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Showing papers on "Low-pass filter published in 1985"


Journal ArticleDOI
TL;DR: A description is given of a high-performance fifth-order low-pass switched-capacitor filter operating form a single 5-V supply that uses a fully differential topology combined with input-to-output class AB amplifier design, dynamic biasing, and switched-Capacitor common-mode feedback to meet the PCM channel filter requirements.
Abstract: A description is given of a high-performance fifth-order low-pass switched-capacitor filter operating form a single 5-V supply. The filter uses a fully differential topology combined with input-to-output class AB amplifier design, dynamic biasing, and switched-capacitor common-mode feedback. An experimental prototype fabricated in a 5-/spl mu/m CMOS technology requires only 350 /spl mu/W of power to meet the PCM channel filter requirements. Typical measured results are: a dynamic range of 92 dB; a supply rejection (PSRR) of 40 dB over the entire Nyquist range; and a total harmonic distortion of -73 dB for a 2-V r.m.s. differential output signal. The chip active area is about 3900 mil/SUP 2/.

278 citations


Journal ArticleDOI
TL;DR: In this article, simple algebraic methods may be used to design three-dimensional (3D) recursive digital filters for two important applications: first, the selective enhancement of a two-dimensional signal that is moving with time along a linear trajectory at known velocity.
Abstract: It is shown that simple algebraic methods may be used to design three-dimensional (3-D) recursive digital filters for two important applications: first, the selective enhancement of a two-dimensional (2-D) signal that is moving with time along a linear trajectory at known velocity and, second, the selective enhancement of 3-D spatially planar waves. The design techniques involve first-order 3-D networks in the continuous domain and proceed by analogy with an extension of the simple circuit theoretic concepts of resonance and Q factor. A 3-D spatial straight-line filter is designed in the frequency domain as a 3-D planar filter and, conversely, a 3-D spatially planar filter is designed in the frequency domain as a 3-D straight-line filter.

187 citations


Journal ArticleDOI
F. Mintzer1
TL;DR: It is shown that the class of quadrature mirror filters (QMF's) that satisfiesThese conditions is quite limited, and a class of filters which does satisfy these conditions is given, and an simple procedure for designing filters from this class is presented.
Abstract: In this paper, conditions are given for a two-band multi-rate filter bank to be alias free and to have a unity frequency response. It is shown that the class of quadrature mirror filters (QMF's) that satisfies these conditions is quite limited. A class of filters which does satisfy these conditions is given, and a simple procedure for designing filters from this class is presented with an example.

181 citations


Journal ArticleDOI
TL;DR: A set of real-time digital filters each implemented as a subroutine that can be implemented on a diversity of available microprocessors to implement a desired filtering task on a single microprocessor.
Abstract: Traditionally, analog circuits have been used for signal conditioning of electrocardiograms. As an alternative, algorithms implemented as programs on microprocessors can do similar filtering tasks. Also, digital filter algorithms can perform processes that are difficult or impossible using analog techniques. Presented here are a set of real-time digital filters each implemented as a subroutine. By calling these subroutines in an appropriate sequence, a user can cascade filters together to implement a desired filtering task on a single microprocessor. Included are an adaptive 60-Hz interference filter, two low-pass filters, a high-pass filter for eliminating dc offset in an ECG, an ECG data reduction algorithm, band-pass filters for use in QRS detection, and a derivative-based QRS detection algorithm. These filters achieve real-time speeds by requiring only integer arithmetic. They can be implemented on a diversity of available microprocessors.

178 citations


Journal ArticleDOI
TL;DR: The distortion mechanism in switched-capacitor (SC) filters are considered, and closed-form expression relating switched-Capacitors filter distortion to circuit parameters are derived and applied to a sixth-order experimental filter.
Abstract: The distortion mechanism in switched-capacitor (SC) filters are considered, and closed-form expression relating switched-capacitors filter distortion to circuit parameters are derived. Design techniques for low-distortion applications are discussed and are applied to a sixth-order experimental filter. The filter design uses a fully differential class A/B op amp with a continuous-time common-mode feedback circuit. Distortion measurements show that for 82-dB dynamic range (relative to noise floor) the total harmonic distortion of 0.02% within the whole 4-kHz bandwidth and 0.07% within 20-kHz bandwidth.

