-to-digital and digital-to-analog converters as near the antenna as possible, leaving the implementation of the most radio functionality to a programmable micro or signal processor. One way to accomplish this in a radio receiver front end is by direct downconverting the desired radio frequency (RF) signal to a target intermediate frequency (IF) using Bandpass Sampling. Although the Bandpass Sampling theory for a single RF signal is well developed, its counterpart for two or more RF signals is relatively immature. For direct downconverting multiple distinct RF signals, determining valid Bandpass Sampling frequencies using the conventional approach could be a computationally exhaustive process. In this paper, we propose an efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiple distinct RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of bandwidths and frequency locations of the RF signals are derived. The result can be used to efficiently choose an appropriate Bandpass Sampling frequency for multiple RF signals.

  • Bandpass Sampling criteria for nonlinear systems
    IEEE Transactions on Signal Processing, 2002
    Co-Authors: Ching-hsiang Tseng
    Abstract:

    Sampling criteria for nonlinear systems with a band-pass input are developed in this paper. It is well known that nonlinear systems may produce an output signal with a larger bandwidth than that of their input signal. According to the Nyquist Sampling theorem, the Sampling rate needs to be at least twice the maximum frequency of the output signal; otherwise, the sampled output would be aliased. However, if the input is a Bandpass signal, the spectrum of the output signal often occupies multiple frequency bands. In this case, it is possible, by using the Bandpass Sampling concept, to sample the output signal at a rate much lower than the Nyquist Sampling frequency. In this paper, all conditions in which Bandpass Sampling can be achieved are derived for nonlinear systems up to the third order. Furthermore, for nonlinear systems higher than the third order, some conditions in which Bandpass Sampling can be guaranteed are derived. The result can be used to choose an appropriate Sampling frequency for nonlinear systems of an arbitrary order.

  • ICC - Direct downconversion of multiple RF signals using Bandpass Sampling
    IEEE International Conference on Communications 2003. ICC '03., 1
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    The center idea behind the software radio architecture is to place analog-to-digital and digital-to-analog converters as near the antenna as possible, leaving the implementation of the most radio functionality to a programmable micro or signal processor. One way to accomplish this in a radio receiver front end is by direct downconverting the desired radio frequency (RF) signal to a target intermediate frequency (IF) using Bandpass Sampling. Although the Bandpass Sampling theory for a single RF signal is well developed, its counterpart for two or more RF signals is relatively immature. For direct downconverting multiple distinct RF signals, determining valid Bandpass Sampling frequencies using the conventional approach could be a computationally exhaustive process. In this paper, we propose an efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiple distinct RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of bandwidths and frequency locations of the RF signals are derived. The result can be used to efficiently choose an appropriate Bandpass Sampling frequency for multiple RF signals.

Feifei Yin - One of the best experts on this subject based on the ideXlab platform.

  • Polarization-Modulation, I/Q-Demodulation Photonic Bandpass Sampling for Wideband, Multicarrier RF Application
    IEEE Photonics Journal, 2017
    Co-Authors: Jieyu Ning, Yitang Dai, Feifei Yin, Junyi Zhang
    Abstract:

    Radio frequency (RF) photonic link under phase or polarization modulation and coherent in-phase/quadrature (I/Q) demodulation (ΦM/IQ or PolM/IQ) has been reported with unprecedented dynamic range performance, benefiting from the ultrahigh linear transfer function of electro-optic phase modulator. But the ideal linear demodulation cannot be preserved during traditional down-conversion, which is a must from high-carrier application. In this paper, we propose and demonstrate that PolM/IQ link employing ultrashort optical Bandpass Sampling delivers both multicarrier down-conversion and full linearization. The pulse train, equivalently a frequency comb with uniform amplitude and phase in frequency domain, is able to down-convert signal and all nonlinear spurs that are collected by the following analog-to-digital convertor (ADC), so that the original linearization algorithm stands. Our method releases the requirement of ADC and digital processing greatly. The bandwidth after Bandpass Sampling is confined within the first Nyquist zone, and the minimum value can be as small as signal bandwidth, much less than original which should be several times of the maximum carrier frequency. We demonstrate such linearization experimentally with two dual-carrier RF signals as input, covering multiple octave spans.

