The most important and crucial tasks in online/ offline handwritten document recognition is line/word segmentation. As compared to a printed document, line/word segmentation of handwritten document is a complicated task. The typical handwritten document have irregular skews, overlapped lines, variable gaps between lines and different size words. The recent improvements in machine learning algorithms introduced an end-to-end line level recognition of printed and handwritten text with good performance. But still line segmentation of paragraph is required before proceeding for recognition. In this paper, we proposed an improved piece-wise projection based line segmentation method for handwritten documents which is more accurate than existing methods without compromising the execution speed. Our novel methodology applies signal approximation (using fourier series in trigonometric form) and statistical approach for better line segmentation. The proposed method is capable of segmenting lines, independent of language, with performance of 99.53% on in-house CDAC dataset (having 5974 lines) and 98.11% on ICDAR Competition 2013 dataset (having 2649 lines). The dataset used for experiments consists of english, spanish, hindi and bangla handwritten paragraphs.