173 citations


Journal ArticleDOI
TL;DR: In this article, a voice-band continuous-time filter was designed based on the technique of fully balanced networks and was fabrication in a 3.5/spl mu/CMOS technology.
Abstract: A voice-band continuous-time filter is described which was designed based on the technique of fully balanced networks and was fabrication in a 3.5-/spl mu/ CMOS technology. The filter implements a fifth-order elliptic low-pass transfer function with 0.05-dB passband ripple and 3.4 kHz cutoff frequency. A phase-locked loop control system fabricated on the same chip automatically references the frequency response of the filter to an external fixed clock frequency. The cutoff frequency was found to vary by less than 0.1% for an operating temperature range of 0-85/spl deg/C. The absolute value accuracy of the cutoff frequency was 0.5% (standard deviation). With /spl plusmn/5-V power supplies the measured dynamic range of the filter was approximately 100 dB.

172 citations


Journal ArticleDOI
P. Chu1
TL;DR: A key feature of this filter structure is that the number of multiplies, adds, and stored coefficients required for implementation is significantly less than those needed for the conventional QMF structure, given the same number of channels.
Abstract: The two-channel quadrature mirror filter structure of Croisier and Esteban may be extended to an arbitrary number of equal bandwidth channels, given certain restrictions on the bandpass filters. The most serious restriction is that the stopband attenuation of eacli band-pass filter must be high for all frequencies outside twice the nominal 3 dB bandwidth of the filter. This restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise. A key feature of our filter structure is that the number of multiplies, adds, and stored coefficients required for implementation is significantly less than those needed for the conventional QMF structure, given the same number of channels. Fortran code for a 16-channel filter structure is listed as an example of efficient implementation.

161 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed, from certain basic assumptions, ultimate limits on dynamic range, chip area, and power consumption in SC integrators and low-pass filters, and showed that the minimum area and power requirements vary as the square of desired dynamic range.
Abstract: Switched-capacitor (SC) filters continue to improve in performance mainly through progress in the design of MOS operational amplifiers (op amps). Ultimate limits to achievable filter performance, however, stem from factors more fundamental than op amp nonidealities, factors independent of process and circuit improvements. This paper develops, from certain basic assumptions, ultimate limits on dynamic range, chip area, and power consumption in SC integrators and low-pass filters. For integrators, minimum area and power requirements are shown to vary as the square of desired dynamic range. Some physically realistic approximations lead to expressions relating filter area, power consumption, and dynamic range which involve only fundamental process parameters, supply voltage and filter cut-off frequency. Comparison with actual performance in typical commercially manufactured SC filters suggests that there is still a strong motivation in improving op amp specifications. A typical commercial fifth-order voiceband filter operating from a \pm 5-V supply with a dynamic range of 95 dB consumes approximately 5 mW and requires an area of approximately 5000 {mil}^{2} compared with the theoretical minima of 8.5 \mu W and 11.2 {mil}^{2} , respectively.

102 citations


Journal ArticleDOI
TL;DR: The analytic optimum for odd order low-pass filters of this new class turns out to be the elliptic filter itself, but in a new configuration, and Analytic solution is obtained for filters used in decimation/interpolation by a factor of 2.
Abstract: A new structure for multiband recursive digital filters is proposed. For meeting low-pass filter specifications, it uses fewer multiplications than conventional elliptic filter realizations. An approximation to the minimax solution is obtained numerically by minimizing the LP error norm. The analytic optimum for odd order low-pass filters of this new class turns out to be the elliptic filter itself, but in a new configuration. Analytic solution is also obtained for filters used in decimation/interpolation by a factor of 2. There are several realizations for this new structure, the choice of which depends on the location of poles and zeros. Some selected realizations always have low roundoff noise and small limit cycle bounds.

96 citations


Journal ArticleDOI
TL;DR: The necessary and sufficient conditions for a digital filter transfer function to be implementable as a sum of two all-pass filters are derived directly in the z-plane as mentioned in this paper. But these conditions are not applicable to analog filters.
Abstract: The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the z -plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.

