Showing papers on "Linear phase published in 1974"

On the behavior of minimax fir digital Hilbert transformers

Abstract: Optimum (in a minimax sense) linear phase FIR Hilbert transformers can be designed efficiently using a Remez optimization procedure. This paper presents useful design data on wideband Hilbert transformers with even and odd values of N, the impulse response duration (in samples) of the filter. Based on these data, the following observations can be made: (i) In the case of equal lower and upper transition regions, Hilbert transformers with odd values of N can be realized more efficiently than those with even values of N, assuming the same peak errors of approximation for both cases. This is because every other impulse response sample is exactly zero for odd values of N. (ii) The peak approximation error for Hilbert transformers with odd values of N is determined primarily by the minimum of the values of the lower and upper transition widths. (iii) The peak approximation error for Hilbert transformers with even values of N is determined primarily by the lower transition width of the filter. (iv) The smaller the bandwidth of the Hilbert transformer, the faster the decrease of peak error of approximation with decreasing bandwidth of the Hilbert transformer. (v) The larger the value of N, the faster the decrease of peak approximation error with decreasing bandwidth of the Hilbert transformer. These observations lead to the conclusion that the bandwidth of the Hilbert transformer should be made as small as possible, and that odd values of N should be used, whenever possible, for efficient direct form realizations. A set of tables of values of the impulse response coefficients is included for several different bandwidth Hilbert transformers and for both even and odd values of N.

On the behavior of minimax relative error fir digital differentiators

Abstract: Optimum (in a minimax relative error sense) linear phase FIR digital differentiators can be designed in an efficient manner using a Remez optimization procedure. This paper presents data on wideband differentiators designed with even and odd values of N, the filter impulse response duration in samples. Based on these data, several interesting observations can be made, including: (i) Differentiators with even values of N have peak relative errors which are approximately one to two orders of magnitude smaller than identical bandwidth differentiators with odd values of N, and with the same number of multiplications per sample in a direct convolution realization. (ii) The smaller the bandwidth of the differentiator, the faster the decrease of the peak relative error with increasing N. (iii) The larger the value of N, the faster the decrease of the peak relative error with decreasing bandwidth. These observations lead to the conclusions that the bandwidth of a differentiator should be made as small as possible, and that even values of N should be used whenever possible. Complete tables of values of the impulse response coefficients are included for several wideband differentiators for even and odd values of N.

Two channel test instrument with active electronicphase shift means

Abstract: A network analyzer is provided with an electronically variable phase shifter in the IF portion of the reference channel, and the phase shifter is connected to sweeping signal generator (sweeper) driving the device under test. As the output frequency of the sweeper changes, the control signal to the phase shifter changes the phase shift in the IF portion of the reference channel, compensating for phase differences between the test and reference signals due to different line lengths in the two signal paths. The electronically variable phase shifter may comprise a linear phase shifter such as a phase lock loop along with a frequency mulitplier and down converter to multiply the phase shift produced by the phase shifter.

Phase Distortion of Averaged Electroencepha

Abstract: Analog filters employed in most averaged electroencephalic response (AER) recording systems impose some phase distortion on recorded AER. Phase distortion of the response results in a real time shift of peak latencies. The extent of this distortion, in general, is determined by the cutoff frequencies of the filter band in relation to the spectrum of the response. If the filter band employed is quite restrictive, the shift of latencies can be large. For purposes of threshold audiometry, filter-imposed phase shifts will not usually prevent simple response identification. However, if such time shifts in the data are not accounted for in interclinic or published communications, the response information could be misleading and confusing.

Optimizing non-recursive digital filters to non-liner phase characteristics

Abstract: Various methods based on optimization have been used to design linear phase filters. One such method has been to use a general-purpose optimization program to minimize some error criterion, a function of the filter coefficients and of the error between the specified and achieved gain responses. However, if this were to be used with arbitrary phase designs, the error criterion would have to be formulated as a function that combines the gain and phase errors in a meaningful way. It is shaown here that this particular difficulty can be avoided by regarding the phase specification as a deviation from the linear phase and splitting the characteristic into real and imaginary components, rather than gain and phase, and optimizing separately.

Phase change measuring circuit

Abstract: A device for measuring the phase change of an input signal over a specified period comprising a phase-locked tracking filter including a high frequency voltage-controlled oscillator (VCO), a frequency divider to give local oscillator signal at the same frequency as the input signal and a counter counting cycles of the VCO whose phase change in any period is N times the input phase change to allow 1/N period resolution, N being an arbitrary integer. The phase change measuring circuit thus allows phase measurement with a resolution within a small fraction of one cycle.

