Relationship between PCM and PWM audio

It depends on how your drive circuit and speaker respond to different PWM duty cycles, and what manufacturer-supplied hardware, firmware and software magic sits between your original sample, the converted, compiled version, and the actual speaker. There will be an import phase in the compiler (if we're talking about the chips I think we're talking about), and some hardware magic in the chip itself.

If this is apropos of the chips we've been talking about in email, you should at the very least low-pass filter your audio with a cutoff of say 7200Hz. You should also try high-pass filters with a cutoff of

60-65Hz. There is a lot of trial and error here.

Once you've massaged the audio to sound passable out of a toy squeaker, there's no going back. Keep backups of the original files for any future re-processing! What's the thrust of this last question?

I assume that your pulse starts at regular intervals every 1/14400 s and the length of the pulse is controlled by a (say) 8 bit counter, thus the pulse width can have 256 different values. To do this, you would have to run the counter at 14.4 kHz * 256 or 3686.4 kHz or nearly 4 MHz.

If your audio samples are linear 8 bit PCM in sign magnitude representation, you would have to convert to offset notation by adding

128, so that the original 0 becomes 128, creating a 50 % duty cycle. After this, the sample can be directly loaded into the counter, but of course this has to happen _synchronously_ between the pulses.

Thus, this would be a simple 1 bit DAC.

However, if the original data is 8 bit PCM from some telephone system, this would be compressed according to the A or u-law, which in fact are floating point representations. This would have to be converted into linear 12 bit representation, requiring a clock frequency of 14.4 kHz * 4096 or about 59 MHz !

It is quite clear that simple 1 bit PWM DACs are usable only up to

8-10 bit audio conversions, since the quantisation noise would be the limiting factor.

While most audio DACs today are 1 bit devices, they have to use various oversampling and "noise shaping" tricks, so that most of the quantisation noise is concentrated above the audio passband, thus reducing the amount of quantisation noise in the audio pass. The analog low pass (anti-aliasing) filter will take care of the excessive quantisation noise. This noise shaping requires quite a lot of computations, so if it is done in software, will require some amount of computational power, which the smallest controllers might not have.

Paul

How many bits is the counter in this PWM generator?

Your wav file probably has 8 or 16 bits per sample, which surely more bits of resolution than the PWM generator uses. You can truncate the samples to the most significant bits, but it will sound better if you add the appropriate amount of dither noise first, though for the presumed two to four bits, that could be a lot of noise.

The samples should be put into a properly formatted .wav file.

For comparison, the original Macintosh used an 8-bit counter running at 5-something Megahertz (256 times the sample rate) as part of a PWM generator for its 8-bit, 22ksps A/D that drove the speaker. That was "good quality computer sound" at the time.

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That's exactly right. This is coming from a PIC running at 3.6864MHz. I guess the freqeuency choice the original engineer made makes a lot more sense now :-)

I am upgrading a system from and the old PIC and moving over to a DSP running at muchos of MHz and I need to make sure the old PWM audio system still works just like the PIC did. I am assuming that I can pick a crystal frequency for the DSP that will let me duplicate the PWM of the PIC.

The reason I am asking about the PCM/PWM difference is that the DSP has a serial port that will bolt up directly to a serial DAC, and I was wondering if I should port the PIC algorithm with its external hardware to the DSP solution, or if there was some easy way to use a serial DAC instead of the PWM solution.

Are you saying that a PWM running at 14.4KHz, with 8-bit values, with, for example, the following series of timer reloads:

1) 50% [ 0x80 ] 2) 25% [ 0x40 ] 3) 75% [ 0xC0 ]

is equivalent to running an 8-bit serial DAC at 14.4KHz with the following samples:

1) 0x80 2) 0x40 3) 0xC0 ?

--Keith

Good guess, based on our previous conversation, but those other chips are for another part of the board :-)

Check out my response to Paul...I give a detailed description of what I am trying to do.

--Keith

How do you do that? You just randomize the lowest bit or two and it sounds better?

--Keith

The purpose of the last question is to better my understanding of what, exactly, I am doing with this embedded audio stuff.

After I get the PIC/(PWM) stuff moved over to the DSP/(PWM or DAC) I would like to be able to, in future projects, take audio samples I capture on the computer and embed them in something that uses a PWM peripheral instead of a DAC. Since I am trying to take existing code that PWMs and maybe move it to a DAC, I referred to it as "going the other way"...

--Keith

Yes, assuming the serial DAC expect unipolar 00..FF range. However, if the DAC expects the 2's complement format (with the FF->00 transition in the middle of the range), an offset must be added. If the expected format is sign/magnitude then some extra calculations are required.

Paul

Wow, that is so not what my intuition would have told me.

That means that a constant output to the PWM would result in a constant DC on the DAC.

Yet, I would have thought that a square wave PWM would yield a sine-wave audio output...

--Keith

If the PWM generates a constant duty cycle square wave, the low pass (anti-alias) filter will convert it to a constant DC voltage and since audio systems are usually AC coupled, the output is actually zero for any constant duty cycle. If the AC coupling capacitor is before the LPF, the output is a DC potential depending on the duty cycle. With 50 % duty cycle the output is 0 V.

The only way to get a clean sine wave from a constant 50 % PWM square wave is to put a high-Q band-pass filter at the _sampling_ frequency, in this case 7.2 kHz to filter out the third, fifth, etc odd harmonics of the square wave.

Please note that the low pass (anti-alias/reconstruction) filter after any DAC should have a cut-off frequency less than _half_ the sampling frequency, in this case below 3.6 kHz. The response from that filter should be severely attenuated at the 7.2 kHz sampling frequency, so you can not get any useable sine waves out with a constant duty cycle square wave.

Paul

I thought 14.4KHz was the sampling frequency. Is it not in my case?

--Keith

Yes. In your case the sampling frequency is 14.4 kHz and the low pass filter should cut off around 7 kHz.

Paul

That's the gist of it, though perhaps oversimplified. You create a random number for each sample (a simple random number generate program will do), then add it in scaled so the peak values of the random numbers are about equal to the lowest bit value of the bit-reduced samples. "Noise shaping" or filtering the noise before it is added may help the final wave file sound less noisy, though perhaps at your sample rate it could actually increase the percieved noise level. Here are the usual links I give that explain dither. It's specifically for A/D conversion, but if you think of a .wav file with more bits resolution as "analog" and one with less bits as "digital" the same principle applies:

Here's a long explanation: click on articles, then dither:

As far as sound quality ane the PWM discussion, the DAC solution is MUCH better than using PWM. PWM is a cheap way to get analog from a purely digital device, but the PWM output has lots of nasty harmonics in its output at the sampling frequency and above, and for most apps these really need to be filtered. The extra analog filtering on the output of the PWM can increase the cost to the point where (nowadays) it's often as cheap to use a DAC in the first place. OTOH considering low cost in this app may be more important than good sound quality, and presuming this chip has PWM built in that you wouldn't otherwise use, see if you can live with a 'simple' filter on the output. A twin-t R-C notch filter at the 14.4kHz sample rate would be cheap, and would work well into your audio amp if it has a high input impedance.

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