  • Amplitude modulation to phase distortion conversion in photonic Bandpass Sampling link
    2016 IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (AVFOP), 2016
    Co-Authors: Xiaodong Liang, Yitang Dai, Junyi Zhang, Feifei Yin, Yue Zhou
    Abstract:

    Recently, for the rapidly improved performance of femtosecond lasers, photonic Bandpass Sampling based radio frequency (RF) photonic link has shown performance that rivals that of the standard continuous wave (CW) architecture. The front-end photonic Bandpass Sampling technique overcomes the back-end high Sampling rate and multilevel down-conversion requirement, which has found more and more applications in high-performance radars and antennas, aeronautics and astronautics system and compressive sensing, etc. [1-3]. As with the traditional CW-based analog photonic link (APL), the sampled RFs are also distorted by all kinds of nonlinearities arising from the mostly adopted Mach-Zehnder modulator (MZM), due to the nonlinear electronics-optics-electronics conversion in photonic Bandpass Sampling link. To improve the link's spurious free dynamic range (SFDR) and fidelity, all the generated nonlinear distortions need to be concerned and well suppressed. Specially, both the target signals and derived nonlinear distortions are sampled and frequency-folded within the first Nyquist zone in Bandpass Sampling link. In our previous work [2], for example, all of the 3rd-order nonlinearities arising from the MZM were well compensated except the significant 2nd-order nonlinear spurs generating from photo-detector (PD). In most situations, distortions caused by PD are not under consideration since the PD shows un-conspicuous nonlinearity in non-saturated linear range. However, high optical incident eventually leads to saturation and causes nonlinear behavior in the PD under pulsed illumination, since the peak optical power is much higher than CW light. It has been demonstrated that the directly detected electrical signal phase changes as a function of the applied optical energy for the un-modulated optical pulse trains due to the PD saturation effect [4-5]. The significant saturation produces the conversion of optical amplitude noise to microwave phase retardation (AM-PM), which resulting in worsening the extracted microwave signal phase noise.

  • Multiband Phase-Modulated RoF Link With Coherent Detection and Bandpass Sampling
    IEEE Photonics Technology Letters, 2015
    Co-Authors: Minghua Cao, Yitang Dai, Feifei Yin
    Abstract:

    Bandpass Sampling-based coherent detection of multiband subcarrier multiplexed signals was experimentally demonstrated over phase-modulated radio-over-fiber links. Theoretical analysis and experiments are conducted to evaluate the transmission performance. In addition, for multiband transmission, an effective method for determining the valid analog-to-digital converter Sampling frequency ranges is derived to ensure no aliasing in the presence of frequency offset. Two quadrature phase-shift keying subcarrier signals were successfully transmitted and recovered over 50.6-km fiber transmission. The experimental results demonstrate that the Bandpass Sampling performs error free transmission with $\sim 9$ dB the sensitivity penalty when the Sampling rate decreases from 10 to 1 GSa/s. The hardware independence and computational complexity reduction is worth of this performance loss.

  • Digital linearization of multi-carrier RF link with photonic Bandpass Sampling
    Optics express, 2015
    Co-Authors: Yitang Dai, Xiaodong Liang, Feifei Yin, Yue Zhou, Junyi Zhang
    Abstract:

    Due to the capacity in simultaneously down-converting and receiving ultra-wideband, multi-carrier radio frequency (RF) or microwave signals, the photonic Bandpass Sampling has found more and more applications in multi-carrier communication, frequency-agile coherent radar, compressive sensing, etc. The nonlinear transfer during the electronics-to-optics conversion results in distortions, which are Bandpass sampled and frequency-folded within the first Nyquist zone, together with the target signals. Because of the multi-octave-span operation, all nonlinearities must be considered besides the usually-concerned third-order inter-modulation distortion (IMD3). We show theoretically that a photonic Bandpass Sampling link is equivalent to a baseband digital nonlinear link, and then propose a corresponding linearization scheme for the output signal. Such digital linearization is capable of suppressing all types of distortions. Both numerical and experimental examples are demonstrated, where all of the 3rd-order nonlinearities, including the internal and external IMD3, the cross modulation, and 3rd-order harmonics, are well eliminated.

  • Bandpass Sampling based digital coherent receiver with free-running local oscillator laser for phase-modulated radio-over-fiber links
    Optics express, 2014
    Co-Authors: Minghua Cao, Yitang Dai, Feifei Yin
    Abstract:

    A Bandpass Sampling based digital coherent receiver is presented for phase modulated radio-over-fiber links with coherent detection. In the scheme, the Bandpass Sampling technique is introduced in RoF systems to overcome the high Sampling rate requirement and front-end hardware dependency of conventional digtal coherent receivers. In particular, the selection rule of Bandpass Sampling rate was defined by taking into account the frequency offset induced by free-running optical local oscillator. Analytical assessment and simulations are used to determine the ultimate performance in terms of tolerances to ADC bit resolution and laser linewidth. Thereafter, a 40Mbps QPSK modulated data signal at 2.4GHz RF carrier frequency is experimentally demonstrated over the proposed 50.6-km radio-over-fiber link employing Bandpass Sampling.