Transitional Legendre Thomson filters

Abstract: Among those filters which exhibit both a good frequency and transient behavior, we suggest a new kind of filter, of the transitional type, whose characteristics lie between those of monotonic with maximum cutoff rate (Legendre) and linear phase (Thomson) filters. Attenuation, group delay, and step responses are given. Characteristics curves for the design of a fifth-order transitional Legendre-Thomson (TLT) filter are also presented.

Phase-Locked Loop Pull-In Frequency

Abstract: A computerized procedure for obtaining the pull-in frequency of a phase-locked loop is described. The procedure, which consists of solving for the limit cycle of the out-of-lock loop and finding the frequency offset below which no solution exists, is quite general with respect to phase detector function and loop filter. It is applied in this study to the case of a second-order loop with a sinusoidal phase detector. The results of the study give normalized pull-in frequency X as a function of the damping factor \zeta and normalized natural frequency β of the linearized closed loop. A review of several previously published investigations of this case is given, and the limitations identified point the way to the more exact solution described here. In addition, an experimental study is described which produces excellent agreement with the new results, and a curve-fitting procedure is outlined which leads to a highly accurate functional description of X in terms of β and \zeta .

Phase modulation and self-modulation of light in three-photon processes

Abstract: An analysis shows that phase changes in the phase-matched conversion of the frequency of light in piezoelectric crystals can be utilized in fast-response self-bleachable filters and controlled switches. A one-dimensional steady-state approximation is used to study phase modulation of a weak signal in up or down frequency conversion in a transparent piezoelectric crystal pumped at a fixed level. The same approximation is used in considering phase self-modulation of the pumping radiation under frequency doubling conditions. Dependence of various quantities on the input amplitude are obtained for different degrees of detuning; these quantities are the relative intensity and phase shift of the pumping radiation at the output of a frequency doubler, and the degrees of self-bleaching and bleaching in the case of parametric amplification and frequency addition.

Color subcarrier frequency comparator

Abstract: Apparatus for measuring the frequency of a reference signal which utilizeshe color subcarrier signal of a television receiver as a standard frequency signal. In a first embodiment, the reference signal controls a circuit to develop bursts of a synthesized color subcarrier signal, gated at the horizontal line rate of a color television receiver. The synthesized signal is superimposed on the broadcast television signal and applied to the receiver to produce a modulation bar on the screen. Any frequency/phase difference between synthesized and broadcast color subcarrier signals will cause the modulation bar to move laterally across the screen, and/or cause the sequence of colors within the modulation bar to vary. Movement of the modulation bar is a coarse indication of frequency difference and change of the color sequence within the bar is a precise indication of phase difference. In a second embodiment, the locally synthesized color subcarrier signal and the color subcarrier signal of the television receiver are compared in a linear phase comparator to develop a signal having an instantaneous voltage proportional to the phase difference between the two signals. The phase signal controls a generator which develops a cursor line on the screen. Movement of the line across the screen provides a coarse indication of phase difference between the subcarrier signals. The phase signal is also applied to a digital counter which affords a precise readout of the phase difference between the signals.

The equidistant linear phase polynomial for distributed and digital networks

Abstract: A closed form expression for the recurrence formula for the generation of polynomials whose phase interpolates to linear characteristics at equidistant frequencies is presented. This polynomial may be used directly in the design of both distributed and digital networks and, due to the recurrence formula, readily generated. Since the complete proof of this formula is extensive and not required for normal use of this polynomial, it has been outlined in an Appendix.

Surface acoustic wave code generator

Abstract: There is disclosed a phase shift modulated pseudo-noise code generator. This generator employs a surface acoustic wave tapped delay line with feedback. A radio frequency phase reference signal is provided at the tapping points. The radio frequency phase of the modulated carrier is compared with the radio frequency phase of the reference signal at each tapping point from which the feedback is derived. The comparison is performed in a surface acoustic wave modulo-2 adder. This comparison overcomes the phase shift due to temperature effects.

Receiver for the reception of pulse signals transmitted by means of frequency shift modulation

Abstract: In a receiver for frequency shift modulation an accurate demodulation of the received signal and a low sensitivity to noise and interference is obtained by using a frequency discriminator in which a number of parallel channels are incorporated between a common frequency generator and a phase comparator and in which each channel includes a frequency divider provided with a phase adjusting circuit, while the different frequency dividers are cyclically adjusted in phase as a function of the zero crossings in the received signal and the demodulated signal is derived from a lowpass filter connected to the phase comparator.

