FIR filters in image processing

New results are obtained for designing two-dimensional Finite Impulse Response (FIR) filters as well for their implementation. Both computational efficiency and edge loss due to filtering are addressed.; In the design stage, a technique is presented for designing 2-D FIR filters using the frequency-weighted least-squares design and the properties of a block Toeplitz matrix. A method for designing 1-D FIR filters by smoothing the transition-band with a polynomial or a cosine roll-off is also developed. This method is integrated with McClellan's transformation for extending the design to 2-D FIR filters.; In the implementation stage, an algorithm is created that can reduce computation time by converting the impulse response of a non-separable 2-D FIR filter to a sum of separable ones. The problem of edge loss or error near the edges after convolving an image is addressed, and an algorithm is designed to restore the edges.