Hi, I had to open another thread because this keeps bugging me. I have a confusion in the process of DAC. (Method-1) Couple of books (Bernard Widro/ Proakis) states that DAC process consists of sample-and-hold filter followed by a low-pass filter. The LPF smooths the sharp edges of S/H filter. (Method-2) But, the 'Whittaker–Shannon interpolation formula' (http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula) states that signal can be reconstructed (DAC) by sending the digital signal through a sinc filter. And I have read in other texts that DAC process is basically sending the discrete samples through a interpolation (low-pass) filter. Thinking about it, at sampling instants, both method-1 and method-2 have the same values. Disregarding the values between sampling instants (which are not required to when ADC at the other end), is there a difference between the methods? Thank you.
In D/A conversion, is sample-and-hold necessary?
Started by ●July 23, 2009
Reply by ●July 23, 20092009-07-23
On Thu, 23 Jul 2009 04:05:44 -0500, m26k9 wrote:> Hi, > > I had to open another thread because this keeps bugging me. > > I have a confusion in the process of DAC. > > (Method-1) > Couple of books (Bernard Widro/ Proakis) states that DAC process > consists of sample-and-hold filter followed by a low-pass filter. The > LPF smooths the sharp edges of S/H filter. > > (Method-2) > But, the 'Whittaker–Shannon interpolation formula' > (http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula)> states that signal can be reconstructed (DAC) by sending the digital > signal through a sinc filter. And I have read in other texts that DAC > process is basically sending the discrete samples through a > interpolation (low-pass) filter. > > Thinking about it, at sampling instants, both method-1 and method-2 have > the same values. Disregarding the values between sampling instants > (which are not required to when ADC at the other end), is there a > difference between the methods? > > Thank you.I think you are confused about the difference between the actual process and the mathematical model thereof. Every DAC that I've ever worked with has inherently acted as a sample and hold, or as a flow-through of the digital information applied to it's input port, which is generally a register that acts as a sample and hold. You can posit a DAC _process_ that doesn't involve this sample and hold (e.g. the Whittaker-Shannon process), but when you go to model _real world processes_ you'll find yourself needing to deal with that sample and hold action. Note that a train-of-impulses DAC model can be turned into a sample-and- hold DAC model by following it with a FIR filter that produces boxcar pulses that are exactly the width of the sampling rate. So the train-of- impulses model, which is easier to deal with on a theoretical basis, can be easily applied to real-world situations, as long as you remember the implicit filtering carried out by the sample and hold process. -- www.wescottdesign.com
Reply by ●July 23, 20092009-07-23
On Jul 23, 5:05�am, "m26k9" <maduranga.liyan...@gmail.com> wrote:> Hi, > > I had to open another thread because this keeps bugging me. > > I have a confusion in the process of DAC. > > (Method-1) > Couple of books (Bernard Widro/ Proakis) states that DAC process consists > of sample-and-hold filter followed by a low-pass filter. The LPF smooths > the sharp edges of S/H filter. > > (Method-2) > But, the 'Whittaker�Shannon interpolation formula' > (http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_...) > states that signal can be reconstructed (DAC) by sending the digital signal > through a sinc filter. And I have read in other texts that DAC process is > basically sending the discrete samples through a interpolation (low-pass) > filter. > > Thinking about it, at sampling instants, both method-1 and method-2 have > the same values. Disregarding the values between sampling instants (which > are not required to when ADC at the other end), is there a difference > between the methods? > > Thank you.Yes you can implement a DAC without a sample and hold. An example is in the Yamaha nine channel synthesizer chip, YM2413. Each channel's output is a stream of impulses. The 9 different outputs are combined together by simple multiplexing. Thus 1 single sample period is divided into 9 time slices. The actual pulses are narrower in time than 1/9th of the sample period, so they are very much like impulses even in this multiplexing scheme. Now this was done in this case to simplify the hardware - i.e., no mixers. A drawback of this approach is with the chip running on 5 volts, the pulses have a maximum amplitude of 5 volts, so when the pulses go through the lowpass filter, the amplitude ends up in the millivolt range. This was okay in the application, since it is assumed the output after the lowpass filtering will go right into a "microphone" level input of an amplifier. Apart from the Yamaha applications, I have seen the lack of a sample and hold used a few times, for example Motorola use to do this their CVSDM (Continuously Variable Slope Delta Modulation) chips. I thought you should know that if there is more than one way to do something, it probably has been implemented since each way often offers unique advantages that can sometimes make it worth it. IHTH, Clay
Reply by ●July 23, 20092009-07-23
