From: bos1234 on 20 Jun 2010 21:41 A continuous data signal is quantized and transmitted using a PCM system. If each data sample at the receiving end of the system must be known to within 0.5 percent of the peak-to-peak full-scale value, how many binary symbols must each transmitted digital word contain? I assumed that pk-pk of the signal is some constant A. So what is represented by Ax0.5%?? From: Tim Wescott on 21 Jun 2010 01:40 On 06/20/2010 06:41 PM, bos1234 wrote:> A continuous data signal is quantized and transmitted using a PCM system. > If each data sample at the receiving end of the system must be known to > within 0.5 percent of the peak-to-peak full-scale value, how many binary > symbols must each transmitted digital word contain? > > I assumed that pk-pk of the signal is some constant A. > So what is represented by Ax0.5%?? Homework? What does your prof say? If you represent A with an N-bit binary number that's all ones, then what's the value of 00 ... 01 (i.e. N-1 zeros and a 1 in the least significant place). -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com From: bos1234 on 21 Jun 2010 09:13 >On 06/20/2010 06:41 PM, bos1234 wrote:>> A continuous data signal is quantized and transmitted using a PCM system.>> If each data sample at the receiving end of the system must be known to >> within 0.5 percent of the peak-to-peak full-scale value, how many binary>> symbols must each transmitted digital word contain? >> >> I assumed that pk-pk of the signal is some constant A. >> So what is represented by Ax0.5%?? > >Homework? What does your prof say? If you represent A with an N-bit >binary number that's all ones, then what's the value of 00 ... 01 (i.e. >N-1 zeros and a 1 in the least significant place). > >-- >Tim Wescott >Control system and signal processing consulting >www.wescottdesign.com > studying for exam. This is what the soln. says... q=2^n=A/del note: del --> delta --> the distance between a quantisation level. del/2 < 0.5/100* A where A is the pk-pk value of the data signal. del < 0.01A de/A < 0.01 A/del > 100 so q =128 and n=7 But does this even answer the question when they ask "how many binary symbols must each transmitted digital word contain" Isn't binary symbol a 0 or 1? From: Tim Wescott on 21 Jun 2010 11:25 On 06/21/2010 06:13 AM, bos1234 wrote:>> On 06/20/2010 06:41 PM, bos1234 wrote: >>> A continuous data signal is quantized and transmitted using a PCM > system. >>> If each data sample at the receiving end of the system must be known to >>> within 0.5 percent of the peak-to-peak full-scale value, how many > binary >>> symbols must each transmitted digital word contain? >>> >>> I assumed that pk-pk of the signal is some constant A. >>> So what is represented by Ax0.5%?? >> >> Homework? What does your prof say? If you represent A with an N-bit >> binary number that's all ones, then what's the value of 00 ... 01 (i.e. >> N-1 zeros and a 1 in the least significant place). >> >> -- >> Tim Wescott >> Control system and signal processing consulting >> www.wescottdesign.com >> > studying for exam. This is what the soln. says... > q=2^n=A/del > note: > del --> delta --> the distance between a quantisation level. > > del/2< 0.5/100* A where A is the pk-pk value of the data signal. > > del< 0.01A > de/A< 0.01 > A/del> 100 so q =128 and n=7 > > But does this even answer the question when they ask "how many binary > symbols must each transmitted digital word contain" > Isn't binary symbol a 0 or 1? Isn't it? If it were, would you need to send 128 of them, or 7, or some other number, to slice the pulse into 128 levels? -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com From: bos1234 on 21 Jun 2010 18:59 >On 06/21/2010 06:13 AM, bos1234 wrote:>>> On 06/20/2010 06:41 PM, bos1234 wrote: >>>> A continuous data signal is quantized and transmitted using a PCM >> system. >>>> If each data sample at the receiving end of the system must be known to>>>> within 0.5 percent of the peak-to-peak full-scale value, how many >> binary >>>> symbols must each transmitted digital word contain? >>>> >>>> I assumed that pk-pk of the signal is some constant A. >>>> So what is represented by Ax0.5%?? >>> >>> Homework? What does your prof say? If you represent A with an N-bit >>> binary number that's all ones, then what's the value of 00 ... 01 (i.e.>>> N-1 zeros and a 1 in the least significant place). >>> >>> -- >>> Tim Wescott >>> Control system and signal processing consulting >>> www.wescottdesign.com >>> >> studying for exam. This is what the soln. says... >> q=2^n=A/del >> note: >> del --> delta --> the distance between a quantisation level. >> >> del/2< 0.5/100* A where A is the pk-pk value of the data signal. >> >> del< 0.01A >> de/A< 0.01 >> A/del> 100 so q =128 and n=7 >> >> But does this even answer the question when they ask "how many binary >> symbols must each transmitted digital word contain" >> Isn't binary symbol a 0 or 1? > >Isn't it? If it were, would you need to send 128 of them, or 7, or some >other number, to slice the pulse into 128 levels? > >-- >Tim Wescott >Control system and signal processing consulting >www.wescottdesign.com what you mean??? So there are 128 levels and 7 bits/sample. 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