90 citations


Proceedings ArticleDOI
01 Jan 1985
TL;DR: This approach requires no internal D/A converter, nor does it produce a coarser quantization with larger inputs, and can display a net resolution exceeding the performance of the internal analog components, and since the bulk of the circuitry is digital, it benefits from continued technology scalmg.
Abstract: AN OVERSAMPLE-AND-DECIMATE ARCHITECTURE yielding a analog-to-digital interface system with a built-in maskprogrammable digital antialias filter in standard 5V digital MOS technology will be reported. Unlike other MOS A/D converter techniques, this approach requires no precision component ratios or precision comparator, nor a double-polysilicon or other special capacitor structure. Prototype devices display approximately 12b converter linearity at an 8kHz output rate with a single 5V power supply and a total die area of 4 8mm? The low supply voltage and simplified process requirements are attractive for scaled MOS fabrication technologies. This is intended as a linear (non-companding) analog-interface block for constant-sampling-rate applications uch as speech processing. The system is based on l b A/D conversion, downsampled 256 times by a 1024-point, finite-impulse-response (FIR) digital lowpass filter. Such a configuration can display a net resolution exceeding the performance of the internal analog components, and since the bulk of the circuitry is digital, it benefits from continued technology scalmg. It differs also from interpohtiue A/D circuits’, in that it requires no internal D/A converter, nor does it produce a coarser quantization with larger inputs. A delta-sigma-modulator front end, used elsewhere in disCrete2, bipolar3 and passive grounded-capacitor MO!? circuitry, has been realized with a parasitic-insensitive switchedcapacitor integrator; Figure 1. The parasitic insensitivity allows

Patent
Charles L. Saxe1, Roydn Jones1
27 Aug 1985
TL;DR: In this paper, a digital storage oscilloscope is provided with an anti-aliasing filter circuit utilizing a first plurality of switchable analog filters that bandwidth limit frequencies greater than half the oscilloscope's sampling frequency.
Abstract: A digital storage oscilloscope is provided with an anti-aliasing filter circuit utilizing a first plurality of switchable analog filters that bandwidth limit frequencies greater than half the oscilloscope's sampling frequency, and a digital transversal filter effective at lower sweep rates and sampling rates for also bandwidth limiting frequencies greater than half the sampling frequency. The digital transversal filter is controllable to provide a different band pass characteristic for different sweep and sample rates. Both the selection of filters and the control of the digital filter are responsive to the oscilloscope's selection of sweep rate.

Journal ArticleDOI
TL;DR: Analysis based on perceptual rather than mathematical considerations has been carried out, and it has shown that substantial improvement over usual techniques can be achieved by the use of a cascade of a presharpening filter combined with Gaussian presampling and interpolation filters.
Abstract: The transformation of image signals between the continuous domain of the real world and the discrete domain of modern data processing can have a significant effect on quality and efficiency. Analysis based on perceptual rather than mathematical considerations has been carried out. A series of experiments based on the analysis has shown that substantial improvement over usual techniques can be achieved by the use of a cascade of a presharpening filter combined with Gaussian presampling and interpolation filters. The resulting ``sharpened Gaussian'' filter, although not exactly circularly symmetrical, gives a high degree of isotropy. Each element in the cascade is separable, so that computational efficiency is high. A favorable tradeoff is achieved among sharpness, smoothness, and the effects of aliasing. Subjective testing, in comparison with other commonly used filters, has shown the clear superiority of this filter.

Journal ArticleDOI
TL;DR: In this paper, a new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented, which does not involve iterative approximations and is therefore fast.
Abstract: A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included.

Patent
29 Nov 1985
TL;DR: In this paper, a sinusoidally weighted pulse width modulated signal is used to switch a pair of solid state power switches on and off in alternation in order to connect the motor alternately across positive and negative power supplies.
Abstract: A substantially perfect single phase sinusoidal shaped voltage waveform may be generated for driving a single phase a-c induction motor by employing a sinusoidally weighted pulse width modulated signal to switch a pair of solid state power switches on and off in alternation in order to connect the motor alternately across positive and negative power supplies. A low pass filter is effectively connected in series with the single phase motor to filter out all of the signal components except the fundamental of the sine wave modulating frequency. In this way, only a sinusoidal voltage is applied to the motor. By making the switching frequency very high relative to the sine wave modulation component, the filter size and cost are minimized and it is unnecessary to correlate or synchronize the sine wave modulation and switching frequencies.

