# Frequency-varying waveform [closed]

My situation is as follows: i am trying to generate a waveform the hard way, by constructing the samples one by one and then saving the result to a .wav file using Python.

When the frequency is constant, everything is fine: i use y(t) = sin(2*πtf). However, if i change the frequency to be a function of time, things go wrong. If the function is a linear one of the form f(t) = a + bt, it still works. But if i choose, for exemple, f(t) = 40 + 10*sin(t), the max frequency increases over time, reaching a maximum higher then the expect 50Hz.

I have read something about instantaneous frequency, namely, this: Why does a wave continuously decreasing in frequency start increasing its frequency past the half of its length?. But doing the integral evaluation makes the sound even weirder. And the method i currently have works for linear function of time, so i figured there must be something else wrong.

I also tried to generate chunks of sound in the frequency i need, at each time, and then glue them together. I calculated the period of the oscillation, so that a chunk has as many samples as necessary to make a whole period on that frequency, so that there are no "jumps" between different frequencies. But generates a cracking sound in the sample.

Here is an example of the kind of a JavaScript implementation of the kind of sound i need: http://jsfiddle.net/m7US6/4/.

Any help would be appreciated. Thanks.

• This appears to be on topic over on DSP, like the other question, not here. I'll migrate this over. – Rory Alsop May 22 '14 at 9:47