Ambiguity free digital averaging phase meter

Abstract: The inherent phase ambiguity that results from the measurement of the phase difference between a reference signal and a data signal having a zero phase relationship is eliminated by adding 360° to phase differences between 0° and 180° Phase differences between 180° and 360° are measured in the conventional manner Both the reference signal and the data signal are divided in frequency and the phase difference between the divided signals are compared The data signal is inhibited for only 180° of the original reference signal to prevent an initial comparing of phase differences between the data signal and the reference signals to establish the proper polarity relationship between the half rate data signal and the half rate reference signal

Design of minimum-phase digital filters from linear-phase prototypes

Abstract: General methods are described for transforming any linear-phase f.i.r. filter into one having minimum phase, half the degree and a magnitude response that is (or approximates to) the square root of that of the original linear-phase filter.

Random phase modulating time base and method to improve measurement averaging counter resolution

Abstract: A time base and method to provide resolution improvement for measurement averaging counters when measuring an applied signal comprising time intervals or pulsed frequencies repetitively occurring at rates synchronous to a counter''s clock frequency. The phase of a reference frequency is varied in response to a random signal. The phase modulated reference frequency is applied to a frequency multiplier chain which multiplies both the frequency and the effective amount of phase modulation. The randomly phase shifting output of the frequency multiplier chain is applied as a clock signal to a measurement averaging counter thereby destroying coherence between the clock signal and the applied signal and allowing statistical averaging to take place.

Phase sensitive detector and reference generator for use in third derivative locking of the frequency of a laser to a saturated absorption feature

Abstract: Design criteria are discussed and circuits are presented for a phase sensitive detector and its reference signal generator to be used in third derivative locking of the frequency of a laser to the centre of a saturated absorption feature. The use of a phase locked loop enables the operating frequency to be continuously variable over the range 4.7-47 kHz so that it can be matched to a mechanical resonance of the transducer used to frequency modulate the laser.

Phase and frequency comparator

Abstract: The comparator comprises a circuit for detecting the sign of the phase-shift of the reference signal relatively to the second signal for a predetermined phase of the latter. It delivers a corresponding binary phase difference signal. A second circuit selects those changes in values of the phase difference signal which occur for a phase of the reference signal comprised in a predetermined phase interval, and are thus surely representative of a change in the sign of the frequency difference.

Low pass filter apparatus

Abstract: The combination of a linear phase bandpass filter between a modulator and demodulator wherein the equivalent of a lowpass filter is produced by increasing the frequency of the signal to be lowpass filtered by carrier modulating it, bandpass filtering the increased frequency signal and demodulating the bandpass filtered signal to produce a lowpass filtered output having linear phase characteristics.

In-Line Waveguide Selective Linear Phase Filters

Abstract: A procedure is described whereby narrow-band waveguide selective linear phase filters may be designed from a low-pass prototype linear phase network. The structure is comprised of a cascade connection of basic sections, each containing a direct-coupled cavity together with a dual-mode resonator. Each dual-mode resonator takes the form of a square guide mounted on the broad wall of the main rectangular guide and coupled to this guide by a small aperture. Explicit formulas for the susceptance of the coupling apertures and electrical lengths of the cavities are given in terms of the low-pass prototype.

Band-pass filter for frequency modulated signal transmission

Abstract: A band-pass filter comprises a delay circuit comprising a plurality of unit delay elements connected in cascade arrangement and receiving as input a signal including a frequency modulated signal and a coefficient summing circuit for carrying out coefficient summing of the outputs of specific delay units of the delay circuit and producing as output the frequency moudlated signal which has been band-pass filtered. This band-pass filter has a transmission characteristic representable by H(jω) = [ 1 - a(ω - ω.sub.o).sup.2] e - j .sup.ω.sup.τd , where: a is a constant imparting an attenuation characteristic of the filter; ω o is an angular frequency of a carrier wave of a frequency modulated signal and a center angular frequency of the band-pass filter; and τd is a delay time of the band-pass filter.

Optimal Detection of a Signala with Time-Varying Carrier Phase

Abstract: The problem considered in this paper is the detection of a signal known except for time-varying carrier phase in white Gaussian noise. The method of attacking this problem is to model the time-varying carrier phase as a Markov process. Fourier transform techniques are then applies to yield a simple time-wise adaptive form for the phasetracking detector. Optimal accounting for the time variations in phase is accomplished via a simple algorithm which serves to update the detector memory. Furthermore, it is shown that this memory updating operation is a discrete linear filter whose impulse response is a simple function of the previous memory state and the Markov transitional statistics on the phase. A priori knowledge regarding the phase is summarized in the initial impulse response of the updating filter.

