Re: [Discuss-gnuradio] Relation between a vocodec, bitrate and CPFSK modulation

[Marcus Müller]

Hello Giancarlo,

this is an interesting system; I have a few notes below:

On 12.03.2016 04:59, Giancarlo Murillo wrote:

First, thanks for reading my question experts.

Im trying to implement a Continous Phase Frequency Shift Keying Modulation (CPFSK) to stream audio, for the design of the modulator, i implemented my modulation system in the GNUradio for simulate it in prior to use a USRP1 from Ettus Research.

Some details

I decided to put every variable in function of the bit rate needed. in my example im using a bitrate R=1024e3 (bits per second), this means.

• Sample_Rate=16*R (Samples/Second)

That won't work; 16*1024e3 S/s is not a valid sample rate for the USRP1; all sampling rates must be integer divisors of 64e6 Hz on the USRP1, and also at least 64e6/512 = 125kS/s.

• Modulation_Rate=R/2 (Symbols/Second)

ok; that means 2 samples per symbol. Is that really what you're after?
Especially, demodulation of FSK with just 2 samples per symbol isn't trivial; think about the timing synchronization requirements. You might want to apply oversampling at the receiver side at least.

• Modulation_index=1.05

So 5% of the carrier frequency is your maximum frequency deviation.

• -/+ FM_Deviation_rate=h*R/2 (Hertz)

Does that lead to the same numbers as the modulation index? What's h?

• Samples_per_Symbol=2*Fs/R (Samples/Symbol)

That contradicts your modulation rate above; 2*Fs/R = 2* (16*R)/R = 32, but Modulation Rate says samples_per_symbol=2.

The CPFSK block needs 2 variables: K, which is Modulation index and SPS whis is Samples_per_Symbol.

yep, that makes sense; the absolute frequencies don't matter to the FSK modulator.

My problem is when im trying to import a WAV file to stream, which has a frecuency spectrum detail in music.png,

 That almost certainly doesn't look like the spectrum of voice. Useful voice signal is typically below 4kHz, and everything above is usually filtered out before being fed into the classical vocoders.
The filename also indicates you're trying to apply a vocoder (voice coder!) to general audio; that's not the worst thing to do, because even with music low-pass signals still lead to recognizability, but being frank:
You're applying something application-specific to something that it is explicitly not meant for.

Sample_Rate=44.1 KHz and one channel of audio.

The CPFSK doesn't care the least about absolute sample rate; modulation index tells it what is the ratio of the maximum deviation to the sampling rate.

Im using the vocoder CVSD since it works better for my application, it needs2 fields

• Resample: To increase the Samples (Interpolation)
• Fractional Bandwidth: 0.5 (The best quality)

My question is related to this Resample field (How can i use this variable to obtain a Bitrate variable?)

Bitrate=function(R,fa)

Well, the job of a vocoder is to exploit the properties of a digital speech signal to reduce the bandwidth occupied by it, thus making it either possible to send it using less bandwidth, or within the same bandwidth optimize quality by adding robustness.

As the Documentation says

It converts an incoming float (+-1) to a short, scales it (to 32000; slightly below the maximum value), interpolates it, and then vocodes it.

The resampler is really just used to parameterize the interpolation above.

So I assume you want to achieve a certain fixed bitrate R, and though you don't mention it, I assume fa ist the audio sampling rate.

Now, the question is what the proper interpolation is; well, you would need to know the bitrate ratio of your vocoder. Haven't read the "CVSD (raw bits)" encoder's documentation too closely, but if I remember correctly, CVSD is dead simple: you just convert your signal values to the difference to the previous sample, and quantize that to 1bit (which is the sign and nothing more).
Because that obviously strongly distorts that signal a lot, you first interpolate to a higher rate. Of that higher rate, 8 samples are converted to 8 bits of sign info, and that is one byte of output.
So, the higher the interpolation, the more bits you make out of your input sample. In fact, of the 16 bit input information per input sample, you make 1bit * interpolation output info. So any interpolation greater than 16 is senseless; you could as well send the original signal.

For your target bit rate of 1000 kb/s, and your 44.1kHz input sampling rate I wouldn't even bother with vocoding:
Let's round this to 1 Mb/s, and divide that by the 44.1kHz input sampling rate: you have 22.7 bit of channel bit rate to spend per input sample. Assuming your audio file is 16bit quantized, you can simply take the input, and still have more than 7 bits per sample to spend -- for example, on channel coding. If you really had a voice signal, you could virtually losslessly decimate to 8kHz (or 44.1kHz/5=8.82kHz for the sake of integer decimation). That would lead to 125 (or 113) bit on the air per input sample. Really, no need for vocoding; if you still applied an e.g. interpolation=8 vocoder, you'd get that up to 250 bit (226 bit) per input sample. That's enough for a rate-1/15 channel coder; I don't think this is what anyone would aim for.

I think you should more carefully sit down and design your system's requirements; get a proper test signal for a vocoder, and orientate on existing vocoder parametrizations.

Best regards,
Marcus