How to: transmitting modulated RF bits

I am trying to emulate RF remote that controls Pan/Tilt device. Using RTL-SDR dongle and Radio Hacker software I recorded packages that remote transmits, determined the bit length and recorded bit code for each of 4 buttons of remote, all nice and dandy. I just ordered standard Arduino RF transmitters 433 MHz, and while waiting for them to arrive I am trying to understand how I should code transmission of these packages. As I understand, RF library accepts just a bit code as a string (like, '111011010100' etc) and a pulse length, that is, what is a length of a bit in microseconds; and then it transmits 433 MHz wave modulated by rectangular pulses, and width of each pulse is equal to 'pulse length' parameter (AM modulation)
Now the problem:
as I see from recorded remote packages, bits are represented not by rectangular shape, but by a 4100Hz sinusoidal modulation:

(Audacity screenshot).
The length of each bit is 1 ms, each contains ~3 periods of sine at 4100Hz frequency.

So how I can reproduce such structure with Arduino transmitters? I cannot split 'bits' into sine periods and use them as new '0' and '1's because each bit of a package contains fractional number of periods.

I am going to find out if this modulation is required for communication, but have to wait until transmitter board arrives.

That waveform results from some sort of interference or sampling artifact at the receiving end, either the receiving radio or audio sampling. It is extremely difficult to transmit such a waveform.

Could be that some signal is beating with the (41 kHz ?) sampling digitizer in the computer running Audacity.

If sampling at, say 41 kHz, you cannot permit a signal at frequency higher than 20.5 kHz in the input stream (look up the "sampling theorem"). Try adding a low pass filter to the receiver output (e.g. 10K + 0.01 uF).

Turned out this waveform is software artifact plus incorrect recording settings. First of all, SDR# produces way better recordings; I also recalled someones note that recording should not be done at the peak frequency; So when I recorded in SDR# at 433.76 MHz I got a perfect waveform; surprisingly, when recording at center frequency 433.92 the waveshape is totally distorted:

This is Audacity screenshot;
at the top is the package produced by remote I am trying to emulate;
in the middle is emulated package by HS1000A transmitter at 433.76,
and at the bottom - the same package from HS1000A but recorded at peak frequency.

Here is HS1000A emission spectrum, prepared to record at peak frequency (bad, bad!):

Original remote has quite different spectrum and recording at the peak is not different from recording off-center:

That makes perfect sense, thanks.