On the Usefulness of Group Delay and/or Phase Delay Parameters for Low Distortion Transmission

Abstract: It is argued that transmission systems/filters, etc., design must be carried out basically in the time domain in terms of rise time, overshoot or undershoot of the instantaneous amplitude/ phaselfrequency specifications. No attempt should be made to define the group delay characteristics because it is neither sufficient, nor necessary. Group delay approximating functions and measurements should be kept where they belong; in the design and measurements concerned with delay, lines.

Linear phase filter with determinable gain characteristic

Abstract: Amplifiers are added at selected junctions between the reactances of a linear phase LC filter of the kind having an open circuit termination, and the outputs of the amplifiers are added to produce an output signal linear in phase with the input signal, but compensated as desired in respect of its frequency vs. amplitude characteristic. The characteristic is determinable by selecting various different values for the gains of the amplifiers.

Frequency response characteristics of an isolated photoreceptor

Abstract: The transmembrane voltage change in response to light was studied in the barnacle photoreceptor by using sinusoidal and impulse changes in light intensity. The input-output relation is linear if the transmembrane voltage change does not exceed 10 mV. The frequency response is of low pass character with attenuation beginning at 1 cps. The system can best be represented by a third order transfer function consisting of a first order pole, a complex second order pole, and a transport delay. Lower temperature causes greater high frequency attenuation of the voltage response. Background illumination, depolarization, and wavelength do not affect the frequency response within the linear range. Beyond the linear range the elements of a differentiating process are introduced. This is probably due to a disproportionate increase in cell conductance.

Dielectric Loss in Coaxial Cables via Phase Delay Measurements

Abstract: Determining dielectric loss as a function of frequency in high frequency coaxial cables is a requirement for efficient design of long cable systems. A method for determining dielectric loss based on attenuation and phase delay measurements along with low frequency capacitance data and nominal cable specifications is presented in Part I. The pi-point method of making precision phase delay measurements is reviewed and contrasted to earlier methods in Part II. A 10-nmi-length of SF ocean cable at frequencies up to 10 MHz is considered as an example. For this case the number of wavelengths N is approximately 1000 at 10 MHz. A measurement technique is described and a test setup, including circuitry, is presented for making pi-point phase measurements and for determining N with zero error. Measurement errors, converted to equivalent frequency errors, with detector noise, mismatch, attenuator phase shift, and frequency counter errors being the significant contributors are considered in Part III. When all worst case errors are added, the accuracy of the delay measurement is better than 0.3 ppm at 10 MHz for the sample case under study.

The step responses for even degree equidistant linear phase filters

Abstract: The step response curves for the above class of filters are presented for degrees 4–12. The filters have been normalized so that their 3 dB point occurs at ω = 1 rad sec, to permit comparison with published step responses. The curves show that for n > 6 they closely approximate the ideal case.

This paper presents a new dual mode circular waveguide cavity structure which realizes the general class of coupled cavity transfer functions. Included are the exact elliptic function response and the linear phase and arbitrary phase responses. Experimental data taken on 4- and 8-pole narrowband elliptic function filters centered at approximately 4 GHz are described and shown to correlate well with theory.

Abstract: This paper presents a new dual TF ~ ~ ~ mode circular waveguide cavity structure which realizes the optimum electrical response and retains all the mechanical advantages of the longitudinal dual mode filter. The filter design procedure is presented with specific emphasis on the input-output port design and on the improvement of the out-of-band rejection. Experimental results for 4- and 8-pole elliptic function narrow-bandpass filters centered at approximately 4 GHz are described.

Phase shifting circuit

Abstract: A phase shifting circuit having a first delay element with a time constant τ1, a second delay element with a time constant τ2 smaller than τ1 and a pulse generating element such as p-n-p-n transistor produces phase shifting pulses with respect to a reference phase upon application of a step-up voltage to the first delay element and periodic pulses to the second delay element. The two signals rise at different rate following respective curves and the two curves intersect at various points. The pulses generating element compares the two signals and produces a pulse at the instant the two signals coincides at the intersecting points. The phase shifting pulses have a linear phase relation with respect to the reference phase which is equal to the phase of the periodic pulses applied to the second delay element.