The thesis covers a series of PC programs that we have written that will enable users to easily design FIR linear phase lowpass digital filters and multistage sampling rate conversion systems. The first program is a rewrite of the McClellanParks computer program with some slight modifications. The second program uses an algorithm proposed by Rabiner that determines the length of a lowpass digital filter. Rabiner used a formula proposed by Herrmann et al. to initially estimate the filter length in his algorithm. The formula, however, assumes unity gain. We present a modification to the formula so that the gain of the filter is normalized to accommodate filters that have a gain greater than one (as in the case of a lowpass filter used in an interpolator). We have also changed the input specifications from digital to analog. Thus, the user supplies the sampling rate, passband frequency, stopband frequency, gain, and the respective maximum band errors. The program converts the specifications to digital. Then, the program iteratively estimates the filter length and interacts with the McClellan-Parks Program to determine the actual filter length that minimizes the maximum band errors. Once the actual length is known, the filter is designed and the filter coefficients may be saved to a file. Another new finding that we present is the condition that determines when to add a lowpass filter to a multistage decimator in order to reduce the total number of filter taps required to implement the system. In a typical example, we achieved a 34% reduction in the total required number of filter taps. The third program is a new program that optimizes the design of a multistage sampling rate conversion system based upon the sum of weighted computational rates and storage requirements. It determines the optimum number of stages and the corresponding upsampling and downsampling factors of each stage of the design. It also determines the length of the required lowpass digital filters using the second program. Quantization of the filter coefficients may have a significant impact on the frequency response. Consequently, we have included a routine within our program that determines the effects of such quantization on the allowable error margins within the passband and stopband. Once the filter coefficients are calculated, they can be saved to files and used in an appropriate implementation. The only requirements of the user are the initial sampling rate, final sampling rate, passband frequency, stopband frequency, corresponding maximum errors for each band, and the weighting factors to determine the optimization factor. We also present another new program that implements a sampling rate conversion from CD (44.1 kHz) to DAT (48 kHz) for digital audio. Using the third program to design the filter coefficients, the fourth program converts an input sequence (either samples of a sine wave or a unit sample sequence) sampled at the lower rate to an output sequence sampled at the higher rate. The frequency response is then plotted and the output block may be saved to a file.
| Identifer | oai:union.ndltd.org:pdx.edu/oai:pdxscholar.library.pdx.edu:open_access_etds-5768 |
| Date | 07 May 1993 |
| Creators | Hagerty, David Joseph |
| Publisher | PDXScholar |
| Source Sets | Portland State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations and Theses |
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