Journal ArticleDOI
TL;DR: Frequency characteristics of the electroreceptive system in Scyliorhinus canicula were determined both by electrophysiological recording of the primary afferent responses and by optical recording of respiratory reflexes after electrical stimulation, concluding that the low pass filter properties are not imposed by the time constant of the ampulla wall.
Abstract: 1. Frequency characteristics of the electroreceptive system in Scyliorhinus canicula were determined both by electrophysiological recording of the primary afferent responses and by optical recording of respiratory reflexes after electrical stimulation. 2. The frequency response of the primary afferents shows a maximum gain at about 5 Hz, with slopes of +2.3 and −3.4 dB octave −1 at the low and high frequency side respectively. The phase changes from +60° at 0.03 Hz to −120° at 15 Hz. 3. The sensitivity curve determined by recording the respiratory reflex has a plateau from 0.1 to 1 Hz, with slopes of +2.8 and -;11.4dB octave −1 . The highest sensitivity for sinusoidal electrical stimuli was 40nV cm −1 peak-to-peak, in the frequency range 0.1 to 1 Hz. 4. We suggest that the difference between the two curves reflects the convergence of primary afferents on to secondary neurones. 5. We conclude that the low pass filter properties are not imposed by the time constant of the ampulla wall. 6. The low frequency slope found in the behavioural curve presumably represents the slope of the receptor-cell-synapse complex. 7. The Lorenzinian ampullae apparently act as peripheral filters with different tuning curves; these must play a part in frequency discrimination.

Journal ArticleDOI
TL;DR: In this article, a new high-performance surface-acoustic-wave (SAW) filter for use in mobile telephones is presented, from the new filter configuration to the final device operation, a low-loss weighting technique in an interdigital transducer, a new resonant structure, computer simulation procedures, and material properties are treated.
Abstract: A new high-performance surface-acoustic-wave (SAW) filter for use in mobile telephones is presented in this paper. The design for the actual realization of the new filter is examined, from the new filter configuration to the final device operation, A low-loss weighting technique in an interdigital transducer (IDT), a new resonant structure, computer simulation procedures, and material properties are treated. Experimental results with this SAW filter included an 830-MHz center frequency, 3-percent bandwidth, insertion loss of as low as 3.5 ~ 4.0 dB, and 50-dB sidelobe suppression filter.

Journal ArticleDOI
TL;DR: A wave digital filter (WDF) two-port has two input and two output-terminals and by using these to appropriately connect a WDF to its transpose, the filtering effect is fully compensated except for an all-pass phase.
Abstract: A wave digital filter (WDF) two-port has two input and two output-terminals. By using these to appropriately connect a WDF to its transpose, the filtering effect is fully compensated except for an all-pass phase, and this independently of any selectivity requirement. This remains true if at the points of interconnection, every second sample is reduced to zero, provided that a certain condition, easily to be satisfied exactly, is fulfilled. Very efficient solutions are then possible. The method is of interest, e.g., for subband coding.

Proceedings ArticleDOI
Vatche Vorperian1
24 Jun 1985
TL;DR: In this paper, the small-signal response of resonant converters to perturbations in the switching frequency and the input voltage is obtained under high-Q approximation and operation away from resonance.
Abstract: The load parameter Q and the ratio of switching frequency to resonant frequency F s /F o completely characterize the operation of resonant converters. The dc and exact analysis have been reported earlier whereby the results were obtained numerically. In this work approximate and simple results of the small-signal response of resonant converters to perturbations in the switching frequency and the input voltage is obtained under high-Q approximation and operation away from resonance. The results of the approximate and exact analysis are in good agreement.