Gerhard Fettweis - One of the best experts on this subject based on the ideXlab platform.

  • the impact of jitter on the signal to noise ratio in uniform Bandpass Sampling receivers
    Vehicular Technology Conference, 2014
    Co-Authors: Bjoern Almeroth, Gerhard Fettweis
    Abstract:

    Receiver front-ends, enabling multi-mode multi-band operation, are essential for future efficient mobile communications and require a proper parametrization to achieve certain performance requirements. A key component in the receive chain is the analog-to-digital converter (ADC). To determine feasible configurations of the ADC, an abstract model is investigated in order to evaluate the performance in terms of the signal-to-noise ratio (SNR) of Bandpass Sampling receivers. It models the available types of Sampling circuits, the impact of stationary and non-stationary jitter processes, as well as limited quantization resolution. The derived ADC model is used to determine the dominating jitter effect, either aperture or clock jitter, depending on the receiver setup. Furthermore, required root mean square jitter values are derived analytically for a predefined receiver noise figure. A properly designed Bandpass Sampling receiver, matching the proposed maximum jitter requirements, avoids significant SNR performance losses and can be employed in mobile communications.

  • jitter requirements for Bandpass Sampling receivers utilizing sample and hold circuits
    International Conference on Acoustics Speech and Signal Processing, 2014
    Co-Authors: Bjoern Almeroth, Gerhard Fettweis
    Abstract:

    The uncertainty of the Sampling time is of major concern for Bandpass signal reception. It reduces the achievable signal-to-noise ratio of the Bandpass Sampling receiver. Traditionally, only the absolute Sampling time is considered to be subject to timing errors, which then result in corresponding amplitude errors. But jitter also has an impact on the integration duration of the sample-and-hold circuit. In this paper we investigate the impact of jitter on the signal-to-noise ratio performance of the Bandpass Sampling receiver utilizing a sample-and-hold Sampling circuit. In addition, a bound on the acceptable standard deviation of the jitter for different receiver setups is given.

  • ICASSP - Jitter requirements for Bandpass Sampling receivers utilizing sample-and-hold circuits
    2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2014
    Co-Authors: Bjoern Almeroth, Gerhard Fettweis
    Abstract:

    The uncertainty of the Sampling time is of major concern for Bandpass signal reception. It reduces the achievable signal-to-noise ratio of the Bandpass Sampling receiver. Traditionally, only the absolute Sampling time is considered to be subject to timing errors, which then result in corresponding amplitude errors. But jitter also has an impact on the integration duration of the sample-and-hold circuit. In this paper we investigate the impact of jitter on the signal-to-noise ratio performance of the Bandpass Sampling receiver utilizing a sample-and-hold Sampling circuit. In addition, a bound on the acceptable standard deviation of the jitter for different receiver setups is given.

  • VTC Spring - The Impact of Jitter on the Signal-to-Noise Ratio in Uniform Bandpass Sampling Receivers
    2014 IEEE 79th Vehicular Technology Conference (VTC Spring), 2014
    Co-Authors: Bjoern Almeroth, Gerhard Fettweis
    Abstract:

    Receiver front-ends, enabling multi-mode multi-band operation, are essential for future efficient mobile communications and require a proper parametrization to achieve certain performance requirements. A key component in the receive chain is the analog-to-digital converter (ADC). To determine feasible configurations of the ADC, an abstract model is investigated in order to evaluate the performance in terms of the signal-to-noise ratio (SNR) of Bandpass Sampling receivers. It models the available types of Sampling circuits, the impact of stationary and non-stationary jitter processes, as well as limited quantization resolution. The derived ADC model is used to determine the dominating jitter effect, either aperture or clock jitter, depending on the receiver setup. Furthermore, required root mean square jitter values are derived analytically for a predefined receiver noise figure. A properly designed Bandpass Sampling receiver, matching the proposed maximum jitter requirements, avoids significant SNR performance losses and can be employed in mobile communications.

Yitang Dai - One of the best experts on this subject based on the ideXlab platform.

