RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves.

Or whatever set of orthonormal functions as well, as sines & cosines are not the only useful functions for decomposing audio signals.

In signal processing terms, a function of time is a representation of a signal with perfect time resolution, but no frequency information, while the Fourier transform has perfect frequency resolution, but no time information.

The magnitude of the Fourier transform at a point is how much frequency content there is, but location is only given by phase (argument of the Fourier transform at a point), and standing waves are not localized in time – a sine wave continues out to infinity, without decaying.

This limits the usefulness of the Fourier transform for analyzing signals that are localized in time, notably transients, or any signal of finite extent.

As alternatives to the Fourier transform, in time-frequency analysis, one uses time-frequency transforms or time-frequency distributions to represent signals in a form that has some time information and some frequency information – by the uncertainty principle, there is a trade-off between these.

These can be generalizations of the Fourier transform, such as the short-time Fourier transform or fractional Fourier transform, or can use different functions to represent signals, as in wavelet transforms (mostly used in seismic analysis) and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.

Best Regards
Luca

This post is made possible by the generous support of people like you and our sponsors:

Follow Ups Full Thread

Topic - All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - Tre' 14:14:53 03/18/12 (23)

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - Michael Koster 08:21:03 03/21/12 (5)

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - Tre' 14:13:02 03/21/12 (0)

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - Michael Koster 08:30:47 03/21/12 (3)

No (nt) - Tre' 14:03:29 03/21/12 (0)

Way to GO Michael !!! - drlowmu 12:12:40 03/21/12 (1)

RE: Way to GO Michael !!! - Michael Koster 17:02:35 03/21/12 (0)

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - 6AS7_6SN7 12:50:49 03/20/12 (1)

Thanks Luca as always a very coherent response... - Minussss3db 23:45:08 03/21/12 (0)

I am afraid I'm strongly with the first responder - It's an abstraction - Timbo in Oz 21:24:00 03/18/12 (3)

RE: I am afraid I'm strongly with the first responder - It's an abstraction - Tre' 14:15:02 03/21/12 (2)

RE: I am afraid I'm strongly with the first responder - It's an abstraction - Timbo in Oz 14:38:40 03/21/12 (1)

Thank you (nt) - Tre' 16:32:14 03/21/12 (0)

Are Triangle waves and square waves made up of sine waves? - Chris O 14:39:56 03/18/12 (8)

RE: Are Triangle waves and square waves made up of sine waves? - Eli Duttman 17:33:07 03/18/12 (0)

yes - Tre' 15:07:07 03/18/12 (6)

" made up of sine waves " - FenderLover 17:42:40 03/19/12 (5)

Yes I covered Fourier in my 'mid-life crisis degree' - Timbo in Oz 04:35:40 03/21/12 (4)

RE: Yes I covered Fourier in my 'mid-life crisis degree' - drlowmu 12:14:29 03/21/12 (3)

Possibly at his misuse or overemphasis by others? - Timbo in Oz 14:17:07 03/21/12 (0)

RE: Yes I covered Fourier in my 'mid-life crisis degree' - DanK tubes 12:42:12 03/21/12 (1)

Sharing Bob Fulton's work....... - drlowmu 15:14:09 03/21/12 (0)

Not really... - op48no1 14:39:14 03/18/12 (1)

RE: Not really... - Michael Koster 08:03:52 03/21/12 (0)

Follow Ups

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves. - 6AS7_6SN7 12:50:49 03/20/12 (1)

Thanks Luca as always a very coherent response... - Minussss3db 23:45:08 03/21/12 (0)

RE: All sounds, from the screech of nails on a blackboard to a symphony orchestra, are made up of sine waves.

Post a Message!