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In the digital filter design, an important factor is the word length necessary to implement the filter. In this paper, an estimate of the word length was defined such that the magnitude of the system function was maintained within a prescribed error. A procedure was also presented for minimizing this word length for realization of a give filter. In order to compute the values W_P and W_S, we calculated the maximum error in passband and stopband frequencies. These frequencies were determined by elliptic functions. Three examples were given and improvements of 1.5 bits in the word length were observed. We also investigated and compared word length according to the filter structure.
To improve the poor characteristics of passive bandpass filter, R-C active bandpass filters are deigned with operational amplifier in a single stage and a double stage, and their characteristic is theoretically analyzed. It is shown that the attenuation of gain in R-C active filter is remarkably less than in the passive filter and the desired frequency passband Outside of cutoff frequency, one-stage amplifier's characteristics has the slope 6dB paero octave but that of double stage has the slope 6dB per octave but that of double stage has the slope 12dB per octave byt, that of double stat has the slope 12dBper octave.
The modified slant transform(MST) discussed in this paper represents the properties of the slant transform and Hadamard(or Walsh) transform, and provides more convenient methods for a fast algorithm in image processing. Pattern recognition For applications and performance measurements of the MST, we compare the MST with other transforms in terms of the number of operations (additions and multiplications), variance distribution, rate distortion, and mean square error(MSE).
The discrete cosine transform(DCT) has been widely used in digital image processing because of its nearly optimal performance. For computational requirements, efficient methods reported for DCT are the Algorithms proposed by chen et al and by Hein et al . The CMT, called the conversion matrix transform has the following properties. 1. The conversion matrix has sparse block diagonal structure. 2. The conversion matrix has only integers as its elements. Only integer arithmetic is involved. 3. Its performance is very close to the DCT. The hardware requirements and implementation are also presented for the CMT. Because of the integer arithmetic, computationally it is much simpler. Image coding for the GIRL is simulated and performance measurements for the various discrete transforms are compared. The CMT is found to yield almost the same picture quality.