The circuit has an input terminal (1) for supplying a picture signal (CS) formed line and field-sequentially with line and field or frame periods (TV) and an output terminal (2) for supplying a processed picture signal (CS') to be applied to a picture display device (5) comprising a picture display tube operating by way of electron beam scanning (e) of a display screen (8). In the circuit the input terminal (1) is coupled to a filter circuit (10) which has a first output (11) and a second output (12) for supplying a low-frequency (CS.sub.L) or high-frequency (CS.sub.H) picture signal component, respectively. The first output (11) is coupled via an amplifier circuit (16) to a first input (21) of a time-division multiplex circuit (20) having a second input (22) to which the first output (11) and the second output (12) of the filter circuit (10) are coupled each via an amplifier circuit (17, 18) and an adder circuit (19). The time-division multiplex circuit (20) has a switching input (23) which is coupled to an output (29) of a switching signal generator (28) for supplying a periodical switching signal (VS) of the double field or frame period (2TV). An output (24) of the time-division multiplex circuit (20) is coupled to the output terminal (2) of the picture signal processing circuit. The resultant spatial time-division multiplex display yields the improved high-frequency picture resolution.