Nyquist pulse criteria states that the summation of the spectrum of pulse shapes should be flat. But if we see in time domain there are many pulse shapes that satisfy the nyquist criteria and they dont have a spectrum that's summation is flat. For example, triangular function f = { t + T for -T<t<0 ; -t+T for 0<t<T; 0 else where } This function doesn't introduce ISI at the neighboring symbol instants but the summation of pulse shape is not flat. i.e. it is a multiplication of the two sincs. So in summary my question is whether we should see in the time domain to qualify a pulse shape as nyquist or we should see in the frequency domain that the summation of pulse shape spectrum is flat or not. Thanks Aitezaz

# Nyquist Pulse

Started by ●October 9, 2009

Reply by ●October 9, 20092009-10-09

On Oct 9, 1:00�am, Aitezaz <aitezaz....@gmail.com> wrote:> Nyquist pulse criteria states that the summation of the spectrum of > pulse shapes should be flat......> This function doesn't introduce ISI at the neighboring symbol instants > but the summation of pulse shape is not flat..... What is the difference, if any, between the phrases "summation of the spectrum of pulse shapes" "summation of pulse shape" ? If they mean the same thing, why use unnecessary words such as "the spectrum of" in the first phrase? If they don't mean the same thing, which summation do you want to be flat? And what does it mean when you say a summation is flat? For |x| < 1, 1 + x + x^2 + ... = 1/(1-x). Is the summation flat? If x has value 1/2, the sum has value 2. Is it flat now, but is not flat for general values of x?

Reply by ●October 9, 20092009-10-09

On Oct 9, 8:15�am, "dvsarw...@yahoo.com" <dvsarw...@gmail.com> wrote:> On Oct 9, 1:00�am, Aitezaz <aitezaz....@gmail.com> wrote: > > > Nyquist pulse criteria states that the summation of the spectrum of > > pulse shapes should be flat. > > ..... > > > This function doesn't introduce ISI at the neighboring symbol instants > > but the summation of pulse shape is not flat. > > .... > > What is the difference, if any, between the phrases > > "summation of the spectrum of pulse shapes" > > "summation of pulse shape" ? > > If they mean the same thing, why use unnecessary words > such as "the spectrum of" in the first phrase? �If they don't > mean the same thing, which summation do you want to be > flat? �And what does it mean when you say a summation is > flat? �For |x| < 1, 1 + x + x^2 + ... = 1/(1-x). �Is the summation > flat? �If x has value 1/2, the sum has value 2. �Is it flat now, > but is not flat for general values of x?i'm sorry if it caused confusion. Please refer to the following pdf. http://radio-1.ee.dal.ca/~ilow/4503/lectures/nyquist.pdf im referring to the formula written in the middle of slide no. 2. Sum over all k (P(f+k/T)) = T ----> A So if we want to know if the pulse shape is nyquist or not we should take its spectrum, add the shifted versions of it and we should get a flat spectrum dictated by T in above equation. My question is if we only want to remove the ISI, the following pulse shape can do the job. p(t) = { t + T for -T<t<0 ; -t+T for 0<t<T; 0 else where } Now, the value of this pulse shape is zero for all the signaling intervals except t=0. So, no ISI is introduced. But, if we want to satisfy the criteria of equation A, it doesn't as the spectrum of the pulse shape is not flat i.e. the sum of the shifted copies of this spectrum is not flat as well. So, should we call it a nyquist pulse? or alternatively, if we want to know if some pulse is a nyquist pulse or not what should we see ? 1. p(t) should have zero values for signaling intervals other than t=0. 2. it should satisfy the criteria of equation A Thanks for ur time

Reply by ●October 9, 20092009-10-09

On Oct 9, 11:04�am, Aitezaz <aitezaz....@gmail.com> wrote:> But, if we want to > satisfy the criteria of equation A, it doesn't as the spectrum of the > pulse shape is not flat i.e. the sum of the shifted copies of this > spectrum is not flat as well.Just because the spectrum of the pulse shape is not flat, how can you conclude that the SUM of shifted copies of the spectrum is not flat? Are you just eyeballing it? Or do you have any actual computed result that the sum over all k (P(f+k/T)) does not equal T for some specific value of f for the spectrum that you are using? Hint: Look at formula 4.3.92 in the Abramowitz and Stegun "Handbook of Mathematical Functions" available as a reference book in many libraries and set cosec^2(z) = 1/sin^2(z).

Reply by ●October 9, 20092009-10-09

On Oct 9, 1:46�pm, "dvsarw...@yahoo.com" <dvsarw...@gmail.com> wrote:> On Oct 9, 11:04�am, Aitezaz <aitezaz....@gmail.com> wrote: > > > But, if we want to > > satisfy the criteria of equation A, it doesn't as the spectrum of the > > pulse shape is not flat i.e. the sum of the shifted copies of this > > spectrum is not flat as well. > > Just because the spectrum of the pulse shape is not flat, how > can you conclude that the SUM of shifted copies of the spectrum > is not flat? �Are you just eyeballing it? �Or do you have any > actual computed result that the sum over all k (P(f+k/T)) does > not equal T for some specific value of f for the spectrum that > you are using? > > Hint: �Look at formula 4.3.92 in the Abramowitz and Stegun > "Handbook of Mathematical Functions" available as a reference > book in many libraries and set cosec^2(z) = 1/sin^2(z).Thanks dvsarwate for reply. I got your point. The P(f) in the case of my pulse shape is sinc^2 type and when they overlap in between the 0 and 1/T the addition becomes flat. And it is justified both in time and frequency domain. Correct me if i'm wrong. Thank you again .... Aitezaz