From what I've learned in university and what common sense says, a shift in frequency of a signal results in a change in its length in time. For example, if a sinusoid signal of frequency $f$ and length $t$ is transferred to frequency domain, it's $f$ divided by $2$, then converted back to time domain, the length of the signal would be $2t$.
Correct me if I'm wrong! But this is quite intuitive. If you make a signal slower, it would take more time to finish and vice versa.
This is a reason why I've been told it's impossible to change frequency of a streaming signal and output it with the same speed. For example, it would be impossible to take a man's speech and change it to sound like a woman without making it faster.
Now I've had various observations:
- In Coursera, you can increase the speed of course lectures and the sound is also of course sped up. However, there is no rise in the pitch of the voice of the speaker. In fact, the speaker sounds very similar to the normal speed. How is it possible to change in speed of the signal didn't affect its frequency?
- My amplifier has a dial for shifting the pitch. So, while playing, you can here the output with a different pitch. Again, how is this possible? If the amplifier is rising the pitch, shouldn't its output be faster than its input? (i.e. a contradiction!) I'm suspecting some trick though, as the output sounds rather "artificial".
It seems that it is somewhat possible to change the frequency of a signal without affecting its length. One (theoretical) way I can think of would be to understand the current "notes" playing (i.e. the different frequencies making the signal) in very small intervals, change the note and replay them for the duration of that interval.
My question is, first if my understanding is at all correct. Either way, is there a mathematical way for changing the pitch of a signal without affecting its length in time? If not, how can they be doing it in practice?