The graph shows one of the two central figures from Campbell & Robson (Fig. 3, p. 556). What is plotted for the open symbols are the [contrast thresholds; contrast sensitivities (1 over detection threshold); luminance thresholds; luminance sensitivities (1 over detection threshold)] on the y-axis against [line width in deg; spatial frequency in wavelength lambda; line width in cpd; spatial frequency in cpd; luminance modulation rate]. The open squares show the data for the [square-wave grating; sin-wave grating; rectangular-wave grating; sawtooth-grating], the open circles for the [square-wave grating; sin-wave grating; rectangular-wave grating; sawtooth-grating] . The filled black circles show the ratio of the [square-to-sine; square-to-rectangular; square-to-sawtooth; sin-to-rectangular; sin-to-sawtooth] [thresholds; sensitivities]. The solid black line marks the prediction at [4/pi; pi/4; 4/3; 3/4] derived from the Fourier series of the stimuli. The dashed line marks the prediction of a [simple corner detector; simple edge detector; multi-channel; simple peak-detector] model of early spatial vision.
The graph shows one of the two central figures from Campbell & Robson (Fig. 3, p. 556). What is plotted for the open symbols are the contrast sensitivities (1 over detection threshold) on the y-axis against spatial frequency in cpd. The open squares show the data for the [square-wave grating, the open circles for the sin-wave grating. The filled black circles show the ratio of the square-to-sine sensitivities. The solid black line marks the prediction at 4/pi derived from the Fourier series of the stimuli. The dashed line marks the prediction of a simple peak-detector model of early spatial vision.
In [______] Campbell and Robson published their seminal paper entitled
Application of Convolution Analysis to the Visibility of Natural Stimuli
Application of Fourier Synthesis to the Visibility of Natural Stimuli
Application of Fourier Analysis to the Visibility of Natural Stimuli
Application of Fourier Synthesis to the Visibility of Gratings
Application of Fourier Analysis to the Visibility of Gratings
Application of Convolution Analysis to the Visibility of Gratings
In 1968 Campbell and Robson published their seminal paper entitled Application of Fourier Analysis to the Visibility of Gratings
What is Fourier analysis and why is it useful for understanding perception? How is Fourier analysis related to the types of stimuli that psychophysicists use?
Fourier analysis is a mathematical procedure for decomposing a complex signal into its component sine waves. If the individual sine waves are re-combined, they will reproduce the original signal. Fourier analysis is used extensively by perception researchers because it provides a good description of stimuli and also because several perceptual systems perform Fourier analysis when processing stimuli (e.g., the visual and auditory systems). In terms of stimuli based on sine waves, psychophysicists tend to use pure tones in the auditory domain and sine wave gratings in the visual domain. Sine waves may vary in their wavelength (distance for one full cycle of oscillation of the wave), period (time for one full cycle of oscillation of the wave), phase (relative shift of the sine wave) and amplitude (height of the sine wave, i.e. contrast in vision and loudness in hearing).
[________] is a mathematical procedure by which a signal can be separated into component sine waves at different frequencies. Combining these sine waves will reproduce the original signal.
Bruce Henning and colleagues published a series of experiments in the mid 1970s which were [inconsitent; consistent] with the [non-independent; independent; correlated; covarying] [multi-channel; single-channel] model of Campbell & Robson. Henning et al.'s experiments were inspired by the "missing fundamental" in [object recognition without the fundamental spatial frequency; auditory frequency discrimination; auditory pitch perception; motion perception; auditory aound localization] , and they used both [___________] (AM) as well as [___________] (QFM) gratings as stimuli. Figure A shows the amplitude spectrum of (AM ; QFM ; both) gratings
. Figure B shows the appearance and the cross-section through a __ grating and its constituent 4f, 5f and 6f gratings, Figure C shows the respective graphs for a ___ grating. Henning et al. reported to find strong interactions (masking) between (a sine-wave with frequency 1f and a QFM ; a sine-wave with frequency 1f and an AM) grating composed of 4f, 5f and 6f: According to Campbell and Robson there should have been (a, no) interaction (masking) between the stimuli, however. Furthermore, there was clearly less masking with a (AM ; QFM)
grating as opposed to the (QFM; AM) grating, and this should (not have ; have)
happened, pointing to the importance of (phase relations ; …)
between the stimulus components, contrary to the findings of (Campbell ; Robson; Nachmias ; Graham)
and (Campbell ; Robson; Nachmias ; Graham) .