  • Polarization-Modulation, I/Q-Demodulation Photonic Bandpass Sampling for Wideband, Multicarrier RF Application
    IEEE Photonics Journal, 2017
    Co-Authors: Jieyu Ning, Yitang Dai, Feifei Yin, Junyi Zhang
    Abstract:

    Radio frequency (RF) photonic link under phase or polarization modulation and coherent in-phase/quadrature (I/Q) demodulation (ΦM/IQ or PolM/IQ) has been reported with unprecedented dynamic range performance, benefiting from the ultrahigh linear transfer function of electro-optic phase modulator. But the ideal linear demodulation cannot be preserved during traditional down-conversion, which is a must from high-carrier application. In this paper, we propose and demonstrate that PolM/IQ link employing ultrashort optical Bandpass Sampling delivers both multicarrier down-conversion and full linearization. The pulse train, equivalently a frequency comb with uniform amplitude and phase in frequency domain, is able to down-convert signal and all nonlinear spurs that are collected by the following analog-to-digital convertor (ADC), so that the original linearization algorithm stands. Our method releases the requirement of ADC and digital processing greatly. The bandwidth after Bandpass Sampling is confined within the first Nyquist zone, and the minimum value can be as small as signal bandwidth, much less than original which should be several times of the maximum carrier frequency. We demonstrate such linearization experimentally with two dual-carrier RF signals as input, covering multiple octave spans.

  • Amplitude modulation to phase distortion conversion in photonic Bandpass Sampling link
    2016 IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (AVFOP), 2016
    Co-Authors: Xiaodong Liang, Yitang Dai, Junyi Zhang, Feifei Yin, Yue Zhou
    Abstract:

    Recently, for the rapidly improved performance of femtosecond lasers, photonic Bandpass Sampling based radio frequency (RF) photonic link has shown performance that rivals that of the standard continuous wave (CW) architecture. The front-end photonic Bandpass Sampling technique overcomes the back-end high Sampling rate and multilevel down-conversion requirement, which has found more and more applications in high-performance radars and antennas, aeronautics and astronautics system and compressive sensing, etc. [1-3]. As with the traditional CW-based analog photonic link (APL), the sampled RFs are also distorted by all kinds of nonlinearities arising from the mostly adopted Mach-Zehnder modulator (MZM), due to the nonlinear electronics-optics-electronics conversion in photonic Bandpass Sampling link. To improve the link's spurious free dynamic range (SFDR) and fidelity, all the generated nonlinear distortions need to be concerned and well suppressed. Specially, both the target signals and derived nonlinear distortions are sampled and frequency-folded within the first Nyquist zone in Bandpass Sampling link. In our previous work [2], for example, all of the 3rd-order nonlinearities arising from the MZM were well compensated except the significant 2nd-order nonlinear spurs generating from photo-detector (PD). In most situations, distortions caused by PD are not under consideration since the PD shows un-conspicuous nonlinearity in non-saturated linear range. However, high optical incident eventually leads to saturation and causes nonlinear behavior in the PD under pulsed illumination, since the peak optical power is much higher than CW light. It has been demonstrated that the directly detected electrical signal phase changes as a function of the applied optical energy for the un-modulated optical pulse trains due to the PD saturation effect [4-5]. The significant saturation produces the conversion of optical amplitude noise to microwave phase retardation (AM-PM), which resulting in worsening the extracted microwave signal phase noise.

  • Multiband Phase-Modulated RoF Link With Coherent Detection and Bandpass Sampling
    IEEE Photonics Technology Letters, 2015
    Co-Authors: Minghua Cao, Yitang Dai, Feifei Yin
    Abstract:

    Bandpass Sampling-based coherent detection of multiband subcarrier multiplexed signals was experimentally demonstrated over phase-modulated radio-over-fiber links. Theoretical analysis and experiments are conducted to evaluate the transmission performance. In addition, for multiband transmission, an effective method for determining the valid analog-to-digital converter Sampling frequency ranges is derived to ensure no aliasing in the presence of frequency offset. Two quadrature phase-shift keying subcarrier signals were successfully transmitted and recovered over 50.6-km fiber transmission. The experimental results demonstrate that the Bandpass Sampling performs error free transmission with $\sim 9$ dB the sensitivity penalty when the Sampling rate decreases from 10 to 1 GSa/s. The hardware independence and computational complexity reduction is worth of this performance loss.

