The thesis is concerned with the design of new wavelet filters for discrete wavelet multitone (DWMT) applications. The already existing types of wavelet filter families, like Haar, Daubechies, and Coiflets, when used in DWMT systems produce significant levels of interference. Namely, the inter-symbol Interference (ISI) and inter-carrier interference (ICI), usually, these come from time dispersion and the loss of orthogonality between the signals in the subbands, due to channel distortion. ISI may be considerably reduced via channel equalization, while the level of ICI depends on the amount of energy leakage between adjacent subbands. This is greatly determined by the height of the spectrum sidelobes of the corresponding wavelet filter. This effect can be reduced by using higher order filters at the expense of increased system complexity. For the proposed wavelet filters, the constraint of minimum sidelobes is relaxed to find another condition(s) that can reduce ICI. A new filter family is then produced whose derivation in the work have resulted in the condition that the autocorrelation function of the wavelet filters must be as close as possible to an impulse. The wavelet filters are designed according to the latter condition, together with those already known to maintain orthogonality. The result is orthogonal wavelet filters with very simple structure, where, for any filter order, the sampled impulse response of the designed filters consists of two nonzero components only. The designed filters are assessed from the frequency response and autocorrelation function points of view, and compared to Daubechies and Coiflets filters of the same order. These comparisons showed that the useful properties of the designed filters enable them to be used in DWMT systems. Further results, when simulated data are transmitted over models of distorted channels, have also showed improvement in signal to interference power ratio (SIR) over DWMT systems employing Daubechies and Coiflets filters. Moreover, the bit error rate performance is evaluated for many different structures of DWMT systems. The tests are achieved over different channel conditions. For channels introducing low distortion levels, no significant relative advantage is noticed among the tested systems. They achieve a BER of 10-5 at about 8 dB of SNR. For channels introducing high distortion levels, all of the tested systems perform poorly. When channel equalization is used, the DWMT systems employing the designed filters gain performance improvement greater than that for the other tested DWMT systems by about 9 dB at a BER of 10-2. On the other hand, from the system hardware complexity point of view, the designed DWMT system is much simpler than the other tested systems. As a result, the designed filters provide simple structure for practical implementation, and the designed DWMT system seems to be better than the other tested DWMT systems when tested under similar conditions.