logo (12/05/82)
First, I would like to thank everyone who has been attempting to clear up my misstatment on linear and minimal phase. I realized that I understood it incompletely, although I did not realize the degree of error. I especially appreciate the less flaming, more tutorial responses. I have never come close to reaching my limit of techinal and theoretical interest in audio, but sometimes a discussion jumps out of my technical league without the ladder to reach that level being provided. I think that the most recent suggestion was that the digital recorder/all pass filter pair could or would be used to get to a linear phase response. A recent article in the Journal of the Audio Engineering Society (JAES) (subject was midrange phase differences and timbre perception) indicated that differences in timbre ARE heard in the presence of a constant phase shift in the midrange. A 'easy to conduct' (if you have a couple of sine wave generators and a scope, that is (i don't)) experiment is described which demonstrates the phenomena. If I understood the article correctly, a linear phase response for the recorder system is not good enough, we need zero phase shift. Also, I would appreciate suggestions of references or texts. As calibration, the tail end of chapter one of Rabiner and Gold 'Theory and Application of Digital Signal Processing' becomes to poorly motivated for me to follow well, as well as being on the (far) edge of the mathematics which I am currently facil with. David (Reisner) uucp : ...!ucbvax!sdcsvax!logo arpanet : sdcsvax!logo@nosc
vax2:toms (12/07/82)
For a more readable discussion of signal distortion, try "Communication Systems" by A. Bruce Carlson. Section 4.2 (in the second edition) is entitled 'Signal Distortion in Transmission' and discusses causes and effects of amplitude distortion, phase shift and delay distortion, and nonlinear distortion, as well as covering the concepts of equalization and companding. The math involved requires an understanding of Fourier analysis. It is much simpler than the z-transform analysis involved in Rabiner and Schafer. The idea of using all-pass networks to achieve linear phase delay is very similar to the concepts of equalization discussed in the above reference. In equalization, the idea is to remove undesirable distortions in a signal by passing it through a filter which has the opposite effect of the network causing the distortion. This technique is commonly used to restore voice signals which have been distorted while being transmitted over very long telephone links. The ideal output of the equalization network is an exact duplicate of the original voice signal. In contrast, the ideal output of typical linear phase delay filters is a distorted version of the input. The desired distortion is a change in the amplitude spectrum of the signal. The signal is passed through a filter to achieve the desired amplitude distortion. However the filter will change the phase spectrum of the signal as well as changing the amplitude spectrum. This phase distortion is an undesired effect of the filtering process. To remove this phase distortion, the signal is passed through an all-pass filter which restores the original phase spectrum of the signal in much as an equalization network restores a signal. The difference between an all-pass filter and an equalization network is that the latter will change the amplitude response of the signal whereas the former will not. Tom Sager John Fluke Mfg. Co. Inc. Seattle, WA