  • Digital linearization of multi-carrier RF link with photonic Bandpass Sampling
    Optics express, 2015
    Co-Authors: Yitang Dai, Xiaodong Liang, Feifei Yin, Yue Zhou, Junyi Zhang
    Abstract:

    Due to the capacity in simultaneously down-converting and receiving ultra-wideband, multi-carrier radio frequency (RF) or microwave signals, the photonic Bandpass Sampling has found more and more applications in multi-carrier communication, frequency-agile coherent radar, compressive sensing, etc. The nonlinear transfer during the electronics-to-optics conversion results in distortions, which are Bandpass sampled and frequency-folded within the first Nyquist zone, together with the target signals. Because of the multi-octave-span operation, all nonlinearities must be considered besides the usually-concerned third-order inter-modulation distortion (IMD3). We show theoretically that a photonic Bandpass Sampling link is equivalent to a baseband digital nonlinear link, and then propose a corresponding linearization scheme for the output signal. Such digital linearization is capable of suppressing all types of distortions. Both numerical and experimental examples are demonstrated, where all of the 3rd-order nonlinearities, including the internal and external IMD3, the cross modulation, and 3rd-order harmonics, are well eliminated.

  • Bandpass Sampling based digital coherent receiver with free-running local oscillator laser for phase-modulated radio-over-fiber links
    Optics express, 2014
    Co-Authors: Minghua Cao, Yitang Dai, Feifei Yin
    Abstract:

    A Bandpass Sampling based digital coherent receiver is presented for phase modulated radio-over-fiber links with coherent detection. In the scheme, the Bandpass Sampling technique is introduced in RoF systems to overcome the high Sampling rate requirement and front-end hardware dependency of conventional digtal coherent receivers. In particular, the selection rule of Bandpass Sampling rate was defined by taking into account the frequency offset induced by free-running optical local oscillator. Analytical assessment and simulations are used to determine the ultimate performance in terms of tolerances to ADC bit resolution and laser linewidth. Thereafter, a 40Mbps QPSK modulated data signal at 2.4GHz RF carrier frequency is experimentally demonstrated over the proposed 50.6-km radio-over-fiber link employing Bandpass Sampling.

Sun Chung Chou - One of the best experts on this subject based on the ideXlab platform.

  • Direct downconversion of multiband RF signals using Bandpass Sampling
    IEEE Transactions on Wireless Communications, 2006
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    Abstract-Bandpass Sampling can be used by radio receivers to directly digitize the radio frequency (RF) signals. Although the Bandpass Sampling theory for single-band RF signals is well established, its counterpart for multiband RF signals is relatively immature. In this paper, we propose a novel and efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiband RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of the frequency locations of the multiple RF bands are derived. The result can be used to design a multiband receiver for software defined radios.

  • direct downconversion of multiple rf signals using Bandpass Sampling
    International Conference on Communications, 2003
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    The center idea behind the software radio architecture is to place analog-to-digital and digital-to-analog converters as near the antenna as possible, leaving the implementation of the most radio functionality to a programmable micro or signal processor. One way to accomplish this in a radio receiver front end is by direct downconverting the desired radio frequency (RF) signal to a target intermediate frequency (IF) using Bandpass Sampling. Although the Bandpass Sampling theory for a single RF signal is well developed, its counterpart for two or more RF signals is relatively immature. For direct downconverting multiple distinct RF signals, determining valid Bandpass Sampling frequencies using the conventional approach could be a computationally exhaustive process. In this paper, we propose an efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiple distinct RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of bandwidths and frequency locations of the RF signals are derived. The result can be used to efficiently choose an appropriate Bandpass Sampling frequency for multiple RF signals.

  • ICC - Direct downconversion of multiple RF signals using Bandpass Sampling
    IEEE International Conference on Communications 2003. ICC '03., 1
    Co-Authors: Ching-hsiang Tseng, Sun Chung Chou
    Abstract:

    The center idea behind the software radio architecture is to place analog-to-digital and digital-to-analog converters as near the antenna as possible, leaving the implementation of the most radio functionality to a programmable micro or signal processor. One way to accomplish this in a radio receiver front end is by direct downconverting the desired radio frequency (RF) signal to a target intermediate frequency (IF) using Bandpass Sampling. Although the Bandpass Sampling theory for a single RF signal is well developed, its counterpart for two or more RF signals is relatively immature. For direct downconverting multiple distinct RF signals, determining valid Bandpass Sampling frequencies using the conventional approach could be a computationally exhaustive process. In this paper, we propose an efficient method to find the ranges of valid Bandpass Sampling frequency for direct downconverting multiple distinct RF signals. Simple formulas for the ranges of valid Bandpass Sampling frequency in terms of bandwidths and frequency locations of the RF signals are derived. The result can be used to efficiently choose an appropriate Bandpass Sampling frequency for multiple RF signals.