Clay wrote:> On Jul 23, 5:05 am, "m26k9" <maduranga.liyan...@gmail.com> wrote: >> Hi, >> >> I had to open another thread because this keeps bugging me. >> >> I have a confusion in the process of DAC. >> >> (Method-1) >> Couple of books (Bernard Widro/ Proakis) states that DAC process consists >> of sample-and-hold filter followed by a low-pass filter. The LPF smooths >> the sharp edges of S/H filter. >> >> (Method-2) >> But, the 'Whittaker�Shannon interpolation formula' >> (http://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_...) >> states that signal can be reconstructed (DAC) by sending the digital signal >> through a sinc filter. And I have read in other texts that DAC process is >> basically sending the discrete samples through a interpolation (low-pass) >> filter. >> >> Thinking about it, at sampling instants, both method-1 and method-2 have >> the same values. Disregarding the values between sampling instants (which >> are not required to when ADC at the other end), is there a difference >> between the methods? >> >> Thank you. > > Yes you can implement a DAC without a sample and hold. An example is > in the Yamaha nine channel synthesizer chip, YM2413. Each channel's > output is a stream of impulses. The 9 different outputs are combined > together by simple multiplexing. Thus 1 single sample period is > divided into 9 time slices. The actual pulses are narrower in time > than 1/9th of the sample period, so they are very much like impulses > even in this multiplexing scheme. Now this was done in this case to > simplify the hardware - i.e., no mixers. A drawback of this approach > is with the chip running on 5 volts, the pulses have a maximum > amplitude of 5 volts, so when the pulses go through the lowpass > filter, the amplitude ends up in the millivolt range. This was okay in > the application, since it is assumed the output after the lowpass > filtering will go right into a "microphone" level input of an > amplifier.I think it is worth expanding on why the output voltage is so low with this scheme. The narrow pulses contain less energy than wider ones would. In fact, the energy at low frequencies is directly proportional to the pulse area, height times width. When the pulses are narrow, energy is low, but the response is uniform at all frequencies. As the pulses widen, energy at all frequencies increases, but high=frequency energy increases less. (The width of the pulse "blurs" the highs.) Calculating the magnitude of the effect yields the classical sinc rolloff. For me at least, understanding the phenomenon from a physical viewpoint enlightens the math.> Apart from the Yamaha applications, I have seen the lack of a sample > and hold used a few times, for example Motorola use to do this their > CVSDM (Continuously Variable Slope Delta Modulation) chips.I used narrow pulses in an application where I wanted a pair of the higher images. Have you ever thought of a DAC as an AM modulator?> I thought you should know that if there is more than one way to do > something, it probably has been implemented since each way often > offers unique advantages that can sometimes make it worth it.Evolution works that way too! :-) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 23, 20092009-07-23
Jerry Avins <jya@ieee.org> wrote: (someone wrote) <>> I have a confusion in the process of DAC. < I think it is worth expanding on why the output voltage is so low with < this scheme. The narrow pulses contain less energy than wider ones < would. Thanks for the explanation. Even though I knew that, I didn't think about it that way when I read it. Mostly, I didn't think they were that narrow! < In fact, the energy at low frequencies is directly proportional < to the pulse area, height times width. When the pulses are narrow, < energy is low, but the response is uniform at all frequencies. As the < pulses widen, energy at all frequencies increases, but high=frequency < energy increases less. (The width of the pulse "blurs" the highs.) < Calculating the magnitude of the effect yields the classical sinc < rolloff. For me at least, understanding the phenomenon from a physical < viewpoint enlightens the math. The "high frequencies increase less", yes, but not so much less until the width gets to be a significant fraction of the higher frequencies, which have to be less than the sample rate. For 5V down to millivolts, the pulse width would be about 1/1000th of the sampling rate. For sinc, approximately 1-x**2/3, and 16 bits I wouldn't think you would need to go that narrow. For x**2/3=1/65536, x=1/148. -- glen
Reply by ●July 23, 20092009-07-23
glen herrmannsfeldt wrote:> Jerry Avins <jya@ieee.org> wrote: > (someone wrote) > > <>> I have a confusion in the process of DAC. > > < I think it is worth expanding on why the output voltage is so low with > < this scheme. The narrow pulses contain less energy than wider ones > < would. > > Thanks for the explanation. Even though I knew that, I didn't > think about it that way when I read it. Mostly, I didn't think > they were that narrow! > > < In fact, the energy at low frequencies is directly proportional > < to the pulse area, height times width. When the pulses are narrow, > < energy is low, but the response is uniform at all frequencies. As the > < pulses widen, energy at all frequencies increases, but high=frequency > < energy increases less. (The width of the pulse "blurs" the highs.) > < Calculating the magnitude of the effect yields the classical sinc > < rolloff. For me at least, understanding the phenomenon from a physical > < viewpoint enlightens the math. > > The "high frequencies increase less", yes, but not so much less > until the width gets to be a significant fraction of the higher > frequencies, which have to be less than the sample rate. > > For 5V down to millivolts, the pulse width would be about 1/1000th > of the sampling rate. For sinc, approximately 1-x**2/3, and 16 bits > I wouldn't think you would need to go that narrow. > > For x**2/3=1/65536, x=1/148.As I understand Clay's description, the pulse widths were well under a tenth of the sample time. (I would guess no more than 1/20th to allow for settling and deglitching.) Happily, sinc compensation is hardly necessary, but at T/20, the peak channel signal becomes 5Vx.05 = 1/4 volt. I suppose that's "millivolt range", and the pulses might have been even narrower. Maybe Clay will tell us more. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 23, 20092009-07-23
Clay wrote:> Yes you can implement a DAC without a sample and hold. An example is > in the Yamaha nine channel synthesizer chip, YM2413. Each channel's > output is a stream of impulses.> Apart from the Yamaha applications, I have seen the lack of a sample > and hold used a few times, for example Motorola use to do this their > CVSDM (Continuously Variable Slope Delta Modulation) chips.There is a DSD audio format which is essentially a pulse density modulated signal. There is no sample-hold there. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●July 23, 20092009-07-23
Jerry Avins <jya@ieee.org> wrote: (snip about DACs that generate short pulses)> As I understand Clay's description, the pulse widths were well under a > tenth of the sample time. (I would guess no more than 1/20th to allow > for settling and deglitching.) Happily, sinc compensation is hardly > necessary, but at T/20, the peak channel signal becomes 5Vx.05 = 1/4 > volt. I suppose that's "millivolt range", and the pulses might have been > even narrower. Maybe Clay will tell us more.I thought about sinc compensation in the last post, but didn't write it. It wouldn't seem so hard to modify the filter on the output to compensate for at least a little of the sinc shape as the pulses get longer. I was assuming millivolt meant less than 10mV, or it would have been tens of millivolts. But then that is peak to peak, so divide by two. -- glen
Reply by ●July 23, 20092009-07-23
On Jul 23, 1:49�pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:> > There is a DSD audio format which is essentially a pulse density > modulated signal. There is no sample-hold there.r b-j
Reply by ●July 23, 20092009-07-23
On Jul 23, 1:32�pm, Jerry Avins <j...@ieee.org> wrote:> glen herrmannsfeldt wrote: > > Jerry Avins <j...@ieee.org> wrote: > > (someone wrote) > > > <>> I have a confusion in the process of DAC. > > > < I think it is worth expanding on why the output voltage is so low with > > < this scheme. The narrow pulses contain less energy than wider ones > > < would. > > > Thanks for the explanation. �Even though I knew that, I didn't > > think about it that way when I read it. �Mostly, I didn't think > > they were that narrow! � > > > < In fact, the energy at low frequencies is directly proportional > > < to the pulse area, height times width. When the pulses are narrow, > > < energy is low, but the response is uniform at all frequencies. As the > > < pulses widen, energy at all frequencies increases, but high=frequency > > < energy increases less. (The width of the pulse "blurs" the highs.) > > < Calculating the magnitude of the effect yields the classical sinc > > < rolloff. For me at least, understanding the phenomenon from a physical > > < viewpoint enlightens the math. > > > The "high frequencies increase less", yes, but not so much less > > until the width gets to be a significant fraction of the higher > > frequencies, which have to be less than the sample rate. > > > For 5V down to millivolts, the pulse width would be about 1/1000th > > of the sampling rate. �For sinc, approximately 1-x**2/3, and 16 bits > > I wouldn't think you would need to go that narrow. � > > > For x**2/3=1/65536, x=1/148. � > > As I understand Clay's description, the pulse widths were well under a > tenth of the sample time. (I would guess no more than 1/20th to allow > for settling and deglitching.) Happily, sinc compensation is hardly > necessary, but at T/20, the peak channel signal becomes 5Vx.05 = 1/4 > volt. I suppose that's "millivolt range", and the pulses might have been > even narrower. Maybe Clay will tell us more. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������- Hide quoted text - > > - Show quoted text -Hello Jerry, As I think either you or Glen alluded to, one advantage of narrow pulses, is the sinc for reconstruction becomes so broad as to be effectively flat. I don't recall the exact width of the pulses, but I do remember when I first looked at them on my 'scope. I was impressed with the simplicity yet effectiveness of the design. The chip IIRC was just 18 pins. I used it in a video game design back in 1991. The circuit after the YM2413 chip was a simple lowpass filter (basically an RC) followed with a monlithic 3 or 5 watt amp in a pentawatt (TO-220 sized but with more pins) package. This was a lot better than the currently used (at the time) General Instruments AY3-8912 which had 3 audio channels and a 28 pin package. I recall the "integrated" signal level out of the lowpass filter was on the order of 10 to 20 mV - quite low and not a "line level." Clay
