In North-Indian-Music-System(NIMS),tabla is mostly used as percussive accompaniment for vocal-music in polyphonic-compositions. The human auditory system uses perceptual grouping of musical-elements and easily filters the tabla component, thereby decoding prominent rhythmic features like tala, tempo from a polyphonic composition. For Western music, lots of work have been reported for automated drum analysis of polyphonic composition. However, attempts at computational analysis of tala by separating the tabla-signal from mixed signal in NIMS have not been successful. Tabla is played with two components - right and left. The right-hand component has frequency overlap with voice and other instruments. So, tala analysis of polyphonic-composition, by accurately separating the tabla-signal from the mixture is a baffling task, therefore an area of challenge. In this work we propose a novel technique for successfully detecting tala using left-tabla signal, producing meaningful results because the left-tabla normally doesn't have frequency overlap with voice and other instruments. North-Indian-rhythm follows complex cyclic pattern, against linear approach of Western-rhythm. We have exploited this cyclic property along with stressed and non-stressed methods of playing tabla-strokes to extract a characteristic pattern from the left-tabla strokes, which, after matching with the grammar of tala-system, determines the tala and tempo of the composition. A large number of polyphonic(vocal+tabla+other-instruments) compositions has been analyzed with the methodology and the result clearly reveals the effectiveness of proposed techniques.