Digital Filtering Techniques

This investigation was concerned with various digital filtering techniques and associated constraints. The synthesis procedures discussed in this report emphasize the interplay of the various critical design parameters. Generalized design procedures for lowpass, bandpass and band stop filters are developed using a tabular procedure which enables one to obtain the digital filter coefficients by inspection. This approach allows for a simpler evaluation and interpretation of such problems as coefficient truncation, stability and error constraints as well as illustrating the importance and significance of the concept of normalization in digital filters. The inter-relations among the foregoing are discussed in detail leading to performance curves for various implementations. A bandpass and band stop synthesis technique which is accomplished through a simple conversion of the lowpass coefficients is also developed. Bandpass filters having arithmetic symmetry are then synthesized using a frequency shift technique as well as a lowpass to bandpass transformation. The validation of these approaches for various ratios of sampling rate to carrier frequency is discussed. An analysis of synthesis errors is then accomplished. Under the assumption that tabular data is available, design procedures which minimize the sum-squared error are developed for design of non-recursive digital filters. A second approach to the design of these filters was accomplished under the assumption that a satisfactory recursive digital filter design using the bilinear transform was available.