What is "time resolution"?
Reply #14 – 2006-10-06 04:30:39
The subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information.... You mention periods "less than 2 samples in length". This is a band limited signal, there are no such periods. Exactly, frequencies of that period are required to render time localised energy between the samples, which we obviously dont have until we have access to non-downsampled records. I think you are trying to say that since you can't have frequencies higher then the nyquist frequency, then it must be true that you cannot have frequencies closer together then 2/fs. I would never knowingly say anything to that effect'Regarding your periodic remark, I'm afraid I don't follow. I didnt exactly make the periodic remark, I think woodinville was refering to explainations in the other thread like this:It was shown that the phase of a sinusoidal pattern which is assumed as perfect and constant can be resolved to a fraction of the sampling interval. This subsample accuracy was possible because the pattern recorded is not a discrete event, it's impression is recorded throughout many consecutive samples and its exact formation is inferable (idealy). For all discrete or unassumable events, PCM records can only specify time of occurence to within a whole length of the sampling interval. Time resolution can only be improved when a known pattern can be observed throughout multiple samples -which is the case for computing the phase of synthetic frequency components, but not at all when trying to refine the temporal location of unassumed events. For conversion and processing purposes etc PCM is interprated as a composite of exclusively periodic entities (frequencies) But localised energy need not fit into any periodic cycle, so we cant locate it precisely with the periodic tools (frequencies) even though we can locate all the individual tools precisely. techie: "captain we have located a 'spike' event on the PCM sensor" captain:"what is the position of the spikes peak teki?" techie:"324.37643 sampling intervals exactly captain" captain:"how can you be so precise?" techie:"because time delays are quite precisely encodable in PCM" But a natural spike, will have an unknown frequency spectrum, the tools to locate the true peak with certainty had to be removed before the downsample, so we can make the best guess by assuming the 'subsample deviators' were all flat anyway but thats just a guess, the true peak could have been anywhere in the sample interval. If it was actualy somewhere other than the record suggests most likely, that information was contained in the lowpassed higher frequencies which now manifest as the unrecorded gaps between samples. waffle, waffle, waffle. 'It just refers to how precisely you can localize energy in the time domain. Generally this is just the sample period, but not always. That is how I seesaw it. Ive just been clumsily trying to explain this really, from a few different angles.