Novel, multi-path, time-interleaved digital sigma-delta modulators that can operate at any arbitrary frequency from DC to Nyquist are designed, analysed and synthesized in this study. Dual- and quadruple-path fourth-order Butterworth, Chebyshev, Inverse Chebyshev and Elliptical based digital sigma-delta modulators, which offer designers the flexibility of specifying the centre-frequency, pass-band/stop-band attenuation as well as the signal bandwidth are presented. These topologies are compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity to non-idealities. Detailed simulations performed at the behavioural-level in MATLAB are compared with the experimental results of the FPGA implementation of the designed modulators. The signal-to-noise ratios between the simulated and empirical results are shown to be different by not more than 3-5 dBs. Furthermore, this paper presents the mathematical modelling and evaluation of the tones caused by the finite wordlengths of these digital multi-path sigma-delta modulators when excited by sinusoidal input signals.