Journal ArticleDOI
TL;DR: This work gives a mathematical development of the DPS filter properties, provides information required to easily and accurately construct even many coefficient filters, and compare the properties of this filter with those of the more commonly used filters of the same class.
Abstract: The discrete prolate spheroidal (DPS) filter is one of the class of nonrecursive finite impulse response (FIR) filters. The DPS filter, first introduced by Tufts and Francis [1], is superior to other filters in this class in that it has maximum energy concentration in the frequency passband and minimum ringing in the time domain. Slepian [2] gives a complete discussion of DPS function properties. We give a mathematical development of the DPS filter properties, provide information required to easily and accurately construct even many coefficient filters, and compare the properties of this filter with those of the more commonly used filters of the same class. We note that use of the DPS filter allows for particularly useful statements of data time/frequency resolution "cell" values and that overall it forms an especially useful, though little known tool for digital signal processing.

Journal ArticleDOI
TL;DR: In this article, a method of designing higher-order filters using current conveyors (CCs) is presented in which a new type of impedance scaling of LC ladder prototypes facilitates direct incorporation of a class of nonideal simulated inductors and FDNRs in active filter design.
Abstract: A novel method of designing higher-order filters using current conveyors (CCs) is presented in which a new type of impedance scaling of LC ladder prototypes facilitates direct incorporation of a class of nonideal simulated inductors and FDNRs in active filter design. The resulting structures are minimum-sensitive and require a very small number of CCs (typically, equal to the number of reactive elements in the passive prototype). Experimental results have confirmed the practical validity of the ideas.

PatentDOI
Robert Johannes Sluijter1
TL;DR: In this paper, a digital speech coder of the baseband RELP-type (Residual-Excited Linear Prediction) comprises a transmitter (1) having an LPC-anaylser (10), a first adaptive inverse filter (11), a decimation lowpass filter (26), and an encoding-and-multiplexing circuit (17), and a receiver (2) having a demultiplexing-anddecoding circuit (21), an interpolator (27), an adaptive synthesizing filter (14).
Abstract: @ A digital speech coder of the baseband RELP-type (Residual-Excited Linear Prediction) comprises a transmitter (1) having an LPC-anaylser (10), a first adaptive inverse filter (11), a decimation lowpass filter (26) for selecting the baseband prediction residue and an encoding-and-multiplexing circuit (17), and a receiver (2) having a demultiplexing-and-decoding circuit (21), an interpolator (27) and a first adaptive synthesizing filter (14). The occurrence of "tonal noises" due to the spectral folding in interpolator (27) is effectively counteracted by arranging prior to the decimation lowpass filter (26) in the transmitter (1) a second adaptive inverse filter (28) which with the aid of an autocorrelator (31) removes possible periodicy from the speech band residue, and by including subsequent to the interpolator (27) in the receiver (2) a corresponding second adaptive synthesis filter (32), which reintroduces the desired periodicity in the excitation signal.

Journal ArticleDOI
TL;DR: In this paper, a priori knowledge that the input of a linear system is weighted by some kind of profile function can be exploited for restoring the output signal by means of the singular value technique.
Abstract: The a priori knowledge that the input of a linear system is weighted by some kind of profile function can be exploited for restoring the output signal by means of the singular value technique. The authors determine the analytic expression of the singular system for two typical cases in which the system behaves like a low-pass filter and the profile function has the same form as the impulse response of the filter. The analysis leads us to predict the performance of the restoration process in the presence of noise. It is shown that under suitable conditions the resolution of the restored signal can be twice that of the unrestored output.

Journal ArticleDOI
01 Oct 1985
TL;DR: In this paper, a parallel form adaptive pole-zero filter implemented in the frequency domain is presented, which can exactly model any proper rational system with distinct poles and it permits direct monitoring of pole trajectories during adaptation so that instability of the filter is easily prevented.
Abstract: A parallel form adaptive pole-zero filter implemented in the frequency domain is presented. This filter can exactly model any proper rational system with distinct poles and it permits direct monitoring of pole trajectories during adaptation so that instability of the filter is easily prevented.

Patent
Daniel Senderowicz1
28 May 1985
TL;DR: An integrated circuit for filtering signals by having cascaded switched capacitor sampling filters is described in this paper. But it does not specify the number of filters that need to be sampled at a lower rate to inhibit anti-aliasing.
Abstract: An integrated circuit for filtering signals by having cascaded switched capacitor sampling filters. The circuit includes a transmit section which has an anti-aliasing filter, a core section filter, a highpass filter and an encoder for providing analog-to-digital conversion. Each successive filter is sampled at a lower rate to inhibit anti-aliasing. The circuit also includes a receive section which has a digital-to-analog decoder, an output buffer, a receiver core filter and a power amplifier.

