tag:blogger.com,1999:blog-5751595370381900014.post3327536884312489678..comments1969-12-31T16:00:00.000-08:00Comments on Signals and Systems Redux: SigSys, piano styleMelhttp://www.blogger.com/profile/15598380941676945491noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5751595370381900014.post-26475452096693744952007-01-27T23:06:00.000-08:002007-01-27T23:06:00.000-08:00The transform depends on the orthogonality of sine...<I>The transform depends on the orthogonality of sines...</I><br /><br />This is an extremely fundamental idea here.<br /><br />Although not *quite* the right way to put it, the "time domain" and "frequency domain" (as signal processing people tend to put it) are like different bases of a vector space.<br /><br />A "system" is a function from signals to signals. A "signal" most commonly a function mapping a[1] real value (often time) to a[1] real value (eg, voltage, or what have you). In a DSP context, the function maps from integers instead of reals...<br /><br />In many of the simple contexts, particularly in DSP, the "systems" are actually a linear transformation.<br /><br />[1] Or k-tuples alsoDavid Klempnerhttp://www.blogger.com/profile/15071168259563698171noreply@blogger.com