1. A cosine transforming and quantizing device for use in a video compressing apparatus, comprising: a discrete cosine transforming unit for performing discrete cosine transform (DCT) on an input data block based on a six-stage DCT fast algorithm, said discrete cosine transforming unit dispensing with a sixth intrinsic multiplication stage of the DCT fast algorithm to result in scaled transform data; and a quantizer connected to said discrete cosine transforming unit for quantizing the scaled transform data in accordance with a modified quantizer matrix that is obtained by compensating a predetermined original quantizer matrix with a set of scaling coefficients derived from the sixth intrinsic multiplication stage of the DCT fast algorithm to result in quantized DCT data corresponding to the input data block.