Patent
19 Jun 1985
TL;DR: In this article, an all-pass fiber optic filter is formed by cascading all-pole and all-zero lattice filters, and by processing the resulting filtered output signal in a subtractive detection system.
Abstract: A fiber optic lattice filter having a transfer function wherein the poles and zeros are adjustable independently of each other. The filter comprises a cascaded configuration of recursive (100) and non-recursive (102) fiber optic lattice filters. In one preferred embodiment, an all-pass fiber optic filter is formed by cascading all-pole and all-zero lattice filters, and by processing the resulting filtered output signal in a subtractive detection system (104). This detection system produces a signal which represents the difference between two signal outputs provided by the all-zero filter section, and which is adjustable in magnitude, thereby providing an overall filtering function which is capable of handling both positive and negative valued input signals.

Patent
20 Aug 1985
TL;DR: In this paper, an integrator (10) comprises a transconductance amplifier (20) and a capacitor (65) which is connected between the amplifier output terminal and the amplifier ground.
Abstract: An integrator that is useful in forming low pass, band pass, high pass, and band stop filters. The integrator (10) comprises a transconductance amplifier (20) and a capacitor (65) which is connected between the amplifier output terminal and the amplifier ground. When implemented as a monolithic IC, the integrator gain is fundamentally process independent. A ladder structure comprising one or more of these integrators provides high order filtering characteristics without many of the problems associated with conventional filter devices. In addition, the integrator (610) provides stop band zero filter characteristics at the filter output terminal when a capacitor (675) is connected across the differential input terminals of the integrator.

Journal ArticleDOI
TL;DR: A multi-output second-order digital filter structure without zero-input and constant-input oscillations is presented, which could be used for the realization of low-pass, high-Pass, band- pass, and band-stop Butterworth, Chebyshev, and elliptic digital filters, and all-pass digital filters.
Abstract: A multi-output second-order digital filter structure without zero-input and constant-input oscillations is presented. It could be used for the realization of low-pass, high-pass, band-pass, and band-stop Butterworth, Chebyshev, and elliptic digital filters, and all-pass digital filters. The overall structure consists of two delays, three multipliers, and nine adders, which could be adopted for VLSI implementation.

Journal ArticleDOI
01 Feb 1985
TL;DR: A gradient ascending algorithm is proposed to update the center-frequency-dependent coefficients of the filter to maximize the performance function.
Abstract: Mean-square output of a center-frequency variable bandpass filter is employed as the performance criterion to make the filter self-adjusting to the center frequency of the input signal. A gradient ascending algorithm is proposed to update the center-frequency-dependent coefficients of the filter to maximize the performance function.

Patent
16 Jul 1985
TL;DR: In this article, the authors proposed an optical recursive filtering system, in which a signal beam of optical radiation is passed through the optical filtering means a multiplicity of times, and subsequent reflections back through the filter with a consequent further filtering of the signal beam can be accomplished by appropriately positioning the reflectors in the Fourier plane of the spatial filter.
Abstract: An optical recursive filtering system in which a signal beam of optical radiation is passed through the optical filtering means a multiplicity of times. The filtering system has an optical Fourier transform means, a spatial filter, optical inverse Fourier transform means and a pair of reflectors in the Fourier plane of the spatial filter. An input signal beam to be filtered is optically Fourier transformed by the transform means and is passed through the spatial filter where unwanted frequencies of the signal beam are attenuated. The filtered beam is reflected by one of the reflectors back through the filter and the second mirror reflects it back through the filter a third time. Subsequent reflections back through the filter with a consequent further filtering of the signal beam can be accomplished by appropriately positioning the reflectors. After multiple filtering passes, the filtered beam is extracted for utilization. By maintaining the recursions of the beam in the Fourier plane of the filter, which preferably is of a programmable type, the optical throw of the filter system can be significantly reduced and a flexible imaging system without the restraints of external recursion is realizable in a robust structure with fewer components. An embodiment of the system being used in a heterodyning RF optical filtering system is described.