Bruce Henning and colleagues published a series of experiments in the mid 1970s which were inconsistent with the independent multi-channel model of Campbell & Robson. Henning et al.'s experiments were inspired by the "missing fundamental" in auditory pitch perception, and they used both amplitude modulated (AM) as well as quasi-frequency modulated (QFM) gratings as stimuli. Figure A shows the amplitude spectrum of both AM and QFM gratings . Figure B shows the appearance and the cross-section through a QFM grating and its constituent 4f, 5f and 6f gratings, Figure C shows the respective graphs for a AM grating. Henning et al. reported to find strong interactions (masking) between a sine-wave with frequency 1f and an AM grating composed of 4f, 5f and 6f: According to Campbell and Robson there should have been no interaction (masking) between the stimuli, however. Furthermore, there was clearly less masking with a QFM grating as opposed to the AM grating, and this should not have happened, pointing to the importance of phase relations between the stimulus components, contrary to the findings of Graham and Nachmias .
Prior to the seminar work of [__________] and [__________] published in [1996; 2010; 1971; 1975; 1968; 1987; 1982; 2003; 1979] , researchers in pattern perception, often referred to as [__________] [no capital letters!], thought of the stimuli exclusively in the [space; Fourier] domain, in terms of [lines, corners and edges; spatial frequency content]. After the publication of "Application of Fourier Analysis to the Visibility of Gratings" in the Journal of Physiology, however, vision researchers up to this day always consider stimuli [also ; only; never] in the [Fourier; space] domain. Additional experimental data [consistent; inconsitent] with the linear, independent multi-channel model came, e.g., from Blakemore and Campbell's [adaptation; masking; recognition; identification; detection] studies, or from the famous 1f, 3f and phase manipulation experiments by [__________] [surname only!] and [__________][surname only!], published in [1996; 2010; 1971; 1975; 1968; 1987; 1982; 2003; 1979] , or the elegant experiment by [__________][surname only!] and [__________] [surname only!] from [1996; 2010; 1971; 1975; 1968; 1987; 1982; 2003; 1979] , showing that [a single; two many] cycle(s) of a sine-wave grating could be [easier; equal] to detect than [many; a single; two] cycle(s) if the signal was [inhibited; masked; adapted away] by [narrow-band; wide-band; broad-band; white; pink] visual noise. Whilst there exists a large body of work [questioning; supporting; non-conclusive with respect to] the linear, independent multi-channel model, there are notable exceptions. One of the most prominent is a study by [__________] [surname only!] and colleagues from [1996; 1968; 1975; 1971; 1982; 1987; 2010; 2003; 1979] , based on an [__________] phenomenon, the "missing fundamental".
Prior to the seminar work of Campbell and Robson published in 1968 , researchers in pattern perception, often referred to as early spatial vision oder spatial vision [no capital letters!], thought of the stimuli exclusively in the space domain, in terms of lines, corners and edges. After the publication of "Application of Fourier Analysis to the Visibility of Gratings" in the Journal of Physiology, however, vision researchers up to this day always consider stimuli also in the Fourier domain. Additional experimental data consistent with the linear, independent multi-channel model came, e.g., from Blakemore and Campbell's adaptation studies, or from the famous 1f, 3f and phase manipulation experiments by Graham [surname only!] and Nachmias [surname only!], published in 1971 , or the elegant experiment by Carter [surname only!] and Henning [surname only!] from 1971 , showing that a single cycle(s) of a sine-wave grating could be easier to detect than many cycle(s) if the signal was masked by narrow-band visual noise. Whilst there exists a large body of work supporting the linear, independent multi-channel model, there are notable exceptions. One of the most prominent is a study by Henning [surname only!] and colleagues from 1975 , based on an auditory phenomenon, the "missing fundamental".
Given is a sine wave, 𝑔_{sine}(𝑥)=sin[𝜔₀𝑥],as a function of 𝑥 with fundamental frequency 𝑓₀ — and thus 𝜔₀=2𝜋𝑓₀— and unit amplitude. Which of the following equations correctly expresses the Fourier series of a rectangular wave 𝑔_{sq}(𝑥) with the same fundamental frequency and the same unit amplitude?
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